Goal

To simulate how the oscillator works.

Methods

1. Establish ODE equations based on Mass-action law;
2. Investigate reasonable parameter sets from previous researches;
3. Simulation;

Results

We solved these DDEs with R language. We also went one step further. We simulated the situation in which lag obeys a specific gaussian distribution, and the lag $\tau$changes in every certain interval. We hoped by running a random test, we could get closer to real life situation. The results are below.

(a) A numeric solve of AraC

(b) 5 random tests numeric solve of AraC

Fig 1.(a)A numeric solve of AraC when lag $\tau$ = 2min, Arabinose concentration is 5%, IPTG concentration is 1mM, time interval is 0.1min. (b)numeric solve of AraC concentration versus time of 5 random tests, when Arabinose concentration is 0.7%, IPTG concentration is 10mM, and $\tau \sim (2.0,0.3^2).