Team:Imperial College London/Modelling/Protein Display/Parameters and Constants

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|style="font-family: helvetica, arial, sans-serif;font-size:2em;color:#ea8828;"|Surface Protein Model
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<h2>Parameters & Constants</h2>
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<table width="775px" border="0">
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    <td style="background-color:#FFFF66;height:50px;width:75;text-align:center;font-family: helvetica, arial, sans-serif;color:#555555;"><b>Type of Constant</b>
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    <td style="background-color:#FFFF99;height:50px;width:700;text-align:center;font-family: helvetica, arial, sans-serif;color:#555555;"><b>Derivation of Value</b>
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    <td style="background-color:#FFCC66;height:100px;text-align:center; font-family: helvetica, arial, sans-serif;color:#555555;"><b>TEV Enzyme Dynamics</b>
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    <td style="background-color:#e7e7e7;height:100px;text-align:center;font-family: helvetica, arial, sans-serif;color:#555555;">Enzymatic Reaction: E+S <var>&harr;</var> ES <var>&rarr;</var> E+P
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<br />
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<ul>
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<li>k<sub>1</sub> = rate constant for E + S <var>&rarr;</var> ES = 10<sup>8</sup> M<sup>-1</sup>s<sup>-1</sup>
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<li>k<sub>2</sub> = rate constant for E + S <var>&larr;</var> ES = 10<sup>3</sup> s<sup>-1</sup>
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<li>k<sub>cat</sub> = rate constant for ES <var>&rarr;</var> E + P = 0.16 <var>&plusmn;</var> 0.01 s<sup>-1</sup>
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</ul>
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<br />
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We are assuming the same cleaving rates of TEV as on other substrates. However, we are planning to measure them to gain more confidence in the model.
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    <td style="background-color:#FFCC66;height:100px;text-align:center; font-family: helvetica, arial, sans-serif;color:#555555;"><b>Production Rate of Surface Proteins</b>
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    <td style="background-color:#e7e7e7;height:100px;text-align:center;font-family: helvetica, arial, sans-serif;color:#555555;">It was found that each cell displays 2.4x10<sup>5</sup> peptides <a href="http://onlinelibrary.wiley.com/doi/10.1111/j.1574-6968.2000.tb09188.x/pdf">[1]</a>.
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Hence, we adjusted our simple production of display protein model to converge to that value. As production rate was the constant that we could not obtain, that value was manipulated.
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<br />
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The result 4.13x10<sup>-8</sup>mol/dm<sup>3</sup>/s seemed to be of reasonable order of magnitude.
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Ideally, we would like to get this value measured as it is resulting from a very vague estimate.
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    <td style="background-color:#FFCC66;height:100px;text-align:center; font-family: helvetica, arial, sans-serif;color:#555555;"><b>Degradation Rate of Surface Proteins (common for all)</b>
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    <td style="background-color:#e7e7e7;height:100px;text-align:center;font-family: helvetica, arial, sans-serif;color:#555555;">Assumption: To be approximated by cell division (dilution of media) as none of the proteins are involved in any active degradation pathways.
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<br />
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k<sub>deg</sub>= 0.000289s<sup>-1</sup>
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<br />
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For all proteins that are outside of cells or the timescale that is short enough to neglect cell division effect: k<sub>deg</sub>=0
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    <td style="background-color:#FFCC66;height:100px;text-align:center; font-family: helvetica, arial, sans-serif;color:#555555;"><b>Diffusion Coefficient of Proteins</b>
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    </td>
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    <td style="background-color:#e7e7e7;height:100px;text-align:center;font-family: helvetica, arial, sans-serif;color:#555555;">We have found two references which quote very similar values for very different media.<br />For protein in agarose gel: D<sub>average</sub> = 1.07x10<sup>-10</sup>m<sup>2</sup>/s - for a protein in agarose gel for pH=5.6 <a href="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">[2]</a>
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<br />
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In the final model the following was used:
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For protein in water: D=10<sup>-10</sup>m<sup>2</sup>/s <a href="http://www.life.illinois.edu/crofts/bioph354/diffusion1.html">[3]</a>
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    <td style="background-color:#FFCC66;height:100px;text-align:center; font-family: helvetica, arial, sans-serif;color:#555555;"><b>Control Volume</b>
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    </td>
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    <td style="background-color:#e7e7e7;height:100px;text-align:center;font-family: helvetica, arial, sans-serif;color:#555555;">The control volume seems to be the weakest point of this model. We have tried to rationalise it as much as we could. However, errors seem to be unavoidable. It is important to realise that the Control Volume needs to be adjusted if a bacterial concentration different than 5x10<sup>8</sup>CFU/ml is used.
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<h2>References</h2>
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<ol>
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<li>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]</li>
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<li>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]</li>
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<li>Crofts, A. (1996) Biophysics 345. [Online] Available from: http://www.life.illinois.edu/crofts/bioph354/diffusion1.html [Accessed 1st September 2010]</li>
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</ol>
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Revision as of 19:20, 17 October 2010

Temporary sub-menu:

Objectives; Detailed Description; Parameters & Constants; Results & Conclusion;Download MatLab Files;

Surface Protein Model

Parameters & Constants

Type of Constant Derivation of Value
TEV Enzyme Dynamics Enzymatic Reaction: E+S ↔ ES → E+P
  • k1 = rate constant for E + S → ES = 108 M-1s-1
  • k2 = rate constant for E + S ← ES = 103 s-1
  • kcat = rate constant for ES → E + P = 0.16 ± 0.01 s-1

We are assuming the same cleaving rates of TEV as on other substrates. However, we are planning to measure them to gain more confidence in the model.
Production Rate of Surface Proteins It was found that each cell displays 2.4x105 peptides [1]. Hence, we adjusted our simple production of display protein model to converge to that value. As production rate was the constant that we could not obtain, that value was manipulated.
The result 4.13x10-8mol/dm3/s seemed to be of reasonable order of magnitude. Ideally, we would like to get this value measured as it is resulting from a very vague estimate.
Degradation Rate of Surface Proteins (common for all) Assumption: To be approximated by cell division (dilution of media) as none of the proteins are involved in any active degradation pathways.
kdeg= 0.000289s-1
For all proteins that are outside of cells or the timescale that is short enough to neglect cell division effect: kdeg=0
Diffusion Coefficient of Proteins We have found two references which quote very similar values for very different media.
For protein in agarose gel: Daverage = 1.07x10-10m2/s - for a protein in agarose gel for pH=5.6 [2]
In the final model the following was used: For protein in water: D=10-10m2/s [3]
Control Volume The control volume seems to be the weakest point of this model. We have tried to rationalise it as much as we could. However, errors seem to be unavoidable. It is important to realise that the Control Volume needs to be adjusted if a bacterial concentration different than 5x108CFU/ml is used.

References

  1. 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]
  2. 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]
  3. Crofts, A. (1996) Biophysics 345. [Online] Available from: http://www.life.illinois.edu/crofts/bioph354/diffusion1.html [Accessed 1st September 2010]

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