IGEM:Imperial/2010/Protein Display

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<h1>Receptor and Surface protein model</h1>
<h1>Receptor and Surface protein model</h1>
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The aim of this model is to determine the concentration of Schistosoma elastase or TEV protease that should be added to the bacteria to trigger the response. It is also attempted to determine how long it will take for the protease or elastase to cleave enough peptides.
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<br /><br />
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Cleavage of protein is an enzymatic reaction, which can be written as:
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<ul>
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<li>E+S <var>&harr;</var> ES <var>&rarr;</var> E+P</li>
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<li>Substrate (S) = Protein</li>
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<li>Enzyme (E) = TEV (Protease)</li>
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<li>Product (P) = Peptide</li>
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</ul><br />
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This can be modelled in a very similar way to the 1-step amplification model, however, all the constants and initial concentrations will be different.
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<br />
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[TEV](t=0) - initial concentration of TEV will be arbitrarily chosen. However, ultimately we would need to measure the concentration of elastase that schistosoma releases.
<h2>Threshold concentration of peptide (20/08/2010)</h2>
<h2>Threshold concentration of peptide (20/08/2010)</h2>
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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 concntration of peptide to give a detectable activation is 0.5ng/ml.
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<br />
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We want to know how long it takes until the threshold is reached:
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<ul>
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<li>The mass of a peptide is 2.24kDa = 3.7184x10<sup>-21</sup>g.</li>
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<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>.</li>
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<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>
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<li>The threshold for minimal activation of receptor is 2.2329x10<sup>-10</sup> mol/L.</li>
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</ul>
<h2>Protein production in B.sub (23/08/2010)</h2>
<h2>Protein production in B.sub (23/08/2010)</h2>

Revision as of 11:24, 9 September 2010

Receptor and Surface protein model

The aim of this model is to determine the concentration of Schistosoma elastase or TEV protease that should be added to the bacteria to trigger the response. It is also attempted to determine how long it will take for the protease or elastase to cleave enough peptides.

Cleavage of protein is an enzymatic reaction, which can be written as:
  • E+S ES E+P
  • Substrate (S) = Protein
  • Enzyme (E) = TEV (Protease)
  • Product (P) = Peptide

This can be modelled in a very similar way to the 1-step amplification model, however, all the constants and initial concentrations will be different.
[TEV](t=0) - initial concentration of TEV will be arbitrarily chosen. However, ultimately we would need to measure the concentration of elastase that schistosoma releases.

Threshold concentration of peptide (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 concntration of peptide to give a detectable activation is 0.5ng/ml.
We want to know how long it takes until the threshold is reached:
  • The mass of a peptide is 2.24kDa = 3.7184x10-21g.
  • The number of molecules in one ml is 10ng/3.7184x10-21g = 2.6893x1012. In a litre, the number of molecules is 2.6893x1015.
  • Dividing this value by Avogadro's constant gives the threshold concentration of cth=4.4658x10^-9 mol/L.
  • The threshold for minimal activation of receptor is 2.2329x10-10 mol/L.

Protein production in B.sub (23/08/2010)

Control volume initial choice (23/08/2010)

Protein production in Control Volume (23/08/2010)

Control volume final choice (23/08/2010)

Using CFU to estimate the spacing between cells (24/08/2010)

Choice of Control Volume allows simplifications (24/08/2010)

Matlab Simulation (24/08/2010)

Sensitivity of our model (24/08/2010)

  • Changing initial concentration of TEV

  • Whether the threshold concentration of AIP is reached is highly dependent on the initial concentration of TEV. The smallest initial concentration of TEV, [TEV>], for which the threshold is reached is 6.0x10-6mol/dm3. On the grap below it can be seen that the optimal [TEV]0 is a concentration higher than 10-4mol/dm3, which corresponds to the threshold being reached within 1.5 minutes.
    Graph showing when threshold AIP concentration is reached (for different initial TEV concentrations). Notice log-log scale.
  • Changing the production rate

  • One order of magnitude change in the production rate results in at least 50s delay of the AIP concentration reaching the threshold concentration.
  • Changing production rate

  • 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.
  • Changing control volume

  • 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

  1. Havarstein, L., Coomaraswamy, G. & Morrison, D. (1995) An unmodified heptadecapeptide pheromone induces competence for genetic transformation in Streptococcus pneumoniae. Proc. Natl. [Online] 92, 11140-11144. Available from: http://ukpmc.ac.uk/backend/ptpmcrender.cgi?accid=PMC40587&blobtype=pdf [Accessed 27th August 2010]
  2. Kobayashi, G. et al (2000) Accumulation of an artificial cell wall-binding lipase by Bacillus subtilis wprA and/or sigD mutants. FEMS Microbiology Letters. [Online] 188(2000), 165-169. Available from: http://onlinelibrary.wiley.com/doi/10.1111/j.1574-6968.2000.tb09188.x/pdf [Accessed 27th August 2010]
  3. Gutenwik, J., Nilsson, B. & Axelsson, A. (2003) Determination of protein diffusion coefficients in agarose gel with a diffusion cell. Biochemical Engineering Journal. [Online] 19(2004), 1-7. Available from: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V5N-4B3MXDC-2-K&_cdi=5791&_user=217827&_pii=S1369703X03002377&_origin=search&_coverDate=07%2F01%2F2004&_sk=999809998&view=c&wchp=dGLzVtb-zSkzS&md5=c17d0e7320f03931006f9b1a10a438b9&ie=/sdarticle.pdf [Accessed August 20th 2010]
  4. Imperial College London (2008) Biofabricator Subtilis - Designer Genes. [Online] Available from: http://2008.igem.org/Imperial_College/18_September_2008 [Accessed 1st September 2010]
  5. Knutsen, E., Ween, O. & Havarstein, L. (2003) Two Separate Quorum-Sensing Systems Upregulate Transcription of the Same ABC Transporter in Streptococcus pneumoniae. Journal of Bacteriology. [Online] 186(10), 3078-3085. Available from: http://jb.asm.org/cgi/reprint/186/10/3078 [Accessed 1st September 2010]

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