Team:BIOTEC Dresden/Modeling

From 2010.igem.org

(Difference between revisions)
Line 7: Line 7:
<div id="content_prim">
<div id="content_prim">
   
   
-
                <p>Detection of cell surface cancer markers is a key diagnostic step during cancer therapy as it allows the efficiency of a therapy to be determined. Current antibody-based flow cytometric detection methods are the gold standard. For our 2010 iGEM project, we hope to develop SensorBricks as a reliable and modular system for antigen recognition, signal amplification and quantification. We want to push the boundaries of detection in order to allow earlier diagnosis and thus improve therapeutic prognosis in cancer therapy. Initial steps of SensorBricks will focus on the detection of CD33 and other leukemic markers to increase diagnostic stringency.</p>
+
<h3>Assumptions</h3>
-
                <p>There are three major components in SensorBricks: (i) monoclonal antibodies that bind to an antigen of interest, (ii) a LuxI-Protein A fusion construct which non-specifically binds antibodies and produces the autoinducer N-Acyl homoserine lactone (AHL), and (iii) a Escherichia coli based biosensor which in the presence of AHL strongly amplifies the production of green fluorescence protein (GFP). By coupling signal detection to a genetic circuit, we will be able to amplify the signal in a quantifiable manner, allowing the identification of cancer markers expressed in minute quantities. The presence of CD33+ cells in the blood of a patient will trigger the production of AHL, which in turn, activates the production of GFP in our E. coli biosensor. As such, we should be able to correlate the concentration of CD33 as a function of GFP fluorescence. </p>
+
<p> (1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.<p>
-
                <p>The modularity of SensorBricks is a key feature as it allows the same system and protocols to be used in combination with any antibody of choice to detect any antigen of interest.</p>
+
<p>(2) For simplicity decay of all products follows first-order kinetics. </p>
 +
<p> (3) All promoters have the same activity resulting in a constant transcription rate. </p>
 +
<p>(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs. </p>
 +
<p>(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.<p>
 +
<p>(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.</p>
 +
<p>(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.</p>
 +
 
 +
<h3>Constants</h3>
 +
 
 +
<table class="tformat" cellspacing="0" cellpadding="0">
 +
<tr class="odd">
 +
<th colspan="3">General Parameters</th>
 +
</tr>
 +
<tr class="even">
 +
<td>growth rate</td>
 +
<td>µ</td>
 +
<td>1.3 h<sup>-1</sup> </td>
 +
</tr>
 +
<tr class="odd">
 +
<td>Promoter Activity</td>
 +
<td>c</td>
 +
<td>0.01 mM/h</td>
 +
</tr>
 +
</tr>
 +
<tr class="even">
 +
<td>Plasmid copy number</td>
 +
<td>l</td>
 +
<td>25 </td>
 +
<td> </td>
 +
</tr>
 +
<tr class="odd">
 +
<th colspan="3">Degradation rates</th>
 +
</tr>
 +
<tr class="odd">
 +
<td>AHL decay rate</td>
 +
<td>AHL_kdec</td>
 +
<td>0.11 h</td>
 +
</tr>
 +
<tr class="even">
 +
<td>LuxR degradation rate</td>
 +
<td>LuxR_kdec</td>
 +
<td>0.11 h</td>
 +
</tr
 +
 
 +
<h3>Simplified Model</h3>
 +
<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>
 +
PICTURE OF SCHEME
 +
<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>
 +
FORMULA 1
 +
<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>
 +
FORMULA 2
 +
<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>
 +
FORMULA 3
 +
<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>
 +
FORMULA 4
 +
<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>
 +
 
 +
<h3>Results</h3>
 +
<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>
 +
 
 +
<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>   
 +
 
 +
<h3>Discussion</h3>
 +
<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>       
 +
<p></p>
             </div>
             </div>
      
      

Revision as of 20:31, 27 October 2010

Assumptions

(1) The cell growth of E.coli DH5α follow logistic growth kinetics with an assigned growth constant µ.

(2) For simplicity decay of all products follows first-order kinetics.

(3) All promoters have the same activity resulting in a constant transcription rate.

(4 ) The rate of translation is considered to be equal yet the degradation rate of proteins differs.

(5 )AHL transport is only restricted by diffusion through the cell membrane following the concentration gradient, AHLout > AHLin.

(6) Binding and dissociation constants of AHL and luxR are based on mass-action kinetics.

(7) The enzymatic activity of LuxI within the fusion protein is not decreased by the fusion event.

Constants

Simplified Model

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.

PICTURE OF SCHEME

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:

FORMULA 1

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).

FORMULA 2

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.

FORMULA 3

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.

FORMULA 4

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.

Results

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.

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.

Discussion

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.

Share to Twitter Share to Facebook Share to Orkut Stumble It Email This More...

Retrieved from "http://2010.igem.org/Team:BIOTEC_Dresden/Modeling"
General Parameters
growth rate µ 1.3 h-1
Promoter Activity c 0.01 mM/h
Plasmid copy number l 25
Degradation rates
AHL decay rate AHL_kdec 0.11 h
LuxR degradation rate LuxR_kdec 0.11 h