IGEM:Imperial/2010/Variables1
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  +  <h2>References</h2>  
  +  <ol>  
  +  <li>Kapust, R. et al (2001) Tobacco etch virus protease: mechanism of autolysis and rational design of stable mutants with wildtype catalytic proficiency. Protein Engineering. [Online] 14(12), 9931000. 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), 719. Available from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC235685/pdf/jbacter003260019.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 (20022010) 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 (20022010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P00722 [Accessed 24th August 2010]</li>  
  +  <li>UniProt Consortium (20022010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P04517 [Accessed 24th August 2010]</li>  
+  <li>UniProt Consortium (20022010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P54721#section_xref [Accessed 24th August 2010]</li>  
+  <li>Wei, J. et al (2009) Rational Design of Catechol2, 3dioxygenase for Improving the Enzyme Characteristics. Appl Biochem Biotechnol. [Online] 162, 116126. Available from: http://www.springerlink.com/content/e3718758m5052214/fulltext.pdf [Accessed 25th August 2010]</li>  
+  </ol>  
+  </html> 
Revision as of 05:56, 9 September 2010
Constants for Modelling
Type of constant  Derivation of value 

TEV Enzyme dynamics  Enzymatic Reaction:
Let
We know that Assuming that k_{cat} < < k_{2} < < k_{1}, we can rewrite K_{m}≈k_{2} / k_{1} From this paper [1] the constants for TEV can be found:
These values correspond with our assumption that k_{cat} = 0.1s^{ − 1} and K_{m} = 0.01mM. Hence, we can estimate the following orders of magnitude for the rate constants:
Using these values should be a good approximation for our model. 
Degradation rate
(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
Growth rate, gr (divisions/h): 0.53<gr<2.18 [2] Hence on average, gr = 1.5 divisions per hour => 1 division every 40mins To deduce degradation rate use the following formula:
Where k...the degradation rate

Production rate
(TEV and dioxygenase) 
We had real trouble finding the production rate values in the literature and we hope to be able to perform experiments to obtain those values for (TEV protease and catechol 2,3dioxygenase). The experiments will not be possible to be carried out soon, so for the time being we suggest very simplistic approach for estimating production rates. 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 aminoacids). As this approach is very vague, it is important to realise its limitations and inconsistencies:
LacZ production = 100 molecules/min[5] (1024 AA[6]) Average production ≈ 100molecules/min 720 AA That gives us:
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 → 2.3808 * 10^{ − 10}mol / dm^{3} / s
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. 
Kinetic parameters
of dioxygenase 
Initial velocity of the enzymatic reaction was investigated at pH 7.5 and 30 °C.
K_{m} = 10μM k_{cat} = 52s^{ − 1}
K_{m} = 40μM k_{cat} = 192s^{1} Consequently, the of the mutant was slightly lower than of the wild type, indicating that the mutation has little effect on catalytic efficiency[9]. 
Dimensions of
Bacillus subtillis cell 
Dimensions of Basillus subtilis (cylinder/rod shape) in reach media (ref. bionumbers):
This gives: 
Split TEV
production rates 
The whole construct is then: 1617 AA → split TEV production rate ≈ 1.2606 * 10^{ − 10}mol / dm^{3} / s 
Relevant concentrations of catechol  We have catechol in the lab in powder form so we're limited only by catechol's solubility.
For concentration of 0.1 M with built up levels of dioxygenase the colour change happens within seconds! We will run our models for 0.1M ± several orders of magnitude to determine the smallest catechol concentration that will give appreciable difference between simple production response and the amplified response. 
References
 Kapust, R. et al (2001) Tobacco etch virus protease: mechanism of autolysis and rational design of stable mutants with wildtype catalytic proficiency. Protein Engineering. [Online] 14(12), 9931000. Available from: http://peds.oxfordjournals.org/content/14/12/993.full.pdf+html [Accessed 20th August 2010]
 Sargent, M. (1975) Control of Cell Length in Bacillus subtilis. Journal of Bacteriology. [Online] 123(1), 719. Available from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC235685/pdf/jbacter003260019.pdf [Accessed 20th August 2010]
 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]
 UniProt Consortium (20022010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P02920 [Accessed 24th August 2010]
 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]
 UniProt Consortium (20022010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P00722 [Accessed 24th August 2010]
 UniProt Consortium (20022010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P04517 [Accessed 24th August 2010]
 UniProt Consortium (20022010) UniProt. [Online] Available from: http://www.uniprot.org/uniprot/P54721#section_xref [Accessed 24th August 2010]
 Wei, J. et al (2009) Rational Design of Catechol2, 3dioxygenase for Improving the Enzyme Characteristics. Appl Biochem Biotechnol. [Online] 162, 116126. Available from: http://www.springerlink.com/content/e3718758m5052214/fulltext.pdf [Accessed 25th August 2010]