Simulations
Now, based on our equations, we can run simulations to estimate αY, the parameter of interest of our model. For that, we decided to try to find the maximum αY that will, according to our model, fit the EC50 time and the maximum value of ρ.
For that, we must assume a new assumption: That all the proteins in the systems (synthases, receptors and reporters) are approximately equal, therefore we can say that their production and degradation rates are the same, if not explicitly given a value.At first, we defined our parameters based on literature values. (To know precisely the parameters used in the runs, see the table at the end of the page).
After establishing the parameters of interest, we created an algorithm that will receive the EC50 time (tEC50) and the maximum ρ (MAX) and return the values of αY. The algorithm is resumed at the flowchart below:
In this flow chart, we can see the process of the algorithm's workings. Where a parallelogram represents the initial data, round rectangles represent processes and diamonds represent decision processes. Af is used as αY and ε is a small increase. From that, we’ve been able to, comparing to our data and using some literature data as proxy, estimate the alphas!
However, to do a proper comparison, we’ve set up a relative measure, we decided to call λ. Is a very simple proposal:
$$\lambda N \mid M = \frac{ ( \frac{\alpha M}{\gamma M}) ^2 } { ( \frac{\alpha N}{\gamma N}) ^2}$$
Where N is the native system, the system of the HSL and Receptor, and M is the system of the promoter. Alfa is the alfa that represents the promoter interaction, and gamma is the basal of expression. With that in mind, we found the following values of Lambda:
- Lux:
- Rhl:
- Tra:
- Rpa:
Parameters
| Name | Value | Description | Reference |
|---|---|---|---|
Parameter References
- MIT's 2010 iGEM Team
- S.Basu , Y.Gerchman, C.H. Collins, F.H. Arnold, R.Weiss. “A synthetic multicellular system for programmed pattern formation” Nature volume 434, pages 1130–1134 (28 April 2005)
- M.Weber, J.Buceta. “Dynamics of the quorum sensing switch: stochastic and non-stationary effects” BMC Systems Biology 7:6 (2013) doi: 10.1186/1752-0509-7-6
- Pai, Anand, and Lingchong You. “Optimal Tuning of Bacterial Sensing Potential.” Molecular Systems Biology 5 (2009): 286. PMC. Web. 17 Oct. 2018.