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=Constants for the Protein Display Model=
{| class="wikitable" style="text-align: center; width: 80%; height: 170px;" border="1"
|-
  ! Type of constant !! Derivation of value
|-
  | TEV Enzyme dynamics
  | Enzymatic Reaction:
<math>E+S\rightleftarrows ES \rightarrow E+P</math>
Derivation of these values is made in [[IGEM:Imperial/2010/Variables1 | Variables for Amplification Module Section]]
*<math>k_1 = rate constant for E + S \rightarrow ES = 10^8 M^{-1}s^{-1}</math>
*<math>k_2 = rate constant for E + S \leftarrow ES = 10^3 s^{-1}</math>
*<math>k_{cat} = rate constant for ES \rightarrow E + P = 0.16 \pm 0.01 s^{-1}</math>
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 [[IGEM:Imperial/2010/Variables1 | Variables for Amplification Module Section]]:
<math>k_{deg}= 0.000289s^{-1}</math>
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 <math>5*10^8CFU/ml</math> concentration of bacteria is used.
|-
| Production rate of surface protein
| It was found that each cell displays <math>2.4*10^5</math> peptides [http://onlinelibrary.wiley.com/doi/10.1111/j.1574-6968.2000.tb09188.x/pdf].
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 <math>4.13*10^{-8}mol/dm^3/s^1</math> 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: <math>D_{average} = 1.07*10^{-10}m^2/s</math>  - for a protein in agarose gel for pH=5.6 [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]
In the final model the following was used:
For protein in water: <math>D=10^{-10}m^2/s</math> [http://www.life.illinois.edu/crofts/bioph354/diffusion1.html]
|}
<html>
<html>
<h1>Constants for the Protein Display Model</h1>
<h1>Constants for the Protein Display Model</h1>
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     <td style="background-color:#FFCC66;height:100px;width:200 px;text-align:center;"><b>TEV Enzyme Dynamics</b>
     <td style="background-color:#FFCC66;height:100px;width:200 px;text-align:center;"><b>TEV Enzyme Dynamics</b>
     </td>
     </td>
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">Enzymatic Reaction: E+S <var>&harr;</var> ES <var>&rarr;</var> E+P
<br />
The derivation of these values is made in <a href="http://www.openwetware.org/wiki/IGEM:Imperial/2010/Variables1">Variables for Amplification Module Section</a>.
<ul>
<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>
<li>k<sub>2</sub> = rate constant for E + S <var>&larr;</var> ES = 10<sup>3</sup> s<sup>-1</sup>
<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>
</ul>
<br />
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.
 
     </td>
     </td>
</tr>
</tr>
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     <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Production Rate of Surface Proteins</b>
     <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Production Rate of Surface Proteins</b>
     </td>
     </td>
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">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>.
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.
<br />
The result 4.13x10<sup>-8</sup>mol/dm<sup>3</sup>/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.
     </td>
     </td>
</tr>
</tr>
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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>
     <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Degradation Rate of Surface Proteins (common for all)</b>
     </td>
     </td>
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">Assumption: To be approximated by cell division (dilution of media) as none of the proteins are involved in any active degradation pathways.
<br />
Derived in <a href="http://www.openwetware.org/wiki/IGEM:Imperial/2010/Variables1">Variables for Amplification Module Section</a>:
<br />
k<sub>deg</sub>= 0.000289s<sup>-1</sup>
<br />
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
 
     </td>
     </td>
</tr>
</tr>
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     <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Diffusion Coefficient of Proteins</b>
     <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Diffusion Coefficient of Proteins</b>
     </td>
     </td>
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">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>
<br />
In the final model the following was used:
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>
     </td>
     </td>
</tr>
</tr>
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     <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Control Volume</b>
     <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Control Volume</b>
     </td>
     </td>
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">
     <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">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.
     </td>
     </td>
</tr>
</tr>

Revision as of 03:43, 9 September 2010

<html> <h1>Constants for the Protein Display Model</h1> </html>

<html> <table width="1000px" border="0">

<tr> 

   <td style="background-color:#FFFF66;height:50px;width:200;text-align:center"><b>Type of Constant</b>
   </td>
   <td style="background-color:#FFFF99;height:50px;width:800;text-align:center"><b>Derivation of Value</b>
   </td>

</tr>

<tr> 

   <td style="background-color:#FFCC66;height:100px;width:200 px;text-align:center;"><b>TEV Enzyme Dynamics</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">Enzymatic Reaction: E+S <var>&harr;</var> ES <var>&rarr;</var> E+P

<br /> The derivation of these values is made in <a href="http://www.openwetware.org/wiki/IGEM:Imperial/2010/Variables1">Variables for Amplification Module Section</a>. <ul> <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> <li>k<sub>2</sub> = rate constant for E + S <var>&larr;</var> ES = 10<sup>3</sup> s<sup>-1</sup> <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> </ul> <br /> 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. 

   </td>

</tr>

<tr> 

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Production Rate of Surface Proteins</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">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>.

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. <br /> The result 4.13x10<sup>-8</sup>mol/dm<sup>3</sup>/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. 

   </td>

</tr>

<tr> 

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Degradation Rate of Surface Proteins (common for all)</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">Assumption: To be approximated by cell division (dilution of media) as none of the proteins are involved in any active degradation pathways.

<br /> Derived in <a href="http://www.openwetware.org/wiki/IGEM:Imperial/2010/Variables1">Variables for Amplification Module Section</a>: <br /> k<sub>deg</sub>= 0.000289s<sup>-1</sup> <br /> 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 

   </td>

</tr>

<tr> 

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Diffusion Coefficient of Proteins</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">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>

<br /> In the final model the following was used: 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> 

   </td>

</tr>

<tr> 

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Control Volume</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">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.
   </td>

</tr>

</table> </html>

<html> <h2>References</h2> <ol> <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> <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> <li>Crofts, A. (1996) Biophysics 345. [Online] Available from: http://www.life.illinois.edu/crofts/bioph354/diffusion1.html [Accessed 1st September 2010]</li> </ol> </html>

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