Construction of ODE equation

At our first step, we wanted to describe the system thoroughly without leaving out any seemingly unimportant actions and factors. As a result, the description of the system contains every possible mass actions as well as some hill kinetics, Henri-Michaelis-Menten. We came up a set of ODEs with 19 equations.

Figure 1 designed circuit of cell I

Figure 2 designed circuit of cell II

Promoter 1 and promoter 2 preceding lasR and luxR genes respectively are constant promoters, which will transcribe and translate into protein PlasR and PluxR. LA1 is the binding association of lasR and 30C12HSL(A2C1) and it can affect the subsequent promoter 2 which can be described by Hill Equation. The same goes to LA2. Gene luxI will be translated into protein PluxI which would generate 30C6HSL(A1C1) through enzymatic reaction. The AHL will diffuse through the membrane to the environment(A1e) and finally enter into Cell 2(A1C2). Protein PtetR which is translated from gene tetR represses promoter 5 which is responsible for transcription of gene lasI. Promoter 6 is constant for translation of protein PlasI. 30C12HSL(A2C2) is generated from Protein PlasI through enzymatic reaction. 30C12HSL in the environment is called A2e which will diffuse to Cell 1. aTc is added manipulatively to change the phase of oscillation by binding the protein PTetR. Therefore, we have these following ODEs:

Parameters

The parameters are inherent factors determining the behaviors, properties of a system. We selected the quantities thoughtfully from previous iGEM teams and some others were found from published papers.

Results

We simulated this system by SIMBIOLOGY, a toolbox embedded in MATLAB. However, unaware of the key parameters to which the system is sensitive, we felt difficult to control or adjust properly, and the simulation result of the system came into a damped oscillation. We ascribed the inability of our model to the fact that the precise descriptions contain too many equations and parameters and we felt obliged to establish a simplified model in place of the precise one for simulation and further analysis.