Team:Tsinghua-A/Modeling/P4

What we have done insofar is focused on two-cell oscillation. Quorum-sensing oscillator is not simply a matter of expansion in magnitude, but a matter of robustness in allowing difference of each individual cell. Moreover, we test the adjustment of phase and amplitude of oscillation in this part.

As we all know, no two things in this world are the same, so do cells. The major difference of individual cell that we take into considerations is twofold:

●Each cell's activity of promoter is varied, so each cell has different rate to generate AHL.

●The initial amount of AHL may be disproportionally distributed among cells.

The rate of generating AHL is closely related to parameter m and n. Therefore, we introduce randomness to both parameters by letting them obey normal distribution, that is:

m(i)= μ1+N(0,σ1);

n(i)= μ2+N(0,σ2);

μ1 and μ2 are the average ability of generating 30C6HSL and 3012CHSL, and normal distribution--(0,σ)--describes the fluctuations of AHL generating rate in individual cell. We then expanded our equations from 2 cells to a population of cells. Each cell share a mutual environment in which we assume that AHL in environment is proportionally distributed.

Figure 16 100 Cells Varied in parameter m and n

The figures indicate that our system can oscillate synchronically being able to tolerate differences among a population of cells. Furthermore, the figures prove that different ability of generating AHLs of cells have nothing to do with the period and phase of the oscillation. We can also see that the oscillation amplitude of each cell is to a greater extent varied when the Variance of interruption is enlarged.

Moreover, we test whether the oscillation is dependent on initial distribution of AHL by changing the initial amount drastically by letting them follow uniform distribution. That is:

Initial(i)= U(0,20);

The results would give evidence to prove that our system can start to oscillate synchronically given variant initial starting numbers.

Based on this distribution restraining the initial AHL concentration in each cell, we simulated out a figure as follows.

Figure 17 100 Cells Varied in initial AHL concentration

The results demonstratively give evidence proving that our system can start to oscillate synchronically given variant initial starting numbers.