Difference between revisions of "IGEM:Imperial/2010/Variables1"

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(Constants for Modelling)
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Revision as of 04:38, 9 September 2010

<html> <h1>Constants for the Output Amplification Model</h1> </html>

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

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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;">Enzymatic Reaction: E+S <var>&harr;</var> ES <var>&rarr;</var> E+P

<br /> Let <ul> <li>k<sub>1</sub> = rate constant for E+S <var>&rarr;</var> ES <li>k<sub>2</sub> = rate constant for E+S <var>&larr;</var> ES</math> <li>k<sub>cat</sub> = rate constant for ES <var>&rarr;</var> E+P </ul> We know that K<sub>m</sub> = (k<sub>cat</sub> + k<sub>2</sub>)/k<sub>1</sub>

Assuming that k<sub>cat</sub> << k<sub>2</sub> << k<sub>1</sub>, we can rewrite K<sub>m</sub> <var>&asymp;</var> k<sub>2</sub>/k<sub>1</sub> <br /> From this paper <a href="http://peds.oxfordjournals.org/cgi/reprint/14/12/993">[1]</a> the constants for TEV can be found: <br /> For example, for wildtype TEV: K<sub>m</sub> = 0.061<var>&plusmn;</var>0.010mM and k<sub>cat</sub> = 0.16<var>&plusmn;</var>0.01s<sup>-1</sup> <br /> These values correspond with our assumption that k<sub>cat</sub> = 0.1 s<sup>-1</sup> and K<sub>m</sub> = 0.01 mM. <br /> Hence, we can estimate the following orders of magnitude for the rate constants: <br /> k<sub>1</sub> = 10<sup>8</sup>M<sup>-1</sup>s<sup>-1</sup> <br /> k<sub>2</sub> = 10<sup>3</sup>s<sup>-1</sup> <br /> Using these values should be a good approximation for our model.

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   <td style="background-color:#FFCC66;height:130px;width:200px;text-align:center;"><b>Degradation rate (common for all)</b>
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   <td style="background-color:#eeeeee;height:130px;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

Growth rate, gr (divisions/h): 0.53 <var>&le;</var> gr <var>&le;</var> 2.18 <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC235685/pdf/jbacter00326-0019.pdf">[2]</a> <br /> Hence on average, gr = 1.5 divisions per hour, which gives one division every 40mins <br /> To deduce degradation rate we use the following formula: <br /> <var>&tau;</var><sub>1/2</sub> = ln2/k, where <var>&tau;</var><sub>1/2</sub> = 0.667 hours and k = degradation rate <br /> k = ln2/<var>&tau;</var><sub>1/2</sub> = 0.000289s<sup>-1</sup>

   </td>

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<tr>

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Production rate (TEV and Dioxygenase)</b>
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   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">We had difficulties finding values of the production rate in the literature and we hope to be able to perform experiments to obtain those values (for TEV protease and catechol 2,3-dioxygenase). Before any values can be obtained from the Lab, we suggest very simplistic approach for estimating production rates.

<br /> We have found production rates for two arbitrary proteins in E.Coli. We want to get estimates of production rates by comparing the lengths of the proteins (number of amino-acids). <br /> As this approach is very vague, it is important to realise its limitations and inconsistencies: <ul> <li>Values are taken from E.Coli not B.sub.</li> <li>The two production rates are of the same value for quite different amino-acid number which indicates that protein folding is limiting the production rates.</li> </ul> LacY production = 100 molecules/min<a href="http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=100738&ver=0&hlid=29205">[3]</a> (417 Amino Acids<a href="http://www.uniprot.org/uniprot/P02920">[4]</a>) <br /> LacZ production = 100 molecules/min<a href="http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=100737&ver=0&hlid=29206">[5]</a> (1024 AA<a href="http://www.uniprot.org/uniprot/P00722">[6]</a>) <br /> Average production ≈ 100molecules/min 720 AA <br /> This gives us: TEV production ≈ 24 molecules/min = 0.40 molecules/s (3054 AA<a href="http://www.uniprot.org/uniprot/P04517">[7]</a>) <br /> As production rate needs to be expressed in concentration units per unit volume, the above number is converted to mols/s and divided by the cell volume: 2.3808x10<sup>-10</sup> mol/dm<sup>3</sup>/s <br /> C23D production ≈ 252 molecules/min = 4.2 molecules/s (285 AA<a href="http://www.uniprot.org/uniprot/P54721#section_x-ref">[8]</a>) → 2.4998x10<sup>-9</sup> mol/dm<sup>3</sup>/s <br /> We will treat these numbers as guiding us in terms of range of orders of magnitudes. We will try to run our models for variety of values and determine system’s limitations.

   </td>

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<tr>

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Kinetic Parameters of Dioxygenase</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">Initial velocity of the enzymatic reaction was investigated at pH 7.5 and 30 °C.

<br /> Wild type (used for our simulations): K<sub>m</sub> = 10 <var>&mu;</var>M; k<sub>cat</sub> = 52s<sup>-1</sup> <br /> Mutated type: K<sub>m</sub> = 40 <var>&mu;</var>M; k<sub>cat</sub> = 192s<sup>−1</sup> <br /> Consequently, the ratio of K<sub>m</sub>/k<sub>cat</sub> of the mutant (K<sub>m</sub>/k<sub>cat</sub> = 4.8) is slightly lower than the ratio of the wild type (K<sub>m</sub>/k<sub>cat</sub> = 5.2), indicating that the mutation has little effect on the catalytic efficiency <a href="http://www.springerlink.com/content/e3718758m5052214/fulltext.pdf">[9]</a>.

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   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Dimensions of B.sub cell</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">Dimensions of B.sub (cylinder/rod shape) in rich media:

<br /> diameter: d = 0.87<var>&mu;</var>m; length: l = 4.7<var>&mu;</var>m <br /> This gives: Volume= <var>&pi;</var>d<sup>2</sup>l/4 = 2.793999<var>&mu;</var>m<sup>3</sup> <var>&asymp;</var> 2.79x10<sup>-15</sup> dm<sup>3</sup>

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<tr>

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Production Rate of split TEV</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">Assuming that both parts of split TEV are half the size of the whole TEV (3054/2=1527 AA).

<br /> The length of the coil is 90 AA. <br /> The whole construct is then: 1617 AA <br /> Therefore, split TEV production rate ≈ 1.2606x10<sup>-10</sup> mol/dm<sup>3</sup>/s

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<tr>

   <td style="background-color:#FFCC66;height:100px;width:200px;text-align:center;"><b>Relevant concentrations of Catechol</b>
   </td>
   <td style="background-color:#eeeeee;height:100px;width:800px;text-align:center;">We have catechol in the lab in powder form so we are only limited by it's solubility.

<br /> For a concentration of 0.1 M with built up levels of dioxygenase the colour change happens within seconds. <br /> We will run our models for 0.1M ± several orders of magnitude to determine the smallest catechol concentration that will give a significant difference between the simple production response and the amplified response.

   </td>

</tr> </table> </html>

<html> <h2>References</h2> <ol> <li>Kapust, R. et al (2001) Tobacco etch virus protease: mechanism of autolysis and rational design of stable mutants with wild-type catalytic proficiency. Protein Engineering. [Online] 14(12), 993-1000. Available from: http://peds.oxfordjournals.org/content/14/12/993.full.pdf+html [Accessed 20th August 2010]</li> <li>Sargent, M. (1975) Control of Cell Length in Bacillus subtilis. Journal of Bacteriology. [Online] 123(1), 7-19. Available from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC235685/pdf/jbacter00326-0019.pdf [Accessed 20th August 2010]</li> <li>Milo, R., Jorgensen, P. & Springer, M. (2007) BioNumbers. [Online] Available from: http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=100738&ver=0&hlid=29205 [Accesed 25th August 2010]</li> <li>UniProt Consortium (2002-2010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P02920 [Accessed 24th August 2010]</li> <li>Milo, R., Jorgensen, P. & Springer, M. (2007) BioNumbers. [Online] Available from: http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=100737&ver=0&hlid=29206 [Accesed 25th August 2010]</li> <li>UniProt Consortium (2002-2010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P00722 [Accessed 24th August 2010]</li> <li>UniProt Consortium (2002-2010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P04517 [Accessed 24th August 2010]</li> <li>UniProt Consortium (2002-2010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P54721#section_x-ref [Accessed 24th August 2010]</li> <li>Wei, J. et al (2009) Rational Design of Catechol-2, 3-dioxygenase for Improving the Enzyme Characteristics. Appl Biochem Biotechnol. [Online] 162, 116-126. Available from: http://www.springerlink.com/content/e3718758m5052214/fulltext.pdf [Accessed 25th August 2010]</li> </ol> </html>