# Team:Imperial College London/Modelling/Protein Display/Parameters and Constants

 Modelling Overview | Detection Model | Signaling Model | Fast Response Model | Interactions A major part of the project consisted of modelling each module. This enabled us to decide which ideas we should implement. Look at the Fast Response page for a great example of how modelling has made a major impact on our design!
 Objectives | Description | Results | Constants | MATLAB Code
Parameters and Constants

 Type of Constant Derivation of Value TEV Enzyme Dynamics Enzymatic Reaction: E+S ↔ ES → E+P k1 = rate constant for E + S → ES = 108 M-1s-1 k2 = rate constant for E + S ← ES = 103 s-1 kcat = rate constant for ES → E + P = 0.16 ± 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. Production Rate of Surface Proteins 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 could not obtain, that value was manipulated. The result 4.13×10-8mol/dm3/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. Degradation Rate of Surface Proteins (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. kdeg= 0.000289s-1 For all proteins that are outside of cells or the timescale that is short enough to neglect cell division effect: kdeg=0 Diffusion Coefficient of Proteins We have found two 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] Localised Concentration Coefficient The localised concentration coefficient 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 value of localised concentration coefficient probably would require adjusting for different bacterial concentrations. Cell Dimensions Bacillus subtillis was treated as a rod unless specifically state otherwise. The following dimensions were used [4]: Diameter: 0.87 μm Length: 4.7 μm Cell Wall thickness The cell wall thickness was found to be around 35nm. [5]: Diffusion constant The diffusion coefficient of small protein in water is of order = 10-6 cm2 s-1 [6]: