Team:ETH Zurich/Model/Environment Sensing/parameter fitting
Fit parameters and evaluate the performance of our system
Goal
Once the initial guidelines for the genetic design given in a first step, we need to measure on our obtained biological system whether it behaves as intended. Therefore, we will submit it to carefully designed experiments, in order to fit our model on the obtained data and retrieve crucial parameters. The tricky part here is that in a test tube, our system will behave differently than in a tumor, as the repartition of bacteria is not the same and diffusion of AHL does not take place in the lab experiments. We therefore have to extend our model to take this discrepancy into account.
In vitro model extension
Compared to the real-life situation happening in the tumor, bacteria are in a very different state: they are in bulk in the liquid culture and not in an open solid medium like they would be around the tumor. Therefore, the diffusion of AHL in the test tube does not take place, and some of our equations used before should be adapted to describe the behavior of our circuit when bacteria are in the situation of our lab experiments.
\[\begin{aligned} \mathrm{d} n &= (( \Phi(x) - \Phi(x + \mathrm{d} x) ) \mathrm{d} S - k_{\text{deg}} \mathrm{d} n) \, \mathrm{d} t \\ \frac{\mathrm{d} n}{\mathrm{d} V \mathrm{d} t} &= D \frac{\mathrm{d}^{2} [\text{AHL}]}{\mathrm{d} x^2} - k_{\text{deg}} \frac{\mathrm{d} n}{\mathrm{d} V} \\ \frac{\mathrm{d} [\text{AHL}]}{\mathrm{d} t} &= D \frac{\mathrm{d}^{2} [\text{AHL}]}{\mathrm{d} x^2} - k_{\text{deg}} [\text{AHL}]\end{aligned}\]References
