IGEM:Imperial/2010/Variables2

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==References==
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#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]
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#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]
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<h1>Constants for the Protein Display Model</h1>
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#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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<table width="1000px" border="0">
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    <td style="background-color:#FFFF66;height:50px;width:200;text-align:center"><b>Type of Constant</b>
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    </td>
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    <td style="background-color:#FFFF99;height:50px;width:800;text-align:center"><b>Derivation of Value</b>
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    <td style="background-color:#FFCC66;height:100px;width:200 px;text-align:center;"><b>TEV Enzyme Dynamics</b>
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    <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
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    <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Production Rate of Surface Proteins</b>
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    <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
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    <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Degradation Rate of Surface Proteins (common for all)</b>
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    </td>
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    <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
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    </td>
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</tr>
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    <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Diffusion Coefficient of Proteins</b>
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    </td>
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    <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
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    <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Control Volume</b>
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    </td>
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    <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
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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 06:04, 9 September 2010

Constants for the Protein Display Model

Type of constant Derivation of value
TEV Enzyme dynamics Enzymatic Reaction:

E+S\rightleftarrows ES \rightarrow E+P

Derivation of these values is made in Variables for Amplification Module Section

  • k_1 = rate constant for E + S \rightarrow ES = 10^8 M^{-1}s^{-1}
  • k_2 = rate constant for E + S \leftarrow ES = 10^3 s^{-1}
  • k_{cat} = rate constant for ES \rightarrow E + P = 0.16 \pm 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.

Degradation rate of surface protein

(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

Derived in Variables for Amplification Module Section: kdeg = 0.000289s − 1

For all proteins that are outside of cells or the timescale that is short enough to neglect cell division effect: k_deg=0

Control volume Control volume seems to be the weakest point of this model. We have tried to rationalise it as much as we could. However, error seems to be unavoidable. It is important to realise that the Control Volume needs to be adjusted if different than 5 * 108CFU / ml concentration of bacteria is used.
Production rate of surface protein It was found that each cell displays 2.4 * 105 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 didn't have a clue about, that value was manipulated.

The resulting 4.13 * 10 − 8mol / dm3 / s1 seemed to be of the probable order of magnitude, so we kept it. Ideally, we would like to get this value measured as it is resulting from really vague estimate.

Diffusion coefficient of protein

We have found to references which quote very similar values for very different media.

For protein in agarose gel: Daverage = 1.07 * 10 − 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]


Constants for the Protein Display Model

Type of Constant Derivation of Value
TEV Enzyme Dynamics
Production Rate of Surface Proteins
Degradation Rate of Surface Proteins (common for all)
Diffusion Coefficient of Proteins
Control Volume

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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