Team:Tsinghua-A/Modeling/Feedforward

System design

The above figure means that we want to produce something after a certain time we add arabinose which can accelerate the degradation of Cre to shorten the time when Cre exists. Then the number of times of flip will decrease and we can expect to get more genes in state ‘B’ we want. Below is the reaction we add to achieve the idea. Here denotes time delay. s denotes the substance which can accelerate the degradation of Cre. denote the production rate of s, the degradation rate of s, the degradation rate of Cre with the affection of s respectively.

Results

The concentration of Cre ：

The concentration of Cre-Loxp ：

The number of the genes in different states:

1 trajectory:

10 trajectory:

100 trajectory:

1000 trajectory:

Compare the result of the model with feed forward with the previous one without feed forward, we can easily find that:
1. The peak of the Cre distribution is narrower in the model with a feed forward part and the number of times of flip decreases a lot.
2. In the stable state that the number of genes in every state does not change any more, more genes have flipped from state ‘A’ to state ‘B’ in the model with a feed forward part. And this result is better than the previous one since we want the system to finally change from the ‘AND’ gate to the ‘OR’ gate which means it is better to have more genes in state ‘B’.

Stability analysis:

We then compare the stability of the system with feed forward with the previous one without feed forward by observing their phase trajectories and we can get the following result.
System without feed forward:

System with feed forward:

Both phase trajectories of the two systems go straight to a point which illustrate that both systems reach to the stable state rapidly. But if we observe carefully, we can see some fluctuations in the Figure 4.8 and almost no fluctuation in Figure 4.9 from which we can get the conclusion that the system with feed forward is more stable than the one without feed forward.