IGEM:Imperial/2010/Variables2

Constants for the Protein Display Model

Type of constant	Derivation of value
TEV Enzyme dynamics	Enzymatic Reaction: [math]\displaystyle{ E+S\rightleftarrows ES \rightarrow E+P }[/math] Derivation of these values is made in Variables for Amplification Module Section [math]\displaystyle{ k_1 = rate constant for E + S \rightarrow ES = 10^8 M^{-1}s^{-1} }[/math] [math]\displaystyle{ k_2 = rate constant for E + S \leftarrow ES = 10^3 s^{-1} }[/math] [math]\displaystyle{ 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 Variables for Amplification Module Section: [math]\displaystyle{ 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]\displaystyle{ 5*10^8CFU/ml }[/math] concentration of bacteria is used.
Production rate of surface protein	It was found that each cell displays [math]\displaystyle{ 2.4*10^5 }[/math] peptides (Reference for protein production (Page 4, Paragraph 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 [math]\displaystyle{ 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]\displaystyle{ D_{average} = 1.07*10^{-10}m^2/s }[/math] - for a protein in agarose gel for pH=5.6 according to paper In the final model the following was used: For protein in water: [math]\displaystyle{ D=10^{-10}m^2/s }[/math] reference