http://2010.igem.org/wiki/index.php?title=Special:Contributions&feed=atom&limit=500&target=Mareike&year=&month=2010.igem.org - User contributions [en]2024-03-29T09:17:28ZFrom 2010.igem.orgMediaWiki 1.16.5http://2010.igem.org/Team:BIOTEC_Dresden/LiteratureTeam:BIOTEC Dresden/Literature2010-10-28T03:59:32Z<p>Mareike: </p>
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<h2>Modelling</h2><br />
<p>1.THE GREEN FLUORESCENT PROTEIN - Annual Review of Biochemistry, 67(1):509.</p><br />
<br />
<p>2.Tian T, Burrage K (2006) Stochastic models for regulatory networks of the genetic toggle switch. Proceedings of the National Academy of Sciences 103: 8372 -8377.</p><br />
<br />
<p>3.Basu S, Mehreja R, Thiberge S, Chen M, Weiss R (2004) Spatiotemporal control of gene expression with pulse-generating networks. Proceedings of the National Academy of Sciences of the United States of America 101: 6355 -6360.</p><br />
<br />
<p>4.Nilsson P, Olofsson A, Fagerlind M, Fagerström T, Rice S, u. a. (2001) Kinetics of the AHL Regulatory System in a Model Biofilm System: How Many Bacteria Constitute a "Quorum"? Journal of Molecular Biology 309: 631-640.</p><br />
<br />
<p>5.Schaefer AL, Val DL, Hanzelka BL, Cronan JE, Greenberg EP (1996) Generation of cell-to-cell signals in quorum sensing: acyl homoserine lactone synthase activity of a purified Vibrio fischeri LuxI protein. Proc. Natl. Acad. Sci. U.S.A 93: 9505-9509.</p><br />
<br />
<p>6.Kaplan HB, Greenberg EP (1985) Diffusion of autoinducer is involved in regulation of the Vibrio fischeri luminescence system. J Bacteriol 163: 1210-1214.</p><br />
<br />
<p>7.Hanzelka BL, Parsek MR, Val DL, Dunlap PV, Cronan JE, u. a. (1999) Acylhomoserine lactone synthase activity of the Vibrio fischeri AinS protein. J. Bacteriol 181: 5766-5770.</p><br />
<br />
<p>8.Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335-338.</p><br />
<br />
<p>9.Goryachev A, Toh D, Lee T Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants. Biosystems 83: 178-187.</p><br />
<br />
<p>10.Müller J, Kuttler C, Hense BA, Rothballer M, Hartmann A (2006) Cell-cell communication by quorum sensing and dimension-reduction. J Math Biol 53: 672-702.</p><br />
<h2>General Literature</h2><br />
<p>1.Dong YH, Xu JL, Li XZ, Zhang LH (2000) AiiA, an enzyme that inactivates the acylhomoserine lactone quorum-sensing signal and attenuates the virulence of Erwinia carotovora. Proc. Natl. Acad. Sci. U.S.A 97: 3526-3531.</p><br />
<br />
<p>2.Skerra A, Schmidt TG (1999) Applications of a peptide ligand for streptavidin: the Strep-tag. Biomol. Eng 16: 79-86.</p><br />
<br />
<p>3.Kigawa T (2010) Cell-free protein preparation through prokaryotic transcription-translation methods. Methods Mol. Biol 607: 1-10.</p><br />
<br />
<p>4.Andersen JB, Heydorn A, Hentzer M, Eberl L, Geisenberger O, u. a. (2001) gfp-based N-acyl homoserine-lactone sensor systems for detection of bacterial communication. Appl. Environ. Microbiol 67: 575-585.</p><br />
<br />
<p>5.Siggaard-Andersen M (1988) Role of Escherichia coli beta-ketoacyl-ACP synthase I in unsaturated fatty acid synthesis. Carlsberg Res. Commun 53: 371-379.</p><br />
<br />
<br />
<br />
<br />
<br />
<h2>Fusion Protein </h2><br />
<p>1. http://www-nmr.cabm.rutgers.edu/photogallery/proteins/htm/page16.htm</a></p><br />
<p>2. Nilsson B, Moks T, Jansson B, Abrahmsén L, Elmblad A, u. a. (1987) A synthetic IgG-binding domain based on staphylococcal protein A. Protein Eng 1: 107-113.</a></p><br />
<p>3. Van Houdt R, Moons P, Aertsen A, Jansen A, Vanoirbeek K, u. a. (2007) Characterization of a luxI/luxR-type quorum sensing system and N-acyl-homoserine lactone-dependent regulation of exo-enzyme and antibacterial component production in Serratia plymuthica RVH1. Research in Microbiology 158: 150-158.</a></p><br />
<br />
<h2>ACP Synthesis </h2><br />
<br />
<p> 1. Schaefer A.L., Val D.L., Hanzelka B.L., Cronan J.E., Grenberg E.P. (1996) Generation of cell-to-cell signals in quorum sensing: Acyl homoserine lactone synthase activity of a purified Vibrio fischeri LuxI protein, Proc. Natl. Acad. Sci., USA, vol.93, pp. 9505-9509 </p> <br />
<br />
<p> 2. Zhiwei Shen, Debra Fice, David M. Byers (1992) Preparation of Fatty-Acylated Derivatives of Acyl Carrier Protein Using Vibrio harveyi Acyl-ACP Synthetase, Analytical biochemistry 204, 34-39 </p> <br />
<br />
<p> 3. http://www.neb.com/nebecomm/products/productP9301.asp </p> <br />
<br />
<p> 4. McAllister KA, Peery RB, Zhao G. (2006) Acyl carrier protein synthases from gram-negative, gram-positive, and atypical bacterial species: Biochemical and structural properties and physiological implications, J Bacteriol., vol 188(13):4737-48 </p> <br />
<br />
<p> 5. R. H. Lambalot, C. T. Walsh , Cloning (1995) Overproduction, and Characterization of the Escherichia coli Holo-acyl Carrier Protein Synthase, The Journal of Biological Chemistry Vol. 270, No. 42, pp. 24658–24661 </p> <br />
<br />
<p> 6. Information for Entry EC 2.7.8.7 - holo-[acyl-carrier-protein] synthase in BRENDA database (A Comprehensive Enzyme Information System). </p> <br />
<br />
<p> 7. J.G. Jaworski, P.K. Stumpf. (1974) Fat metabolism in higher plants: Enzymatic preparation of E. coli stearyl-acyl carrier protein, Arch. Biochem. Biophys. 162, pp. 166–173 </p> <br />
<br />
<p> 8. Flugel RS, Hwangbo Y, Lambalot RH, Cronan JE Jr, Walsh CT. (2000), Holo-(acyl carrier protein) synthase and phosphopantetheinyl transfer in Escherichia coli, J Biol Chem. Jan 14;275(2):959-68.</p><br />
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[[Category:BIOTEC_Dresden/Resource|Literature]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/LiteratureTeam:BIOTEC Dresden/Literature2010-10-28T03:59:09Z<p>Mareike: </p>
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<h2>Modelling</h2><br />
<p>1.THE GREEN FLUORESCENT PROTEIN - Annual Review of Biochemistry, 67(1):509.</p><br />
<br />
<p>2.Tian T, Burrage K (2006) Stochastic models for regulatory networks of the genetic toggle switch. Proceedings of the National Academy of Sciences 103: 8372 -8377.</p><br />
<br />
<p>3.Basu S, Mehreja R, Thiberge S, Chen M, Weiss R (2004) Spatiotemporal control of gene expression with pulse-generating networks. Proceedings of the National Academy of Sciences of the United States of America 101: 6355 -6360.</p><br />
<br />
<p>4.Nilsson P, Olofsson A, Fagerlind M, Fagerström T, Rice S, u. a. (2001) Kinetics of the AHL Regulatory System in a Model Biofilm System: How Many Bacteria Constitute a "Quorum"? Journal of Molecular Biology 309: 631-640.</p><br />
<br />
<p>5.Schaefer AL, Val DL, Hanzelka BL, Cronan JE, Greenberg EP (1996) Generation of cell-to-cell signals in quorum sensing: acyl homoserine lactone synthase activity of a purified Vibrio fischeri LuxI protein. Proc. Natl. Acad. Sci. U.S.A 93: 9505-9509.</p><br />
<br />
<p>6.Kaplan HB, Greenberg EP (1985) Diffusion of autoinducer is involved in regulation of the Vibrio fischeri luminescence system. J Bacteriol 163: 1210-1214.</p><br />
<br />
<p>7.Hanzelka BL, Parsek MR, Val DL, Dunlap PV, Cronan JE, u. a. (1999) Acylhomoserine lactone synthase activity of the Vibrio fischeri AinS protein. J. Bacteriol 181: 5766-5770.</p><br />
<br />
<p>8.Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335-338.</p><br />
<br />
<p>9.Goryachev A, Toh D, Lee T Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants. Biosystems 83: 178-187.</p><br />
<br />
<p>10.Müller J, Kuttler C, Hense BA, Rothballer M, Hartmann A (2006) Cell-cell communication by quorum sensing and dimension-reduction. J Math Biol 53: 672-702.</p><br />
<h2>General Literature</h2><br />
<p>1.Dong YH, Xu JL, Li XZ, Zhang LH (2000) AiiA, an enzyme that inactivates the acylhomoserine lactone quorum-sensing signal and attenuates the virulence of Erwinia carotovora. Proc. Natl. Acad. Sci. U.S.A 97: 3526-3531.</p><br />
<br />
<p>2.Skerra A, Schmidt TG (1999) Applications of a peptide ligand for streptavidin: the Strep-tag. Biomol. Eng 16: 79-86.</p><br />
<br />
<p>3.Kigawa T (2010) Cell-free protein preparation through prokaryotic transcription-translation methods. Methods Mol. Biol 607: 1-10.</p><br />
<br />
<p>4.Andersen JB, Heydorn A, Hentzer M, Eberl L, Geisenberger O, u. a. (2001) gfp-based N-acyl homoserine-lactone sensor systems for detection of bacterial communication. Appl. Environ. Microbiol 67: 575-585.</p><br />
<br />
<p>5.Siggaard-Andersen M (1988) Role of Escherichia coli beta-ketoacyl-ACP synthase I in unsaturated fatty acid synthesis. Carlsberg Res. Commun 53: 371-379.</p><br />
<br />
<p>6.Siggaard-Andersen M (1988) Role of Escherichia coli beta-ketoacyl-ACP synthase I in unsaturated fatty acid synthesis. Carlsberg Res. Commun 53: 371-379.</p><br />
<br />
<br />
<br />
<h2>Fusion Protein </h2><br />
<p>1. http://www-nmr.cabm.rutgers.edu/photogallery/proteins/htm/page16.htm</a></p><br />
<p>2. Nilsson B, Moks T, Jansson B, Abrahmsén L, Elmblad A, u. a. (1987) A synthetic IgG-binding domain based on staphylococcal protein A. Protein Eng 1: 107-113.</a></p><br />
<p>3. Van Houdt R, Moons P, Aertsen A, Jansen A, Vanoirbeek K, u. a. (2007) Characterization of a luxI/luxR-type quorum sensing system and N-acyl-homoserine lactone-dependent regulation of exo-enzyme and antibacterial component production in Serratia plymuthica RVH1. Research in Microbiology 158: 150-158.</a></p><br />
<br />
<h2>ACP Synthesis </h2><br />
<br />
<p> 1. Schaefer A.L., Val D.L., Hanzelka B.L., Cronan J.E., Grenberg E.P. (1996) Generation of cell-to-cell signals in quorum sensing: Acyl homoserine lactone synthase activity of a purified Vibrio fischeri LuxI protein, Proc. Natl. Acad. Sci., USA, vol.93, pp. 9505-9509 </p> <br />
<br />
<p> 2. Zhiwei Shen, Debra Fice, David M. Byers (1992) Preparation of Fatty-Acylated Derivatives of Acyl Carrier Protein Using Vibrio harveyi Acyl-ACP Synthetase, Analytical biochemistry 204, 34-39 </p> <br />
<br />
<p> 3. http://www.neb.com/nebecomm/products/productP9301.asp </p> <br />
<br />
<p> 4. McAllister KA, Peery RB, Zhao G. (2006) Acyl carrier protein synthases from gram-negative, gram-positive, and atypical bacterial species: Biochemical and structural properties and physiological implications, J Bacteriol., vol 188(13):4737-48 </p> <br />
<br />
<p> 5. R. H. Lambalot, C. T. Walsh , Cloning (1995) Overproduction, and Characterization of the Escherichia coli Holo-acyl Carrier Protein Synthase, The Journal of Biological Chemistry Vol. 270, No. 42, pp. 24658–24661 </p> <br />
<br />
<p> 6. Information for Entry EC 2.7.8.7 - holo-[acyl-carrier-protein] synthase in BRENDA database (A Comprehensive Enzyme Information System). </p> <br />
<br />
<p> 7. J.G. Jaworski, P.K. Stumpf. (1974) Fat metabolism in higher plants: Enzymatic preparation of E. coli stearyl-acyl carrier protein, Arch. Biochem. Biophys. 162, pp. 166–173 </p> <br />
<br />
<p> 8. Flugel RS, Hwangbo Y, Lambalot RH, Cronan JE Jr, Walsh CT. (2000), Holo-(acyl carrier protein) synthase and phosphopantetheinyl transfer in Escherichia coli, J Biol Chem. Jan 14;275(2):959-68.</p><br />
</p><br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Resource|Literature]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-28T02:15:46Z<p>Mareike: </p>
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<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
<br />
<a alt="Complete Gene Circuit of SensorBricks" rel="lightbox" href="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png"> <img id="Fusion_Construct" class="border thumb" src="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" style="margin-left: 30%;"></a><br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<br />
<span class="nom" style="width: 90%;"><i>d[AHL]</i></span><br />
<span class="den" style="width: 90%;"><i>dt</i></span><span style="position: relative; left: 48%; bottom: 33px;">= k<sub>diff</sub>(AHL<sub>ex</sub>- AHL<sub>in</sub>) -(k<sub>dec</sub> * AHL<sub>in</sub>)</span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>) the binding and dissociation constant of AHL and LuxR (k<sub>dis</sub>=. </p><br />
<span style="position: relative; left: 42%;">[LuxR-AHL]=k<sub>dis</sub> x [AHL] x [LuxR]</span><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<br />
<span class="nom"><i>G(t)</i></span><br />
<span class="den"><i>dt</i></span><span style="position: relative; left: 55%; bottom: 33px;">= x(t)-γG(t)</span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed.</p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" rel="lightbox" title="Simple Model"><img class="border thumb" src="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" class="border thumb" style="margin-left: 30%;"></a><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/8/89/BiotecDresden_AHL_diffusion.jpg" rel="lightbox" title="Simple Model"><img class="border thumb" src="https://static.igem.org/mediawiki/2010/8/89/BiotecDresden_AHL_diffusion.jpg" class="border thumb" style="margin-left: 30%;"></a><br />
<p>The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<br />
<a href="https://static.igem.org/mediawiki/2010/e/e1/BiotecDresden_GFP_output.jpg" rel="lightbox" title="Simple Model"><img class="border thumb" src="https://static.igem.org/mediawiki/2010/e/e1/BiotecDresden_GFP_output.jpg" class="border thumb" style="margin-left: 30%;"></a><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/1/15/LuxR-AHL_complex.jpg" rel="lightbox" title="Simple Model"><img class="border thumb" src="https://static.igem.org/mediawiki/2010/1/15/LuxR-AHL_complex.jpg" class="border thumb" style="margin-left: 30%;"></a><br />
<br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
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[[Category:BIOTEC_Dresden/Project|Modeling]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/File:LuxR-AHL_complex.jpgFile:LuxR-AHL complex.jpg2010-10-28T02:12:26Z<p>Mareike: </p>
<hr />
<div></div>Mareikehttp://2010.igem.org/File:BiotecDresden_GFP_output.jpgFile:BiotecDresden GFP output.jpg2010-10-28T02:11:37Z<p>Mareike: </p>
<hr />
<div></div>Mareikehttp://2010.igem.org/File:BiotecDresden_AHL_diffusion.jpgFile:BiotecDresden AHL diffusion.jpg2010-10-28T02:09:38Z<p>Mareike: </p>
<hr />
<div></div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/Characterized_Parts/BBa_K407014Team:BIOTEC Dresden/Characterized Parts/BBa K4070142010-10-28T01:46:47Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<html><body><div id="content_prim"> <br />
<h2>Part BBa_K407014</h2> <br />
<a href="https://static.igem.org/mediawiki/2010/6/67/K407014_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/6/67/K407014_%28Custom%29.png" class="border left"></a><br />
<br />
<p> This part was created by the team BIOTEC_Dresden 2010 as a detection device for AHL, which directly includes a normalization system. Basically, this part consists of the part BBa_I13263, in which LuxR is constitutively expressed. In the presence of AHL a LuxR-AHL complex is formed activating luxpR and thereby the expression of Yfp. Our team assembled the part BBa_J04450 to this part, which constitutively expresses RFP. Bacteria carrying this plasmid express RFP yet can after induction with AHL and LuxR additionally produce YFP. Both fluorescent signals are simultanously measured as the fluorescent spectra do not interfer. By dividing the fluorescent signal of Yfp by the fluorescent signal of RFP, one is able to normalize the fluorescence data without considering the cell density generally determined by OD measurements.</p><br />
<br />
<h3>Results</h3><br />
<p>Figure 1 shows the fluorescence signal of RFP plotted against an increasing AHL concentration. It can be seen that the signal intensity stays constant over the whole time.</p><br />
<br />
<div class="border left"><br />
<a href="hhttps://static.igem.org/mediawiki/2010/4/48/1751RFPoverC_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/4/48/1751RFPoverC_%28Custom%29.png" class="border left"></a><br />
<div class="caption"><p>Figure 1: The fluorescence of RFP is shown over increasing</p><br />
<p>AHL concentrations after 2 hours of incubation</p></div><br />
</div><br />
<br />
<br />
<br />
<p>Figure 2 displays the same data as Figure 1 except that the fluorescence of YFP is depicted. A logarithmic trend line can be fit to the data with a fair correlation. Interestingly, after normalizing the YFP data with the RFP data, simply by division, we are still able to fit the curve logarithmic. Hence the correlation improves remarkably through normalization, as displayed in Figure 3. </p> <br />
<br />
<div class="border left"><br />
<a href="hhttps://static.igem.org/mediawiki/2010/6/6e/1751YFPoverC_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/6/6e/1751YFPoverC_%28Custom%29.png" class="border left"></a><br />
<div class="caption"><p>Figure 2: The fluorescence of YFP is shown over increasing</p><br />
<p>AHL concentrations after 2 hours of incubation</p></div><br />
</div><br />
<br />
<div class="border left"><br />
<a href="https://static.igem.org/mediawiki/2010/e/e6/1751YFPRFPoverC_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/e/e6/1751YFPRFPoverC_%28Custom%29.png" class="border left"></a><br />
<div class="caption"><p>Figure 3: The fluorescence of YFP normalized by division through the fluorescence of </p><br />
<p>RFP is shown over increasing AHL concentrations after 2 hours of incubation</p></div><br />
</div><br />
<br />
<p>Figure 4 shows the normalized YFP fluorescence over time for different AHL concentrations. It can be seen that the rate of induction is determined by the AHL concentration and that even concentration of only 50nM already leads to a significant increase in YFP fluorescence.</p><br />
<br />
<div class="border left"><br />
<a href="https://static.igem.org/mediawiki/2010/5/50/YFPRFPovert.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/5/50/YFPRFPovert.png" class="border left"></a><br />
<div class="caption"><p>Figure 4: The fluorescence of YFP normalized by RFP is shown over time for different</p><br />
<p>AHL concentrations ranging from 0 to 2000nM</p></div><br />
</div><br />
<br />
<br />
<br />
<h3>Discussion:</h3><br />
<br />
<p>The stagnation of the fluorescence signal of the RFP was not expected. Actually, it was considered to rise with the amount of bacteria as they divide during the measurement. The fact that the fluorescence does not increase during the measurement must mean that the cells are almost not dividing. Reasons for this phenomenon can be the environmental change as well as the elevated metabolic load caused by the production of the fluorescent proteins. Correspondingly, during the duration of the kinetic measurment the cell number stays constant.<br />
</p><br />
<p>The YFP signal depicted in Figure 2 on the other hand behaved as expected and shows the same behavior could already be detected for the part I13263.</p><br />
<p>The fact that the correlation coefficient R<sup>2</sup> improves after the normalization of the fluorescence signal of YFP by division through those of RFP shows that the system our team created is funtional and is useful.</p><br />
<p>Figure 3 shows that, using this part for the detection of AHL and the novel normalization approach, a sensitive detection system is accomplished. Remarkably even lower concentrations, of 50nM, were detected using this approach compared to the traditional normalization procedure. </p><br />
<br />
<h3>Materials and methods:</h3><br />
<p>The characterization was performed using a 96-well plate and a fluorescence plate reader, which was kept at 37°C during the whole measurement.. Bacteria supplied with the part BBa_K407014 were suspended in medium of a certain concentration of AHL ranging from 0.01 to 2000nM. The fluorescence of both RFP and YFP was measured every 5 minutes. While for RFP an excitation wavelength of 562 nm and an emission wavelength of 612 nm were used, those for YFP were 485nm and 535nm respectively. As controls the optical density at 612nm and the RFP/YFP fluorescence of uninduced bacteria and LB-medium without cells were measured.</p><br />
<br />
<h3>Additional information</h3><br />
<p>For detailed information of the experimental set-up, please have a look at the protocols on our team-wiki <a href="https://static.igem.org/mediawiki/igem.org/7/75/Protocol_AHLassay.pdf"> here. </a In case you want to know more about the normalization and negative controls, please have a look at this page: (Link)</p><br />
<br />
<br />
<br />
</div></body> </html><br />
[[Category:BIOTEC_Dresden/Characterized_Parts|K407014]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/Characterized_Parts/BBa_I13263Team:BIOTEC Dresden/Characterized Parts/BBa I132632010-10-28T01:16:51Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<html><body><div id="content_prim"> <br />
<h2>BBa_I13263</h2> <br />
<a href="https://static.igem.org/mediawiki/2010/6/68/PartI13263_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/6/68/PartI13263_%28Custom%29.png" class="border left"></a><br />
<p>This part is supposed to serve as a potential detection and quantification system for the concentration of the signal molecule N-Acyl homoserine lactone (AHL) in the growth medium. As shown in the parts overview LuxR is constitutively expressed. In the presence of AHL a LuxR-AHL complex is formed activating luxpR and thereby the expression of eyfp. In characterization experiments the amount of AHL required for induction was analyzed. This part is characterized best and was consequently always used for later experiments.</p><br />
<div class="visualClear"></div><br />
<h3>Results</h3><br />
<div class="border left"><br />
<a href="https://static.igem.org/mediawiki/2010/d/dc/17overt_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/d/dc/17overt_%28Custom%29.png"></a><br />
<div class="caption"><p>Figure 1: The fluorescence of YFP is shown over time</p><br />
<p>for different AHL concentrations from 0.1 to 2000nM and for pure LB medium</p></div><br />
</div><br />
<br />
<p>The Figure 1 shows the YFP development over time of different concentrations of AHL, ranging from 10pM to 2µM. It can be seen that the fluorescence signal does not significantly change over time for AHL concentrations below 100nM and that the amount of YFP produced is the same for all concentrations above 300nM.</p><br />
<p>In Figure 2 the fluorescence as a function of the AHL concentration after two hours of incubation is visualized. It can be seen that the YFP signal after 2 hours of incubation increases with increasing AHL concentrations but reaches a plateau at about 700nM. </p><br />
<div class="visualClear"></div><br />
<br />
<h3>Discussion:</h3><br />
<div class="border right"><br />
<a href="https://static.igem.org/mediawiki/2010/9/92/Part17overC_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/9/92/Part17overC_%28Custom%29.png""></a><br />
<div class="caption"><p>Figure 2: The fluorescence of YFP is shown</p><br />
<p>over increasing AHL concentrations after an icubation time of 2h</p></div><br />
</div><br />
<br />
<p>Figure 1 shows nicely that the LB medium (dark blue) has a fluorescence signal of about 2800 raw fluorescence units (RFU). But since the fluorescence signal stayed constant over the time measured, this fluorescence does not qualitatively influence the data and can thus be ignored. Additionally it can be seen that the concentrations below 100nM do not lead to an increase in fluorescence, leading to the conclusion that a minimum concentration of 100nM outside of the bacteria is required for the induction of the LuxpR and in turn for the detectable expression of YFP. Furthermore, the graph shows that after 2h of incubation with AHL the amount of YFP detected can directly by related to the initial concentration of AHL. </p><br />
<p>Figure 2 on the other hand shows a logarithmic behavior of the transcriptional induction of the LuxpR promoter by AHL, which reaches its maximum induction at an AHL concentration of about 750nM. </p><br />
<div class="visualClear"></div><br />
<h3>Materials and methods:</h3><br />
<p>The characterization was performed using a 96-well plate and a fluorescence plate reader. Bacteria supplied with the part BBa_I13263 were suspended in medium of a certain concentration of AHL ranging from 0.01 to 2000nM. The fluorescence was measured every 5 minutes using an excitation wavelength of 485nm and an emission wavelength of 535nm. For every fluorescence value, also the optical density at 612nm was measured. As a negative control the same measurements were done on uninduced bacteria and LB-medium without cells.</p><br />
<h3>Additional information</h3><br />
<p>For detailed information of the experimental set-up, please have a look at the protocols on our team-wiki <a href="https://static.igem.org/mediawiki/igem.org/7/75/Protocol_AHLassay.pdf"> here.</a In case you want to know more about the normalization and negative controls, please have a look at this page: (Link)</p><br />
<br />
</div></body> </html><br />
[[Category:BIOTEC_Dresden/Characterized_Parts|I13263]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/Characterized_Parts/BBa_I13272Team:BIOTEC Dresden/Characterized Parts/BBa I132722010-10-28T01:15:40Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<html><body><div id="content_prim"> <br />
<h2>Part BBa_I13272</h2> <br />
<a href="https://static.igem.org/mediawiki/2010/f/f5/I13272_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/f/f5/I13272_%28Custom%29.png" class="border left"></a> <br />
<p>This part is supposed to serve as a potential detection and quantification system for the concentration of the signal molecule N-Acyl homoserine lactone (AHL) in the growth medium. As shown in the parts overview LuxR is constitutively expressed. In the presence of AHL a LuxR-AHL complex is formed activating lux pR and thereby the expression of EYFP. Technically, it is the same part as BBa_K407014 but it has a different YFP-molecule as a reporter. In characterization experiments, the amount of AHL required for induction was analyzed. .</p><br />
<h3>Results</h3><br />
<p>Figure 1 shows the development of the YFP signal against time for different AHL concentrations. Unexpectedly, the results of the measurements vary greatly from the data we achieved with the part BBa_I13272 that is identical to this part except that it contains a different YFP. Nevertheless, there is an increase in fluorescence signal with increasing AHL concentration. Starting from an AHL concentration of 500nM. The LB medium has a fluorescent signal, which remains almost constant during the measurement.</p> <br />
<p>The same trend can be seen in Figure 2, which displays the fluorescence over increasing AHL concentrations after a two hours incubation time. Here again, the curve looks similar to the one of part BBa_I13272 but the plateau is not as nicely visible.</p><br />
<br />
<br />
<div class="border left"><br />
<a href="https://static.igem.org/mediawiki/2010/c/c3/Part18overt_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/c/c3/Part18overt_%28Custom%29.png" class="border left"></a><br />
<div class="caption"><p>Figure 1: The fluorescence of YFP is shown over time</p><br />
<p>for different AHL concentrations from 0 to 2000nM and for pure LB medium</p></div><br />
</div><br />
<br />
<br />
<div class="border left"><br />
<a href="https://static.igem.org/mediawiki/2010/f/f8/Part18overC_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/f/f8/Part18overC_%28Custom%29.png" class="border left"></a><br />
<div class="caption"><p>Figure 2: The fluorescence of YFP is shown over increasing</p><br />
<p> concentrations of AHL after 2 hours of incubation</p></div><br />
</div><br />
<br />
<br />
<br />
<h3>Discussion:</h3><br />
<br />
<p>The outcome of this experiment was unexpected regarding the same measurement of the part BBa_I13272. This part was expected to show the exact same behavior. It is difficult to explain the discrepancies. Since the only differences between these two parts is the yellow fluorescent protein encoded, it must be concluded that the EYFP (E0034) is either not as well transcribed or translated as the eyfp (E0030) or it is not as functional. Mutations in the coding sequence can lead to an decreased expression correlating to decreased fluorescence signal. </p><br />
<br />
<h3>Materials and methods:</h3><br />
<p>The characterization was performed using a 96-well plate and a fluorescence plate reader, which was kept at 37°C during the whole measurement.. Bacteria supplied with the part BBa_I13272 were suspended in medium of a certain concentration of AHL ranging from 0.01 to 2000nM. The fluorescence was measured every 5 minutes using an excitation wavelength of 485nm and an emission wavelength of 535nm. For every fluorescence value, also the optical density at 612nm was measured. As a negative control the same measurements were done on uninduced bacteria and LB-medium without cells.</p><br />
<br />
<h3>Additional information</h3><br />
<p>For detailed information of the experimental set-up, please have a look at the protocols on our team-wiki <a href="https://static.igem.org/mediawiki/igem.org/7/75/Protocol_AHLassay.pdf"> here.</a In case you want to know more about the normalization and negative controls, please have a look at this page: (Link)</p> In case you want to know more about the normalization and negative controls, please have a look at this page: (Link)</p><br />
<br />
</div></body> </html><br />
[[Category:BIOTEC_Dresden/Characterized_Parts|I13272]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/Characterized_Parts/BBa_I13263Team:BIOTEC Dresden/Characterized Parts/BBa I132632010-10-28T01:08:24Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<html><body><div id="content_prim"> <br />
<h2>BBa_I13263</h2> <br />
<a href="https://static.igem.org/mediawiki/2010/6/68/PartI13263_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/6/68/PartI13263_%28Custom%29.png" class="border left"></a><br />
<p>This part is supposed to serve as a potential detection and quantification system for the concentration of the signal molecule n-acyl homoserine lactone (AHL) in the growth medium. As shown in the parts overview LuxR is constitutively expressed. In the presence of AHL a LuxR-AHL complex is formed activating luxpR and thereby the expression of eyfp. In characterization experiments the amount of AHL required for induction was analyzed. This part is characterized best and was consequently always used for later experiments.</p><br />
<div class="visualClear"></div><br />
<h3>Results</h3><br />
<div class="border left"><br />
<a href="https://static.igem.org/mediawiki/2010/d/dc/17overt_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/d/dc/17overt_%28Custom%29.png"></a><br />
<div class="caption"><p>Figure 1: The fluorescence of YFP is shown over time</p><br />
<p>for different AHL concentrations from 0.1 to 2000nM and for pure LB medium</p></div><br />
</div><br />
<br />
<p>The Figure 1 shows the YFP development over time of different concentrations of AHL, ranging from 10pM to 2µM. It can be seen that the fluorescence signal does not significantly change over time for AHL concentrations below 100nM and that the amount of YFP produced is the same for all concentrations above 300nM.</p><br />
<p>In Figure 2 the fluorescence as a function of the AHL concentration after two hours of incubation is visualized. It can be seen that the YFP signal after 2 hours of incubation increases with increasing AHL concentrations but reaches a plateau at about 700nM. </p><br />
<div class="visualClear"></div><br />
<br />
<h3>Discussion:</h3><br />
<div class="border right"><br />
<a href="https://static.igem.org/mediawiki/2010/9/92/Part17overC_%28Custom%29.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/9/92/Part17overC_%28Custom%29.png""></a><br />
<div class="caption"><p>Figure 2: The fluorescence of YFP is shown</p><br />
<p>over increasing AHL concentrations after an icubation time of 2h</p></div><br />
</div><br />
<br />
<p>Figure 1 shows nicely that the LB medium (dark blue) has a fluorescence signal of about 2800 raw fluorescence units (RFU). But since the fluorescence signal stayed constant over the time measured, this fluorescence does not qualitatively influence the data and can thus be ignored. Additionally it can be seen that the concentrations below 100nM do not lead to an increase in fluorescence, leading to the conclusion that a minimum concentration of 100nM outside of the bacteria is required for the induction of the LuxpR and in turn for the detectable expression of YFP. Furthermore, the graph shows that after 2h of incubation with AHL the amount of YFP detected can directly by related to the initial concentration of AHL. </p><br />
<p>Figure 2 on the other hand shows a logarithmic behavior of the transcriptional induction of the LuxpR promoter by AHL, which reaches its maximum induction at an AHL concentration of about 750nM. </p><br />
<div class="visualClear"></div><br />
<h3>Materials and methods:</h3><br />
<p>The characterization was performed using a 96-well plate and a fluorescence plate reader. Bacteria supplied with the part BBa_I13263 were suspended in medium of a certain concentration of AHL ranging from 0.01 to 2000nM. The fluorescence was measured every 5 minutes using an excitation wavelength of 485nm and an emission wavelength of 535nm. For every fluorescence value, also the optical density at 612nm was measured. As a negative control the same measurements were done on uninduced bacteria and LB-medium without cells.</p><br />
<h3>Additional information</h3><br />
<p>For detailed information of the experimental set-up, please have a look at the protocols on our team-wiki <a href="https://static.igem.org/mediawiki/igem.org/7/75/Protocol_AHLassay.pdf"> here.</a In case you want to know more about the normalization and negative controls, please have a look at this page: (Link)</p><br />
<br />
</div></body> </html><br />
[[Category:BIOTEC_Dresden/Characterized_Parts|I13263]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/SoftwareTeam:BIOTEC Dresden/Software2010-10-28T00:53:41Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<html><br />
<body><br />
<div id="content_prim"><br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th>Name</th><br />
<th>Description</th><br />
<th>Link</th><br />
</tr><br />
<br />
<tr class="even"><br />
<td>ApE</td><br />
<td>ApE was used as DNA construction software to create plasmid maps, fusion constructs and to view restriction sites of commonly used endonucleases </td><br />
<td><a href="http://biologylabs.utah.edu/jorgensen/wayned/ape">biologylabs.utah.edu/jorgensen/wayned/ape</td><br />
</tr><br />
<br />
<tr class="odd"><br />
<td>NCBI Blast</td><br />
<td>The online software tool blast was used both to check nucleotide and protein sequences towards their homology to the original genomic sequence </td><br />
<td><a href="http://blast.ncbi.nlm.nih.gov">blast.ncbi.nlm.nih.gov</td><br />
</tr><br />
<br />
<tr class="even"><br />
<td>Cell Designer</td><br />
<td>Cell Designer represents a tool for molecular modeling allowing to construct molecular circuits</td><br />
<td><a href="http://www.celldesigner.org">www.celldesigner.org</td><br />
</tr><br />
<br />
<tr class="odd"><br />
<td>PartsRegistry Sequence Analysis/BLAST</td><br />
<td>The registry blast was useful to identify nucleotide sequences already submitted to the registry</td><br />
<td><a href="http://partsregistry.org/cgi/sequencing/">partsregistry.org/cgi/sequencing</td><br />
</tr><br />
<br />
<tr class="even"><br />
<td>PlasmaDNA</td><br />
<td>PlasmaDNA was used as a specific tool for the simulation of restriction digests as well as PCR reactions</td><br />
<td><a href="http://research.med.helsinki.fi/plasmadna">research.med.helsinki.fi/plasmadna</td><br />
</tr><br />
<br />
<tr class="odd"><br />
<td>Sequencher</td><br />
<td>Sequencer helped to analyze the sequencing results obtained</td><br />
<td><a href="http://www.genecodes.com/">www.genecodes.com</a></td><br />
</tr><br />
<tr class="even"><br />
<td>OligoAnalyzer 3.1</td><br />
<td>Properties such as T<sub>m</sub>, dimerization and secondary structures of designed primers were identified </td><br />
<td><a href="http://eu.idtdna.com/analyzer/applications/oligoanalyzer/Default.aspx">http://eu.idtdna.com</a></td><br />
</tr><br />
</table><br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Resource|Software]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/SoftwareTeam:BIOTEC Dresden/Software2010-10-28T00:50:17Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<html><br />
<body><br />
<div id="content_prim"><br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th>Name</th><br />
<th>Description</th><br />
<th>Link</th><br />
</tr><br />
<br />
<tr class="even"><br />
<td>ApE</td><br />
<td>ApE was used as DNA construction software to create plasmid maps, fusion constructs and to view restriction sites of commonly used endonucleases </td><br />
<td><a href="http://biologylabs.utah.edu/jorgensen/wayned/ape">biologylabs.utah.edu/jorgensen/wayned/ape</td><br />
</tr><br />
<br />
<tr class="odd"><br />
<td>NCBI Blast</td><br />
<td>The online software tool blast was used both to check nucleotide and protein sequences towards their homology to the original genomic sequence </td><br />
<td><a href="http://blast.ncbi.nlm.nih.gov">blast.ncbi.nlm.nih.gov</td><br />
</tr><br />
<br />
<tr class="even"><br />
<td>Cell Designer</td><br />
<td>Cell Designer represents a tool for molecular modeling allowing to construct molecular circuits</td><br />
<td><a href="http://www.celldesigner.org">www.celldesigner.org</td><br />
</tr><br />
<br />
<tr class="odd"><br />
<td>PartsRegistry Sequence Analysis/BLAST</td><br />
<td>The registry blast was useful to identify nucleotide sequences already submitted to the registry</td><br />
<td><a href="http://partsregistry.org/cgi/sequencing/">partsregistry.org/cgi/sequencing</td><br />
</tr><br />
<br />
<tr class="even"><br />
<td>PlasmaDNA</td><br />
<td>PlasmaDNA was used as a specific tool for the simulation of restriction digests as well as PCR reactions</td><br />
<td><a href="http://research.med.helsinki.fi/plasmadna">research.med.helsinki.fi/plasmadna</td><br />
</tr><br />
<br />
<tr class="odd"><br />
<td>Sequencher</td><br />
<td>Sequencer helped to analyze the sequencing results obtained</td><br />
<td><a href="http://www.genecodes.com/">www.genecodes.com</a></td><br />
</tr><br />
<tr class="even"><br />
<td>Oligo Analyzer</td><br />
<td>Properties such as T<sub>m</sub>, dimerization and secondary structures of designed primers were checked. </td><br />
<td><a href="http://eu.idtdna.com/analyzer/applications/oligoanalyzer/Default.aspx">http://eu.idtdna.com</a></td><br />
</tr><br />
</table><br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Resource|Software]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ProtocolsAHL_assayTeam:BIOTEC Dresden/ProtocolsAHL assay2010-10-28T00:39:23Z<p>Mareike: New page: {{Biotec_Dresden/Header}} <html> <body> <div id="content_prim"> <div id="materials"> <h2>Materials</h2> <ul> <li>Escherichia coli DH5 alpha chemical competent cells</li> <li>1mL SOC (room ...</p>
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<h2>Materials</h2><br />
<ul><br />
<li>Escherichia coli DH5 alpha chemical competent cells</li><br />
<li>1mL SOC (room temperature) for each reaction</li><br />
<li>Ice</li><br />
<li>Plasmid DNA</li><br />
<li>Heating block</li><br />
<li>1.5ml microfuge tube</li><br />
<li>LB-agar plate with corresponding antibiotic</li><br />
</ul><br />
</div><br />
<br />
<div class="visualClear"></div><br />
<div id="procedure"><br />
<h2>Procedure</h2><br />
<ul><br />
<li>Chill DNA samples and tubes on ice.<br />
<li>Place LB-agar plates in <span class="markup temp">37°C</span> incubator to warm.<br />
<li>Remove chemical competent cells from <span class="markup temp">-80°C</span> freezer and thaw on ice. Alternatively, freshly prepared chemical competent cells may be used immediately.</li><br />
<li>Dial a P2 pipetman to either <span class="markup volume">1 or 2μL</span> depending on the salt content of your DNA sample. Use <span class="markup volume">2μL</span> for samples that have been purified in some way.</li><br />
<li>Dial a P200 pipetman to <span class="markup volume">50μL</span> or whatever volume of chemical competent cells you want to use; usually <span class="markup volume">20-50μL</span> .</li><br />
<li>Pipet <span class="markup volume">1-2μL</span> of DNA sample and add to chemical competent cells. Swirl tip around gently in cells to mix DNA and cells. Do not pipet up and down.</li><br />
<li>Place the mix back on <span class="markup temp">ice</span> for <span class="markup time">30 mins</span>.</li><br />
<li>Pulse the cells with a heat shock by placing the microfuge tubes in a heating block for <span class="markup time">45 seconds</span> at <span class="markup temp">42°C</span>.</li><br />
<li>Place sample on ice for <span class="markup time">2 mins</span> and then add SOC medium. This step should be done as quickly as possible to prevent cells from dying off.</li><br />
<li>Chill sample on ice for <span class="markup time">2 mins</span> to permit the cells to recover.</li><br />
<li>Transfer eppendorf tube to <span class="markup temp">37°C</span> incubator and shake to promote aeration. Incubate for <span class="markup time">1 hr</span> to permit expression of antibiotic resistance gene.</li><br />
<li>Plate transformation onto prewarmed LB-agar plate supplemented with appropriate antibiotic.</li><br />
</ul><br />
</div><br />
<h2>Reference</h2><br />
<p>adapted from <a href="http://openwetware.org/wiki/Knight:Electroporation">http://openwetware.org/wiki/Knight:Electroporation</a></p><br />
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[[Category:BIOTEC Dresden/Protocol|AHL assay]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T23:50:27Z<p>Mareike: </p>
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<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
<a alt="Picture of the Bio Campus Dresden" rel="lightbox" href="https://static.igem.org/mediawiki/2010/7/79/BiotecDresden_Campus_with_titles_l.jpg"><img id="campus_pic" class="build_pic border" src="https://static.igem.org/mediawiki/2010/c/c2/BiotecDresden_Campus_with_titles_s.jpg"></a><br />
<br />
<a alt="Complete Gene Circuit of SensorBricks" rel="lightbox" href="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png"> <img id="Fusion_Construct" class="build_pic border" src="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" ></a><br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed.</p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" rel="lightbox" title="Simple Model"><img class="border right" src="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" class="border left"></a><br />
<br />
<p>The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
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[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T23:48:30Z<p>Mareike: </p>
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<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
<a alt="Picture of the Bio Campus Dresden" rel="lightbox" href="https://static.igem.org/mediawiki/2010/7/79/BiotecDresden_Campus_with_titles_l.jpg"><img id="campus_pic" class="build_pic border" src="https://static.igem.org/mediawiki/2010/c/c2/BiotecDresden_Campus_with_titles_s.jpg"></a><br />
<br />
<a alt="Complete Gene Circuit of SensorBricks" rel="lightbox" href="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png"> <img class="border right" src="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" class="border right"></a><br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed.</p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" rel="lightbox" title="Simple Model"><img class="border right" src="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" class="border left"></a><br />
<br />
<p>The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
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[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T23:33:37Z<p>Mareike: </p>
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<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" rel="lightbox" title="SensorBricks"><img class="border right" src="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" class="border left"></a><br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed.</p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" rel="lightbox" title="Simple Model"><img class="border right" src="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" class="border left"></a><br />
<br />
<p>The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
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[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T23:26:49Z<p>Mareike: </p>
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<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" rel="lightbox" title="SensorBricks><img class="border right" src="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" class="border left"></a><br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed.</p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" rel="lightbox" title="Simple Model comprising AHL input and GFP output"><img class="border right" src="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" class="border left"></a><br />
<br />
<p>The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
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</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T23:23:12Z<p>Mareike: </p>
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<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
<a href="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" class="border left"></a><br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed.</p><br />
<br />
<a href="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/b/bb/BiotecDresden_Simple_GFP_reporter.png" class="border left"></a><br />
<br />
<p>The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
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{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/File:BiotecDresden_Simple_GFP_reporter.pngFile:BiotecDresden Simple GFP reporter.png2010-10-27T23:21:40Z<p>Mareike: </p>
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<div></div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T23:19:36Z<p>Mareike: </p>
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<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
<a href="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/0/07/BiotecDresden_Fusion_Construct.png" class="border left"></a><br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
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[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/File:BiotecDresden_Fusion_Construct.pngFile:BiotecDresden Fusion Construct.png2010-10-27T23:18:12Z<p>Mareike: </p>
<hr />
<div></div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/Characterized_Parts/BBa_I13263Team:BIOTEC Dresden/Characterized Parts/BBa I132632010-10-27T22:53:23Z<p>Mareike: </p>
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<h2>Part 17: I13263</h2> <br />
<a href="/wiki/images/a/af/BiotecDresden_Safety1_l.jpg" rel="lightbox"><img src="/wiki/images/b/b7/BiotecDresden_Safety1_s.jpg" class="border left"></a><br />
<p>This part is supposed to serve as a potential detection and quantification system for the concentration of the signal molecule n-acyl homoserine lactone (AHL) in the growth medium. As shown in the parts overview LuxR is constitutively expressed. In the presence of AHL a LuxR-AHL complex is formed activating lux pR and thereby the expression of eyfp. In characterization experiments the amount of AHL required for induction was analyzed. This part is characterized best and was consequently always used for later experiments.</p><br />
<h3>Results</h3><br />
<p>The graph 1.1 shows the YFP development over time of different concentrations of AHL, ranging from 10pM to 2µM. It can be seen that the fluorescence signal does not significantly change over time for AHL concentrations below 100nM and that the amount of YFP produced is the same for all concentrations above 300nM.</p><br />
<p>In the Graph 1.2 the fluorescence as a function of the AHL concentration after two hours of incubation is visualized. It can be seen that the YFP signal after 2 hours of incubation increases with increasing AHL concentrations but reaches a plateau at about 700nM. </p><br />
<br />
<br />
<br />
<h3>Discussion:</h3><br />
<br />
<p>Graph 1.1 shows nicely that the LB medium (dark blue) has a fluorescence signal of about 2800 raw fluorescence units (RFU). But since the fluorescence signal stayed constant over the time measured, this fluorescence does not qualitatively influence the data and can thus be ignored. Additionally it can be seen that the concentrations below 100nM do not lead to an increase in fluorescence, leading to the conclusion that a minimum concentration of 100nM outside of the bacteria is required for the induction of the LuxpR and in turn for the detectable expression of YFP. Furthermore, the graph shows that after 2h of incubation with AHL the amount of YFP detected can directly by related to the initial concentration of AHL. </p><br />
<p>Graph 1.2 on the other hand shows a logarithmic behavior of the transcriptional induction of the LuxpR promoter by AHL, which reaches its maximum induction at an AHL concentration of about 750nM. </p><br />
<br />
<h3>Materials and methods:</h3><br />
<p>The characterization was performed using a 96-well plate and a fluorescence plate reader. Bacteria supplied with the part BBa_I13263 were suspended in medium of a certain concentration of AHL ranging from 0.01 to 2000nM. The fluorescence was measured every 5 minutes using an excitation wavelength of 485nm and an emission wavelength of 535nm. For every fluorescence value, also the optical density at 612nm was measured. As a negative control the same measurements were done on uninduced bacteria and LB-medium without cells.</p><br />
<h3>Additional information</h3><br />
<p>For detailed information of the experimental set-up, please have a look at the protocols on our team-wiki. (Link) In case you want to know more about the normalization and negative controls, please have a look at this page: (Link)</p><br />
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[[Category:BIOTEC_Dresden/Characterized_Parts|I13263]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/EthicsTeam:BIOTEC Dresden/Ethics2010-10-27T22:50:06Z<p>Mareike: </p>
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<h2>Ethics</h2><br />
<h3>General Considerations</h3><br />
<p> Nowadays, the production and use of genetically modified organisms (GMO’s) let them be plants, animals or any other organisms are viewed with big precaution by most societies. There are multiple reasons why people are not accepting this products; some of them accompanied by sound scientific arguments, whereas others by wrong understanding and fears influenced by mass-media. On one hand, the people having nothing in common with biological sciences do not always know all the scientific background behind the problem, on the other hand, people in the biological field, in knowledge of the problem may be considered biased because of their continuous need to find answers by trying new things. As society and scientists look for compromise, there is a big effort all over the world to create the legislative frame which will ensure the careful manipulation of GMO’s in environment, medicine and industry. </p><br />
<p>Synthetic biology is also about genetic manipulation; combining genes or fragments of genes from all kinds of life forms, modifying them in order to produce solutions for many current problems concerning health or living supplies. Regardless of how noble the aims can be, it is necessary to consider the ethical questions arising from this kind of projects.</p><br />
<p>For the iGEM competition, it is important to assure the ethics and safety of the project and the product. That is very important since it is an undergraduate competition having budding scientists from all over the world, whom would consider those safety and ethical measures in their future careers.</p><br />
<p>In order to get a feeling of how society views genetic engineering, synthetic biology, the IGEM competition and our project in particular, conducted a small survey among a pool of about 40 people of age 22-65, of different nationalities and different backgrounds</p><br />
<br />
<p>The survey and its results were as follows </p><br />
<br />
<h3>Survey</h3><br />
<a href="https://static.igem.org/mediawiki/2010/5/56/G1f.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/5/56/G1f.jpg" class="border right"></a><br />
<p> <B>1. Do you regard genetic engineering as an absolute necessity for scientific research?</B> </p> <br />
<p> <i> About 90% of the people answered yes, mostly agreeing that it is an essential step for Biology to move forward and finding new solutions.</i> </p><br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/e/e4/G2f.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/e/e4/G2f.jpg" class="border left"></a><br />
<p> <B>2. Grade the areas below according to the need for approaches involving genetic engineering (you can use marks from 1 to 5, repeating marks allowed): </B> </p> <br />
<p>-medicine (research and therapy)</p><br />
<p>-environmental applications (e.g. fighting pollution, extracting salts from soil other)</p><br />
<p>-farming</p><br />
<p>-industry and energy</p><br />
<p> <i> Scores distributed approximately equally with most for medicine and least for farming. It is quite hard to decide which ones are the most important since nowadays priorities differ from one place to another according to its needs and background.</i> </p><br />
<br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/3/39/G3f.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/3/39/G3f.jpg" class="border right"></a><br />
<p><B> 3. Is there an order for you in terms of ethics regarding gene manipulation performed on bacteria, plants, animals (except humans)? If yes give a score for each group (1 is least ethical).</B></p><br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/8/87/Bac.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/8/87/Bac.jpg" class="border left"></a><br />
<p> <i> Highest ethical concerns were raised for animals.</i> </p><br />
<p><B>4. Could you list one or two main potential risks (for health, environment) arising from the use of genetically modified organisms. </B></p><br />
<p>-for health:</p><br />
<p>-for environment:</p><br />
<p> <i>The results for health was the risk of production of potential pathogenic bacteria and their release into the environment, as well as the production of GM crops and their effect on humans after consumption. Regarding environmental risks included the production of new organisms that would not be controlled nor predicted. Probably, the main ethical concern regarding gene modification is the crossing of the species boundaries by using genes from various organisms which can be in contradiction with how God planned everything. It is just important to mention, that some of the postulated risks are really improbable from the scientific point of view, whereas for others the best approach would be a careful one. </i> </p><br />
<a href="https://static.igem.org/mediawiki/2010/a/a0/G5F.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/a/a0/G5F.jpg" class="border right"></a><br />
<p> <B>5. Synthetic biology deals with the construction of new biological entities such as new proteins with combined functions, genetic circuits and cells, but also with the remodeling of existing biological systems for a specific use. Do you think there are any ethical restrictions to practicing it? </B> </p><br />
<br />
<p> <i> More than 70 % think there ARE ethical restrictions. Oh yes, there are! Ask Craig Venter. Apart from jokes, due to the huge diversity of ideas being experimented, every single designed project in synthetic biology should be analyzed individually for its implications on morality. </i> </p><br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/1/18/6.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/1/18/6.jpg" class="border left"></a><br />
<p> <B> 6. If yes, do you think the potential advantages are overweighting the possible ethical problems. </B> </p><br />
<p> <i> About 56% from the entire pool answered yes. We also think yes, but maybe you would like to consider somebody else's opinion. Synthetic biology can provide new approaches for almost every aspect of human life. </i> </p><br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/e/ed/G7f.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/e/ed/G7f.jpg" class="border right"></a><br />
<p> <B> 7. How would you regard deliberate synthetic biology competitions among undergraduate students which include designing of genetically modified organisms with the aim to find solutions to various global problems. </B> </p><br />
<br />
<p> <i> 78% approved. Allowing students to get an insight into the field of synthetic biology also makes them aware of potential risks and morality concerns. Within the society genetic engineering is still assessed with high concerns also caused by the rather new introduction of the field. The limited knowledge about those benefits and risk contributes to this. Therefore spreading more information about what exactly scientists are planning to do and why would probably also help minimizing fears from outside. <br />
Still we have to be careful when walking home since there are 12% left which not really agree. We avoided telling here that the team members SHOULD HAVE FUN doing their experiments (internal information). <br />
IGEM is not only about students, there are enough people involved in supervising the project and giving advices. The institutions where the projects are being carried out are usually aware of the workflow, aims and methods of these groups of experimenters.</i> </p><br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/8/80/G8f.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/8/80/G8f.jpg" class="border left"></a><br />
<p> <B>8. Do you think the outcome is greater than the risks?</B> </p><br />
<p> <i> 87% think yes. Some teams have already invented amazing things in the short time frame of the competition. Also the idea of having standardized parts improves the whole field and the related work of synthetic biology. Being completely free in the topic choosen also leads to ideas that are out of the box. Interestingly, also industry became aware of iGEM asking for inventive ideas solving industrial problems. </i> </p><br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/3/30/9.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/3/30/9.jpg" class="border right"></a><br />
<p> <B> 9. Do you think that creation of bacterial based biosensors for testing isolated blood samples from humans for certain diseases is in contradiction with any known moral rules or is posing any significant risks? </B> </p><br />
<p>If Yes, please list some of them</p><br />
<p> <i>97% answered NO (except 1 person who stated that the method is invasive). </i> </p><br />
<p> <i> As expected! if it was a YES, we would have sent our T-shirts to the Jamboree (they are nice!). </i>.</p><br />
<div class="visualClear"></div><br />
<a href="https://static.igem.org/mediawiki/2010/a/ae/10.jpg" rel="lightbox"><img src="https://static.igem.org/mediawiki/2010/a/ae/10.jpg" class="border left"></a><br />
<p> <B> 10. If such biosensor systems would be much more sensitive than some of the currently used detection techniques and could make a big difference to the efficiency of disease diagnosis, would you grant its massive use along with the already established detection methods (considering that it is a transgenic organism)? </B> </p><br />
<p> <i> 95% Yes. Straight way to thinking about a business </i> </p><br />
<div class="visualClear"></div><br />
<p> In conclusion, it is worth saying that the SensorBricks project cannot be in contradiction with any moral values, because it is a simple detection method, it is not posing any risks for the health of the patient as it is an in-vitro method performed with patient blood samples collected in advance. More than this it is designed to contribute to the efficiency of medical diagnosis procedures and has the perspectives for making the system cheaper and more available to benefit more people. BIOTEC Dresden IGEM TEAM 2010.</p><br />
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[[Category:BIOTEC Dresden/Human_Practices|Ethics]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:43:34Z<p>Mareike: </p>
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<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Growth Rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
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[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:39:45Z<p>Mareike: </p>
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</style><br />
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</head><br />
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<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
<span class="nom"><span class="dwn">X(t)- γG(t) </span><span><i>G(t)</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:32:50Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
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<html><br />
<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
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.nom { text-decoration: underline; }<br />
.dwn{ bottom:-5px; left:-25px; position:relative; }<br />
</style><br />
<br />
</head><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
<p>[LuxR-AHL]=k<sub>dis</dis> x [AHL] x [LuxR]</p><br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:29:42Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
.den, .nom { display: block; width:100%; text-align:center }<br />
.nom { text-decoration: underline; }<br />
.dwn{ bottom:-5px; left:-25px; position:relative; }<br />
</style><br />
<br />
</head><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>x AHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:27:46Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
.den, .nom { display: block; width:100%; text-align:center }<br />
.nom { text-decoration: underline; }<br />
.dwn{ bottom:-5px; left:-25px; position:relative; }<br />
</style><br />
<br />
</head><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>xAHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:26:56Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
.den, .nom { display: block; width:100%; text-align:center }<br />
.nom { text-decoration: underline; }<br />
.dwn{ bottom:-5px; left:-25px; position:relative; }<br />
</style><br />
<br />
</head><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>xAHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:26:32Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
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<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
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</style><br />
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</head><br />
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<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>xAHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:25:47Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
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<html><br />
<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
.den, .nom { display: block; width:100%; text-align:center }<br />
.nom { text-decoration: underline; }<br />
.dwn{ bottom:-5px; left:-25px; position:relative; }<br />
</style><br />
<br />
</head><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>xAHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:25:19Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
.den, .nom { display: block; width:100%; text-align:center }<br />
.nom { text-decoration: underline; }<br />
.dwn{ bottom:-5px; left:-25px; position:relative; }<br />
</style><br />
<br />
</head><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>xAHL<sub>in</sub></span><span><i>d[AHL]</i></span><span class="lin">/<br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:21:03Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
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<style type="text/css"><br />
.lin { display: none; }<br />
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</style><br />
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</head><br />
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<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>xAHL<sub>in</sub> </span><span><i>d[AHL]</i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>dt</i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T22:19:24Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
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<html><br />
<head><br />
<style type="text/css"><br />
.lin { display: none; }<br />
.den, .nom { display: block; width:100%; text-align:center }<br />
.nom { text-decoration: underline; }<br />
.dwn{ bottom:-5px; left:-25px; position:relative; }<br />
</style><br />
<br />
</head><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in</sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Diffusion Coefficients</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL diffusion coefficient</b></td><br />
<td>k<sub>dif</sub></td><br />
<td>0.001 mm<sup>2</sup>/min</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="dwn">v = </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
<br />
<span class="nom"><span class="dwn">k<sub>dif</sub>(AHL<sub>ex</sub>-AHL<sub>in</sub>)-(k<sub>AHL</sub>xAHL<sub>in</sub> </span><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span class="lin">/</span></span><br />
<span class="den"><span class="lin">(</span><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span></span><br />
<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</sub>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
</div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T21:35:52Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in<sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span><i>V<sub>max</sub> x SAM<sub>ex</sub></i></span><span<br />
class="lin">/</span><br />
<span class="den"><span class="lin">(<i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</dis>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T21:35:10Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in<sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="lin">(</span><i>V<sub>max</sub> x SAM<sub>ex</sub></i><span class="lin">)</span></span><span<br />
class="lin">/</span><br />
<span class="den"><span class="lin">(<i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i><span class="lin">)</span></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</dis>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T21:33:17Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in<sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<br />
<span class="nom"><span class="lin">(</span><i>V<sub>max</sub> x SAM<sub>ex</sub></i><span class="lin">)</span></span><span<br />
class="lin">/</span><br />
<span class="den"><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i></span><br />
<br />
<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</dis>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T21:27:33Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in<sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<table cellspacing="0" cellpadding="0"><br />
<tr><td align="center"><i>V<sub>max</sub> x SAM<sub>ex</sub></i></td></tr><br />
<tr><td valign="middle"><img src="1px.gif" alt="divided by"<br />
width="100%" height="0.5"></td></tr><br />
<tr><td align="center"><i>K<sub>m</sub></i> + <i>SAM<sub>ex</sub></i></td></tr><br />
</table><br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</dis>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T21:22:14Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in<sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
<table cellspacing="0" cellpadding="0"><br />
<tr><td align="center"><i>x</i></td></tr><br />
<tr><td valign="middle"><img src="1px.gif" alt="divided by"<br />
width="100%" height="1"></td></tr><br />
<tr><td align="center"><i>a</i> - <i>b</i></td></tr><br />
</table><br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</dis>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T21:12:15Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in<sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Parameters</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</dis>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T21:10:39Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHL<sub>out</sub> > AHL<sub>in<sub>.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-LuxI. The conversion of S-adenosyl methionine (SAM) to acylated homoserine lactone (AHL) catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (k<sub>dif</sub>), the initial concentration (AHL<sub>ex</sub>) as well as the decay constant of AHL inside the cell (k<sub>AHL</sub>). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation (k<sub>LuxR</sub>, the binding and dissociation constant of AHL and LuxR, k<sub>dis</dis>. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M, where kt is an unknown constant and M is mRNA production remaining constant for all proteins expressed in our model. The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 h<sup>-1</sup> and can be neglected as it is so much smaller than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T20:58:53Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation Rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Enzyme Kinetic Constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>Maximal Velocity LuxI</b></td><br />
<td>V<sub>max</sub></td><br />
<td>1.1 mol/min</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>Km SAM</b></td><br />
<td>K<sub>m</sub></td><br />
<td>130 µM</td><br />
</tr><br />
<br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-luxI. The conversion of S-adenosyl methionine (SAM) to AHL catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (kdif), the initial concentration (AHLex) as well as the decay constant of AHL inside the cell (kdec). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation, the binding and dissociation constant of AHL and LuxR. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M (where kt is an unknown constant, M is mRNA production which is constant for all proteins expressed in our model). The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 hours-1. Can be neglected as it is so much small than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T20:49:23Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Hill Cooperativity</th><br />
</tr><br />
<tr class="even"><br />
<td><b>LuxR cooperativity</b></td><br />
<td>n<sub>LuxR</sub></td><br />
<td>2</td><br />
</tr><br />
</tr><br />
<tr class="odd"><br />
<td><b>AHL-LuxR cooperativity</b></td><br />
<td>n<sub>AHL-LuxR</sub></td><br />
<td>1</td><br />
</tr><br />
<br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-luxI. The conversion of S-adenosyl methionine (SAM) to AHL catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (kdif), the initial concentration (AHLex) as well as the decay constant of AHL inside the cell (kdec). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation, the binding and dissociation constant of AHL and LuxR. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M (where kt is an unknown constant, M is mRNA production which is constant for all proteins expressed in our model). The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 hours-1. Can be neglected as it is so much small than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T20:47:37Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-luxI. The conversion of S-adenosyl methionine (SAM) to AHL catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (kdif), the initial concentration (AHLex) as well as the decay constant of AHL inside the cell (kdec). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation, the binding and dissociation constant of AHL and LuxR. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M (where kt is an unknown constant, M is mRNA production which is constant for all proteins expressed in our model). The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 hours-1. Can be neglected as it is so much small than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T20:46:59Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<td> </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>6.3<sup>-3</sup>min<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Dissociation constants</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL-LuxR dissociation constant</b></td><br />
<td>k<sub>dis</sub></td><br />
<td>0.09 - 1 µM</td><br />
</tr><br />
<br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-luxI. The conversion of S-adenosyl methionine (SAM) to AHL catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (kdif), the initial concentration (AHLex) as well as the decay constant of AHL inside the cell (kdec). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation, the binding and dissociation constant of AHL and LuxR. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M (where kt is an unknown constant, M is mRNA production which is constant for all proteins expressed in our model). The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 hours-1. Can be neglected as it is so much small than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
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<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
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[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T20:42:37Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
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<html><br />
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<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td><b>growth rate</b></td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td><b>Promoter Activity</b></td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>Plasmid copy number</b></td><br />
<td>l</td><br />
<td>25 </td><br />
<td> </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation rates</th><br />
</tr><br />
<tr class="even"><br />
<td><b>AHL decay rate</b></td><br />
<td>k<sub>AHL</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>k<sub>LuxR</sub></td><br />
<td>0.11 h<sup>-1</sup></td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td><b>GFP degradation rate</b></td><br />
<td>k<sub>GFP</sub></td><br />
<td>0.11 h</td><br />
</tr><br />
<tr class="odd"><br />
<td><b>LuxR degradation rate</b></td><br />
<td>LuxR_kdec</td><br />
<td>0.11 h</td><br />
</tr<br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-luxI. The conversion of S-adenosyl methionine (SAM) to AHL catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (kdif), the initial concentration (AHLex) as well as the decay constant of AHL inside the cell (kdec). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation, the binding and dissociation constant of AHL and LuxR. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M (where kt is an unknown constant, M is mRNA production which is constant for all proteins expressed in our model). The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 hours-1. Can be neglected as it is so much small than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T20:32:19Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td>growth rate</td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td>Promoter Activity</td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td>Plasmid copy number</td><br />
<td>l</td><br />
<td>25 </td><br />
<td> </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation rates</th><br />
</tr><br />
<tr class="odd"><br />
<td>AHL decay rate</td><br />
<td>AHL_kdec</td><br />
<td>0.11 h</td><br />
</tr><br />
<tr class="even"><br />
<td>LuxR degradation rate</td><br />
<td>LuxR_kdec</td><br />
<td>0.11 h</td><br />
</tr<br />
</table><br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-luxI. The conversion of S-adenosyl methionine (SAM) to AHL catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (kdif), the initial concentration (AHLex) as well as the decay constant of AHL inside the cell (kdec). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation, the binding and dissociation constant of AHL and LuxR. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M (where kt is an unknown constant, M is mRNA production which is constant for all proteins expressed in our model). The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 hours-1. Can be neglected as it is so much small than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/ModelingTeam:BIOTEC Dresden/Modeling2010-10-27T20:31:50Z<p>Mareike: </p>
<hr />
<div>{{Biotec_Dresden/Header}}<br />
<br />
<html><br />
<br />
<br />
<body><br />
<div id="content_prim"><br />
<br />
<h3>Assumptions</h3><br />
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p><br />
<p>(2) For simplicity decay of all products follows first-order kinetics. </p><br />
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p><br />
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p><br />
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p><br />
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p> <br />
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p><br />
<br />
<h3>Constants</h3><br />
<br />
<table class="tformat" cellspacing="0" cellpadding="0"><br />
<tr class="odd"><br />
<th colspan="3">General Parameters</th><br />
</tr><br />
<tr class="even"><br />
<td>growth rate</td><br />
<td>µ</td><br />
<td>1.3 h<sup>-1</sup> </td><br />
</tr><br />
<tr class="odd"><br />
<td>Promoter Activity</td><br />
<td>c</td><br />
<td>0.01 mM/h</td><br />
</tr><br />
</tr><br />
<tr class="even"><br />
<td>Plasmid copy number</td><br />
<td>l</td><br />
<td>25 </td><br />
<td> </td><br />
</tr><br />
<tr class="odd"><br />
<th colspan="3">Degradation rates</th><br />
</tr><br />
<tr class="odd"><br />
<td>AHL decay rate</td><br />
<td>AHL_kdec</td><br />
<td>0.11 h</td><br />
</tr><br />
<tr class="even"><br />
<td>LuxR degradation rate</td><br />
<td>LuxR_kdec</td><br />
<td>0.11 h</td><br />
</tr<br />
<br />
<h3>Simplified Model</h3><br />
<p>In a first simple model a single cell and its kinetics in output will be analyzed. The major input in this simplified scenario is AHL produced from SAM catalyzed by LuxI. The direct output is GFP or any other fluorescent reporter like RFP and YFP. In the gene design it can be seen that GFP expression is coupled to its induction upon binding of LuxR-AHL complex to the luxR promoter. </p><br />
PICTURE OF SCHEME<br />
<p>In the extracellular environment the enzyme LuxI is present in form of the fusion construct, proteinA-luxI. The conversion of S-adenosyl methionine (SAM) to AHL catalyzed by LuxI follows enzyme kinetics by Michaelis-Menten:</p><br />
FORMULA 1<br />
<p>Next, AHL has to be transported across the membrane of the cell via diffusion. The inside concentration is therefore determined by the diffusion rate across the membrane (kdif), the initial concentration (AHLex) as well as the decay constant of AHL inside the cell (kdec). </p><br />
FORMULA 2<br />
<p>Furthermore AHL as well as constitutively expressed LuxR form a complex which can bind to the luxR promoter. The amount of AHL-LuxR complex binding the luxR promoter is dependent on the concentration of AHL, the concentration of LuxR and its degradation, the binding and dissociation constant of AHL and LuxR. </p><br />
FORMULA 3<br />
<p>A signal can be detected using different reporters like fluorescent proteins, pigments or substances that can be detected. We focused on the detection using fluorescent proteins like GFP which could be detected using absorbance measurements. In this easy model the kinetics of GFP as output signal will be displayed. </p><br />
FORMULA 4<br />
<p>The formula displays GFP expression over time G(t). The term X(t) refers to the mRNA production and degradation as well as fluorescent read out obtained in RFU, composed of kt x M (where kt is an unknown constant, M is mRNA production which is constant for all proteins expressed in our model). The Term γ stands for dilution rate which can also be represented by the growth rate µ of the E.coli Dh5α. The half life of GFP was experimentally determined to be around 24 hours. Therefore the value of γ is about 0.029 hours-1. Can be neglected as it is so much small than dilution rate. </p><br />
<br />
<h3>Results</h3><br />
<p>For the simulation first the model of a growing culture with direct AHL input and GFP output was analyzed. The three graphs shown below demonstrate the behavior of the gene construct upon AHL induction. The higher the concentration of AHL used for the induction the higher is also the fluorescence signal detected from GFP. AHL diffuses basically without any constriction into the bacteria clearly depicted by the exponentially following decay of the graphs (Figure 1). Correspondingly the endpoint fluorescent signals of GFP vary depending on the AHL input which can be seen in Figure 2. For high AHL concentrations the endpoint GFP signal is elevated compared to lower AHL concentrations. </p><br />
<br />
<p>In Figure 3 the LuxR-AHL complex formation is displayed which also increases in endpoint value for increased AHL concentrations caused by the availability of binding partner. </p> <br />
<br />
<h3>Discussion</h3><br />
<p>Even this simplified model shows that the output GFP signal can be used to quantify the amount of AHL present in the sample. This will allow us in the future to accurately determine the amount of cancer cells present in the patient’s blood sample. Using amplification constructs like introducing LuxI downstream of the Lux pR together with a reporter protein even more AHL will be produced. The set-up can be seen in Figure 4. </p> <br />
<p></p><br />
</div><br />
<br />
<br />
<br />
<br />
<div class="visualClear"></div><br />
</body><br />
</html><br />
<br />
[[Category:BIOTEC_Dresden/Project|Project]]<br />
{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/LiteratureTeam:BIOTEC Dresden/Literature2010-10-27T20:01:04Z<p>Mareike: </p>
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<h2>Modelling</h2><br />
<p>1.THE GREEN FLUORESCENT PROTEIN - Annual Review of Biochemistry, 67(1):509.</p><br />
<br />
<p>2.Tian T, Burrage K (2006) Stochastic models for regulatory networks of the genetic toggle switch. Proceedings of the National Academy of Sciences 103: 8372 -8377.</p><br />
<br />
<p>3.Basu S, Mehreja R, Thiberge S, Chen M, Weiss R (2004) Spatiotemporal control of gene expression with pulse-generating networks. Proceedings of the National Academy of Sciences of the United States of America 101: 6355 -6360.</p><br />
<br />
<p>4.Nilsson P, Olofsson A, Fagerlind M, Fagerström T, Rice S, u. a. (2001) Kinetics of the AHL Regulatory System in a Model Biofilm System: How Many Bacteria Constitute a "Quorum"? Journal of Molecular Biology 309: 631-640.</p><br />
<br />
<p>5.Schaefer AL, Val DL, Hanzelka BL, Cronan JE, Greenberg EP (1996) Generation of cell-to-cell signals in quorum sensing: acyl homoserine lactone synthase activity of a purified Vibrio fischeri LuxI protein. Proc. Natl. Acad. Sci. U.S.A 93: 9505-9509.</p><br />
<br />
<p>6.Kaplan HB, Greenberg EP (1985) Diffusion of autoinducer is involved in regulation of the Vibrio fischeri luminescence system. J Bacteriol 163: 1210-1214.</p><br />
<br />
<p>7.Hanzelka BL, Parsek MR, Val DL, Dunlap PV, Cronan JE, u. a. (1999) Acylhomoserine lactone synthase activity of the Vibrio fischeri AinS protein. J. Bacteriol 181: 5766-5770.</p><br />
<br />
<p>8.Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335-338.</p><br />
<br />
<p>9.Goryachev A, Toh D, Lee T Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants. Biosystems 83: 178-187.</p><br />
<br />
<p>10.Müller J, Kuttler C, Hense BA, Rothballer M, Hartmann A (2006) Cell-cell communication by quorum sensing and dimension-reduction. J Math Biol 53: 672-702.</p><br />
<br />
<br />
<h2>Fusion Protein </h2><br />
<p>1. http://www-nmr.cabm.rutgers.edu/photogallery/proteins/htm/page16.htm</a></p><br />
<p>2. Nilsson B, Moks T, Jansson B, Abrahmsén L, Elmblad A, u. a. (1987) A synthetic IgG-binding domain based on staphylococcal protein A. Protein Eng 1: 107-113.</a></p><br />
<p>3. Van Houdt R, Moons P, Aertsen A, Jansen A, Vanoirbeek K, u. a. (2007) Characterization of a luxI/luxR-type quorum sensing system and N-acyl-homoserine lactone-dependent regulation of exo-enzyme and antibacterial component production in Serratia plymuthica RVH1. Research in Microbiology 158: 150-158.</a></p><br />
<br />
<h2>ACP Synthesis </h2><br />
<br />
</p> 1.Generation of cell-to-cell signals in quorum sensing: Acyl homoserine lactone synthase activity of a purified Vibrion fischeri LuxI protein, Proc. Natl. Acad. Sci., USA, 1996, vol.93, pp. 9505-9509 </p> <br />
<br />
</p> 2. Zhiwei Shen, Debra Fice, David M. Byers, Preparation of Fatty-Acylated Derivatives of Acyl Carrier Protein Using Vibrio harveyi Acyl-ACP Synthetase, 1992, Analytical biochemistry 204, 34-39 </p> <br />
<br />
</p> 3. http://www.neb.com/nebecomm/products/productP9301.asp </p> <br />
<br />
</p> 4. McAllister KA, Peery RB, Zhao G., Acyl carrier protein synthases from gram-negative, gram-positive, and atypical bacterial species: Biochemical and structural properties and physiological implications, J Bacteriol., 2006, vol 188(13):4737-48 </p> <br />
<br />
</p> 5. R. H. Lambalot, C. T. Walsh , Cloning, Overproduction, and Characterization of the Escherichia coli Holo-acyl Carrier Protein Synthase , The Journal of Biological Chemistry, 1995 Vol. 270, No. 42, pp. 24658–24661 </p> <br />
<br />
</p> 6. Information for Entry EC 2.7.8.7 - holo-[acyl-carrier-protein] synthase in BRENDA database (A Comprehensive Enzyme Information System). </p> <br />
<br />
</p> 7. J.G. Jaworski, P.K. Stumpf., Fat metabolism in higher plants: Enzymatic preparation of E. coli stearyl-acyl carrier protein, Arch. Biochem. Biophys. 162 (1974), pp. 166–173 </p> <br />
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{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/LiteratureTeam:BIOTEC Dresden/Literature2010-10-27T20:00:38Z<p>Mareike: </p>
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<h2>Modelling</h2><br />
<p>1.THE GREEN FLUORESCENT PROTEIN - Annual Review of Biochemistry, 67(1):509. Available at: http://www.annualreviews.org/doi/abs/10.1146%2Fannurev.biochem.67.1.509. Zugegriffen 20 Oktober 2010.</p><br />
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<p>2.Tian T, Burrage K (2006) Stochastic models for regulatory networks of the genetic toggle switch. Proceedings of the National Academy of Sciences 103: 8372 -8377.</p><br />
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<p>3.Basu S, Mehreja R, Thiberge S, Chen M, Weiss R (2004) Spatiotemporal control of gene expression with pulse-generating networks. Proceedings of the National Academy of Sciences of the United States of America 101: 6355 -6360.</p><br />
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<p>4.Nilsson P, Olofsson A, Fagerlind M, Fagerström T, Rice S, u. a. (2001) Kinetics of the AHL Regulatory System in a Model Biofilm System: How Many Bacteria Constitute a "Quorum"? Journal of Molecular Biology 309: 631-640.</p><br />
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<p>5.Schaefer AL, Val DL, Hanzelka BL, Cronan JE, Greenberg EP (1996) Generation of cell-to-cell signals in quorum sensing: acyl homoserine lactone synthase activity of a purified Vibrio fischeri LuxI protein. Proc. Natl. Acad. Sci. U.S.A 93: 9505-9509.</p><br />
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<p>6.Kaplan HB, Greenberg EP (1985) Diffusion of autoinducer is involved in regulation of the Vibrio fischeri luminescence system. J Bacteriol 163: 1210-1214.</p><br />
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<p>7.Hanzelka BL, Parsek MR, Val DL, Dunlap PV, Cronan JE, u. a. (1999) Acylhomoserine lactone synthase activity of the Vibrio fischeri AinS protein. J. Bacteriol 181: 5766-5770.</p><br />
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<p>8.Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335-338.</p><br />
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<p>9.Goryachev A, Toh D, Lee T Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants. Biosystems 83: 178-187.</p><br />
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<p>10.Müller J, Kuttler C, Hense BA, Rothballer M, Hartmann A (2006) Cell-cell communication by quorum sensing and dimension-reduction. J Math Biol 53: 672-702.</p><br />
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<h2>Fusion Protein </h2><br />
<p>1. http://www-nmr.cabm.rutgers.edu/photogallery/proteins/htm/page16.htm</a></p><br />
<p>2. Nilsson B, Moks T, Jansson B, Abrahmsén L, Elmblad A, u. a. (1987) A synthetic IgG-binding domain based on staphylococcal protein A. Protein Eng 1: 107-113.</a></p><br />
<p>3. Van Houdt R, Moons P, Aertsen A, Jansen A, Vanoirbeek K, u. a. (2007) Characterization of a luxI/luxR-type quorum sensing system and N-acyl-homoserine lactone-dependent regulation of exo-enzyme and antibacterial component production in Serratia plymuthica RVH1. Research in Microbiology 158: 150-158.</a></p><br />
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<h2>ACP Synthesis </h2><br />
<br />
</p> 1.Generation of cell-to-cell signals in quorum sensing: Acyl homoserine lactone synthase activity of a purified Vibrion fischeri LuxI protein, Proc. Natl. Acad. Sci., USA, 1996, vol.93, pp. 9505-9509 </p> <br />
<br />
</p> 2. Zhiwei Shen, Debra Fice, David M. Byers, Preparation of Fatty-Acylated Derivatives of Acyl Carrier Protein Using Vibrio harveyi Acyl-ACP Synthetase, 1992, Analytical biochemistry 204, 34-39 </p> <br />
<br />
</p> 3. http://www.neb.com/nebecomm/products/productP9301.asp </p> <br />
<br />
</p> 4. McAllister KA, Peery RB, Zhao G., Acyl carrier protein synthases from gram-negative, gram-positive, and atypical bacterial species: Biochemical and structural properties and physiological implications, J Bacteriol., 2006, vol 188(13):4737-48 </p> <br />
<br />
</p> 5. R. H. Lambalot, C. T. Walsh , Cloning, Overproduction, and Characterization of the Escherichia coli Holo-acyl Carrier Protein Synthase , The Journal of Biological Chemistry, 1995 Vol. 270, No. 42, pp. 24658–24661 </p> <br />
<br />
</p> 6. Information for Entry EC 2.7.8.7 - holo-[acyl-carrier-protein] synthase in BRENDA database (A Comprehensive Enzyme Information System). </p> <br />
<br />
</p> 7. J.G. Jaworski, P.K. Stumpf., Fat metabolism in higher plants: Enzymatic preparation of E. coli stearyl-acyl carrier protein, Arch. Biochem. Biophys. 162 (1974), pp. 166–173 </p> <br />
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{{Biotec_Dresden/Bottom}}</div>Mareikehttp://2010.igem.org/Team:BIOTEC_Dresden/EthicsTeam:BIOTEC Dresden/Ethics2010-10-27T17:46:45Z<p>Mareike: </p>
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<h2>Ethics</h2><br />
<h3>General Considerations</h3><br />
</p> Nowadays the production and use of genetically modified organisms (GMO’s) let them be plants, animals or any other living beings are viewed with big precaution by most societies. There are multiple reasons why people are not accepting this products some of them accompanied by sound scientific arguments, whereas others by wrong understanding and fears fueled by mass-media. </p><br />
</p>On one hand the people having nothing in common with biological sciences do not always know all the scientific background behind the problem, on the other hand, “bio people” in knowledge of the problem may be considered biased because their profession is usually their interest, belief and not last - their source of income. As society and scientists look for compromise, there is a big effort all over the world to create the legislative frame which will ensure the careful manipulation of GMO’s in environment, medicine, industry, in order to show respect for the people's opinion on this issue. </p><br />
</p>Synthetic biology is also about genetic manipulation – combining genes or fragments of genes from all kinds of life forms, modifying them in order to produce enhanced organisms able to be used for the sake of the mankind. Regardless of how noble the aims can be, it is necessary to consider the ethical questions arising from this kind of projects.</p><br />
</p>In the middle of all this fuss about gene manipulation here comes a synthetic biology competition among STUDENTS !! which offers the chance to apply into practice ambitious concepts harbored by their imagination (which is sometimes OK and sometimes NOT :) . This is an issue that is likely to rise questions from society's part, that’s why there stays a special requirement to accurately consider the ethical and safety aspects of each individual IGEM project.</p><br />
</p>In order to get a feeling of how society views genetic engineering, synthetic biology, the IGEM competition and our project in particular we conducted a small survey among a pool of about 40 young people of age 22-30, of German or other origin (ratio of about 1:1) of biological and non-biological background (same ratio). </p><br />
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</p>You can follow us through the questions... and comments </p><br />
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<h3>Survey</h3><br />
</p></p><br />
</p> <B>1. Do you regard genetic engineering as an absolute necessity for scientific research?</B> </p> <br />
</p>-YES -NO</p> <br />
</p> <i> About 90% answered yes which is actually the only right answer. Biology cannot move forward without altering the genes in so many ways to determine their functions and correlations with other genes in the cell, to enhance the products coded, etc. </i> </p><br />
</p></p><br />
</p> <B>2. Grade the areas below according to the need for approaches involving genetic engineering (you can use marks from 1 to 5, repeating marks allowed): </B> </p> <br />
</p>-medicine (research and therapy)</p><br />
</p>-environmental applications (e.g. fighting pollution, extracting salts from soil other)</p><br />
</p>-farming</p><br />
</p>-industry and energy</p><br />
</p>-other (you can also give your own application area)</p><br />
</p> <i> Scores distributed approximately equally with most for medicine and least for farming. It is quite hard to decide which ones are the most important since nowadays humanity has major problems on all of these lines. Quality of medicine is obvious for a healthy society as is fighting and preventing pollution. However, the need for effective farming which might not be seen as such a big problem today, even though there are people dying of hunger, will definitely become more acute in the future. The same is true fort supplying increasing amounts of energy and extraction/ recycling of scarce resources. </i> </p><br />
</p></p><br />
</p><B> 3. Is there an order for you in terms of ethics regarding gene manipulation performed on bacteria, plants, animals (except humans)? If yes give a score for each group (1 is least ethical).</B></p><br />
</p>-YES -NO</p><br />
</p>-Bacteria -Plants -Animals </p><br />
</p> <i> Highest ethical concerns were raised for animals but nobody cares how would a bacteria feel like. It is probably a consequence of human nature, to show affection for things you can see and that resemble you in so many ways. </i> </p><br />
</p><B>4. Could you list one or two main potential risks (for health, environment) arising from the use of genetically modified organisms. </B></p><br />
</p>-for health:</p><br />
</p>-for environment:</p><br />
</p></p><br />
</p> <i> Most of the answers were too general and focused around the words “uncontrolled”, “unpredictable” and “side effects”. When talking about health risks, the mostly discussed ones are, for instance, the accidental production of pathogenic bacteria and their release into the environment(e.g. bacteria producing toxins, antibiotics). Debated risk for GM crops are supposed to be potential allergenic effects determined by the new genes, the potential of passing antibiotic resistance genes to bacteria inhabiting the human gut. Regarding environmental risks, the most prominent one might be the potential production of new organisms (for instance harboring several resistance genes) able to compete and substitute the natural ones from the environment potentially destabilizing entire ecosystems (e.g. the production of super-weed). Probably, the main ethical concern regarding gene modification is the crossing of the species boundaries by using genes from various organisms which can be in contradiction with how God planned everything. It is just important to mention, that some of the postulated risks are really improbable from the scientific point of view, whereas for others the best approach would be a careful one. </i> </p><br />
</p> <B>5. Synthetic biology deals with the construction of new biological entities such as new proteins with combined functions, genetic circuits and cells, but also with the remodeling of existing biological systems for a specific use. Do you think there are any ethical restrictions to practicing it? </B> </p><br />
</p>-YES -NO</p> <br />
</p> <i> More than 70 % think there ARE ethical restrictions. Oh yes, there are! Ask Craig Venter. Apart from jokes, due to the huge diversity of ideas being experimented, every single designed project in synthetic biology should be analyzed individually for its implications on morality. </i> </p><br />
</p> <B> 6. If yes, do you think the potential advantages are overweighting the possible ethical problems. </B> </p><br />
</p>-YES -NO</p><br />
</p> <i> About 56% from the entire pool answered yes. We also think yes, but maybe you would like to consider somebody else's opinion. Synthetic biology can provide new approaches for almost every aspect of human life. </i> </p><br />
</p> <B> 7. How would you regard deliberate synthetic biology competitions among undergraduate students which include designing of genetically modified organisms with the aim to find solutions to various global problems. </B> </p><br />
</p>-I approve -I disapprove </p><br />
</p> <i> 78% approved. Allowing students to get an insight into the field of synthetic biology also makes them aware of potential risks and morality concerns. Within the society genetic engineering is still assessed with high concerns also caused by the rather new introduction of the field. The limited knowledge about those benefits and risk contributes to this. Therefore spreading more information about what exactly scientists are planning to do and why would probably also help minimizing fears from outside. <br />
Still we have to be careful when walking home since there are 12% left which not really agree. We avoided telling here that the team members SHOULD HAVE FUN doing their experiments (internal information). <br />
IGEM is not only about students, there are enough people involved in supervising the project and giving advices. The institutions where the projects are being carried out are usually aware of the workflow, aims and methods of these groups of experimenters.</i> </p><br />
</p> <B> Do you think the outcome is greater than the risks?</B> </p><br />
</p>-YES -NO</p><br />
</p> <i> 87% think yes. Some teams have already invented amazing things in the short time frame of the competition. Also the idea of having standardized parts improves the whole field and the related work of synthetic biology. Being completely free in the topic choosen also leads to ideas that are out of the box. Interestingly, also industry became aware of iGEM asking for inventive ideas solving industrial problems. </i> </p><br />
</p> <B> 9. Do you think that creation of bacterial based biosensors for testing isolated blood samples from humans for certain diseases is in contradiction with any known moral rules or is posing any significant risks? </B> </p><br />
</p>-YES -NO</p><br />
</p>If Yes, please list some of them</p><br />
</p> <i>97% answered NO (except 1 person who stated that the method is invasive). </i> </p><br />
</p> <i> As expected! if it was a YES, we would have sent our T-shirts to the Jamboree (they are nice!). </i>.</p><br />
</p> <B> 10. If such biosensor systems would be much more sensitive than some of the currently used detection techniques and could make a big difference to the efficiency of disease diagnosis, would you grant its massive use along with the already established detection methods (considering that it is a transgenic organism)? </B> </p><br />
</p></p><br />
</p> <i> 95% Yes. Straight way to thinking about a business </i> </p><br />
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</p> In conclusion, it is worth saying that the SensorBricks project cannot be in contradiction with any moral values, because it is a simple detection method, it is not posing any risks for the health of the patient as it is an in-vitro method performed with patient blood samples collected in advance. More than this it is designed to contribute to the efficiency of medical diagnosis procedures and has the perspectives for making the system cheaper and more available to benefit more people. <br />
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BIOTEC Dresden IGEM TEAM 2010.</p><br />
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{{Biotec_Dresden/Bottom}}</div>Mareike