Team:Imperial College London/Modelling/Protein Display
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Motivation for developing that model came from the design process. The idea of having surface protein that could be cleaved and then activate the receptor was very innovatory. However, with this new approach came questions that could not be easily answered. Hence, the following aims were specified: | Motivation for developing that model came from the design process. The idea of having surface protein that could be cleaved and then activate the receptor was very innovatory. However, with this new approach came questions that could not be easily answered. Hence, the following aims were specified: | ||
<ol> | <ol> | ||
- | <li>Determine the concentration of Schistosoma elastase or TEV protease that should be added to bacteria to trigger the response.</li> | + | <li>Determine the concentration of Schistosoma elastase or TEV protease that should be added to bacteria to trigger the response. That was supposed to allow us to correlate required concentration for the activation with the concentration of Schistosoma elastase in the water.</li> |
<li>Attempt modelling how long it takes for the protease or elastase to cleave enough peptides.</li> | <li>Attempt modelling how long it takes for the protease or elastase to cleave enough peptides.</li> | ||
<li>Assess the risk of false positives (system getting activated without the required stimulus).</li> | <li>Assess the risk of false positives (system getting activated without the required stimulus).</li> | ||
</ol> | </ol> | ||
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</div> | </div> | ||
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<div class="accordionButton">Detailed Description</div> | <div class="accordionButton">Detailed Description</div> | ||
<div class="accordionContent"> | <div class="accordionContent"> | ||
- | This model consists of | + | This model consists of 5 parts that had to be researched or developed: |
<ol> | <ol> | ||
- | <li>Identification of | + | <li>Identification of all active and relevant elements of the isolated part of the system.</li> |
+ | <li>Identification of interactions between the identified elements.</li> | ||
<li>Identification of threshold concentration of auto inducing peptide (AIP) needed for activation of receptor</li> | <li>Identification of threshold concentration of auto inducing peptide (AIP) needed for activation of receptor</li> | ||
<li>Defining control volume around the bacterial cell (surface protein after being cleaved will be floating in the extracellular environment).</li> | <li>Defining control volume around the bacterial cell (surface protein after being cleaved will be floating in the extracellular environment).</li> | ||
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</ol> | </ol> | ||
- | + | <h2>1. Elements of the system</h2> | |
+ | <ol> | ||
+ | <li>Surface protein that consists of cell wall binding domain, linker, AIP (Auto Inducing Peptide). It is being expressed by constitutive gene expression. It was assumed that bacteria would be fully grown before carrying out the detection so the cell wall would be covered with as many surface proteins as the cell can maintain.</li> | ||
+ | <li>Schistosoma elastase (enzyme released by the parasite) cleaves AIP from cell wall binding domain at the linker site. In laboratory we used TEV protease as we could not get handle of Schistosoma elastase, so the model was adjusted appropriately (TEV enzyme kinetic parameters were used).</li> | ||
+ | <li>ComD receptor is being activated by high enough AIP concentration. Once activated, ComD signals into the cell to activate the colour response.</li> | ||
+ | </ol> | ||
+ | |||
+ | <h2>2. Interactions between elements </h2> | ||
+ | Apart from proteins being expressed from genes, there was only one chemical reaction identified in this part of the system. It is cleavage of protein which is an enzymatic reaction: | ||
<ul> | <ul> | ||
<li>E+S <var>↔</var> ES <var>→</var> E+P</li> | <li>E+S <var>↔</var> ES <var>→</var> E+P</li> | ||
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<li>Product (P) = Peptide</li> | <li>Product (P) = Peptide</li> | ||
</ul><br /> | </ul><br /> | ||
- | This | + | This results in 4 partial differential equations (PDEs), which is of similar form as the 1-step amplification model. However, most of the constants and initial concentrations are different. For detailed description and derivation of PDEs, please refer to <a href="https://2010.igem.org/Team:Imperial_College_London/Modelling/Output">"Detailed Description"</a> part of Modelling Output.<br /> |
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- | <h2>Threshold concentration of | + | <h2>3. Threshold concentration of AIP (20/08/2010)</h2> |
- | The optimal peptide concentration required to activate ComD is 10 ng/ml <a href="http://ukpmc.ac.uk/backend/ptpmcrender.cgi?accid=PMC40587&blobtype=pdf">[1]</a>. This is the threshold value for ComD activation. However, the minimum | + | The optimal peptide concentration required to activate ComD is 10 ng/ml <a href="http://ukpmc.ac.uk/backend/ptpmcrender.cgi?accid=PMC40587&blobtype=pdf">[1]</a>. This is the threshold value for ComD activation. However, the minimum concentration of peptide to give a detectable activation is 0.5ng/ml. |
<br /> | <br /> | ||
- | + | The threshold for minimal activation of receptor is c<sub>th</sub>=4.4658x10<sup>-9</sup> mol/L. Click on the button below to uncover the calculations. | |
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+ | <div id="wrapper"> | ||
+ | <div class="accordionButton">Converting 10 ng/ml to 4.4658x10<sup>-9</sup> mol/L</div> | ||
+ | <div class="accordionContent"> | ||
+ | <ul> | ||
+ | <li>The mass of a peptide is 2.24kDa = 3.7184x10<sup>-21</sup>g.</li> | ||
+ | <li>The number of molecules in one ml is 10ng/3.7184x10<sup>-21</sup>g = 2.6893x10<sup>12</sup>. In a litre, the number of molecules is 2.6893x10<sup>15</sup>molecules/ml.</li> | ||
+ | <li>Dividing this value by Avogadro's constant gives the threshold concentration of c<sub>th</sub>=4.4658x10<sup>-9</sup> mol/L.</li> | ||
+ | <li>The threshold for minimal activation of receptor is 2.2329x10<sup>-10</sup> mol/L.</li> | ||
+ | </ul> | ||
+ | </div> | ||
+ | </div> | ||
+ | <br/><br/> | ||
<h2>Protein production in B.sub (23/08/2010)</h2> | <h2>Protein production in B.sub (23/08/2010)</h2> | ||
<ul> | <ul> |
Revision as of 21:19, 13 October 2010
Surface Protein Model | ||||||||||||||||||||||||||
Objectives
Motivation for developing that model came from the design process. The idea of having surface protein that could be cleaved and then activate the receptor was very innovatory. However, with this new approach came questions that could not be easily answered. Hence, the following aims were specified:
Detailed Description
This model consists of 5 parts that had to be researched or developed:
1. Elements of the system
2. Interactions between elementsApart from proteins being expressed from genes, there was only one chemical reaction identified in this part of the system. It is cleavage of protein which is an enzymatic reaction:
This results in 4 partial differential equations (PDEs), which is of similar form as the 1-step amplification model. However, most of the constants and initial concentrations are different. For detailed description and derivation of PDEs, please refer to "Detailed Description" part of Modelling Output. 3. Threshold concentration of AIP (20/08/2010)The optimal peptide concentration required to activate ComD is 10 ng/ml [1]. This is the threshold value for ComD activation. However, the minimum concentration of peptide to give a detectable activation is 0.5ng/ml.The threshold for minimal activation of receptor is cth=4.4658x10-9 mol/L. Click on the button below to uncover the calculations. Converting 10 ng/ml to 4.4658x10-9 mol/L
Protein production in B.sub (23/08/2010)
Hence, we can deduce that the concentration that the protein expression will tend to: c = 1.4289x10-4 mol/dm3 = cfinal. Therefore, we can model the protein production by transcription and translation and adjust the production constant so the concentration value will tend towards cfinal. Using a similar model to the simple production of Dioxygenase for the Output Amplification Model (Model preA), we obtain the following graph:
Control volume initial choice (23/08/2010)All enzymatic reactions that we have modelled so far were confined whithin the bacterial cell. However, this case is different because the molecules are not confined by the bacterial membrane and can diffuse out of the cell.The control volume: The inner boundary is determined by the bacterial cell (proteins after being displayed and cleaved cannot diffuse back into bacterium). The outer boundary is more time scale dependent. We have assumed that after mass cleavage of the display-proteins by TEV, many of these AIPs will bind to the receptors quite quickly (eg. 8 seconds). Our volume is determined by the distance that AIPs could travel outwards by diffusion within that short time. In this way, we are sure that the concentration of AIPs outside our control volume after a given time is approximately 0. This approach is not very accurate and can lead us to false negative conclusions (as in reality there will be a concentration gradient, with highest conentration on the cell wall).
Protein production in Control Volume (23/08/2010)The previously determined constants of protein production in B.sub to obtain the concentration of proteins are not valid in the Control Volume. It has to be adjusted (multiplied) by the following factor:factor=Vbacillus/VCV = 5.7974x10-6 (for the particular numbers presented above) Control volume final choice (23/08/2010)We realized that our initial choice of control volume was not accurate because this assumption was treating bacteria as the medium. However, in reality bacteria live in colonies very close to each other. They are much closer to each other than the diffusion distance (1.9596x10−5m) derived above even if placed in water solution.Using CFU to estimate the spacing between cells (24/08/2010)CFU stands for Colony-forming unit. It is a measure of bacterial numbers. For liquids, CFU is measured per ml. Since we already have data of CFU/ml from the Imperial iGEM 2008, this is an easy way to estimate the number of cells in a given volume using a spectrometer at 600nm wavelength. The graph below is taken from the Imperial iGEM 2008 Wiki page [4].
Choice of Control Volume allows simplifications (24/08/2010)
Matlab Simulation (24/08/2010)Here is the Matlab code for the Matlab simulation
Sensitivity of our model (24/08/2010)
Whether the threshold concentration of AIP is reached is highly dependent on the initial concentration of TEV. The smallest initial concentration of TEV, [TEV>]
One order of magnitude change in the production rate results in at least 50s delay of the AIP concentration reaching the threshold concentration. Changing the production rate influences the time duration of the AIP concentration above the threshold level. The higher it is, the shorter the receptor will be activated (at extreme values, AIP concentration does not reach the threshold). However, the production rate has not much influence on how fast the threshold will be reached. Our model is extremely sensitive to this factor. One order of magnitude change in CV results in several orders of magnitude change in AIP concentration. Hence, special care should be taken in determination of this value. If the model is to be compared with the experimental results, the CFU/ml has to be the same as the one used in the model. Otherwise, the CV has to be readjusted. Risk of False positives (31/08/2010)It was pointed out that we should assess the risk of false positive activation of the receptor. We are particularly concerned about the display protein not binding to the cell wall, but instead diffusing into the extra-cellular environment. In order to be able to assess the risk of false positives, we need to do further research into the affinity of AIP with attached linker and transmembrane proteins for the receptor as compared to the affinity of the AIP itself for the receptor.This paper [5] might have some information on affinity comparison. We need to know how proteins are being transported from intracellular to transmembrane space. Understanding this concept could give us an idea of what could go wrong. References
Parameters & Constants
Constants for the Protein Display Model
References
Results & Conclusions
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