Team:Tsinghua-A/Modeling/Sensitivity

Sensitivity analysis

To get a better result, which means more genes in state ‘B’ int the end, we analyze on some key parameters to find how to improve our system.

Analysis of K3-

is the rate constant that AraC-arabinose complexes separate from araI site. If we change it from the original 1 to 0.01, we can get the following result.
The concentration of Cre ：
The concentration of Cre-Loxp ：
The number of genes in different state:

The result shows that when is very small which means that the rate that AraC-arabinose complexes binds to araI site ( ) is much bigger than that it separates from aral site (), there will be fluctuations before Cre degrade to zero.

Analysis of the rate of flip

We use to denote the rate that genes in state ‘C’ change to state ‘B’, as well as the rate that genes in state ‘D’ change to state ‘A’. Then we change from 100 to 1, we can get the following result.

The result, especially the bottom of the number of genes in state ‘A’, shows clearly that genes in state ‘A’ first change to state ‘C’ before they become state ‘B’.
The following figure can give us more details about the affection of .

Analysis of d(pcre)

is the degradation constant of Cre protein. If we change from 0.14/min to 1.4/min, we can get the following result.
The concentration of Cre ：

The concentration of Cre-Loxp ：

The number of the genes in different states (green line for original state and red line for state after inversion):
1 trajectory:

10 trajectories:

100 trajectories:

1000 trajectories:

From the above results , we can see that if the rate of the degradation of Cre protein increases so that the Cre declines to zero faster and the time when Cre exists decreases , the number of times of flip will be smaller and the inversion may even happen only once when the degradation constant of Cre protein is proper. We can also see that the number of genes in state ‘B’ which we want is bigger for the reason that when lots of genes flip to the state ‘B’ from state ’A’ and ready to flip back , Cre and Cre-Loxp have declined to zero , so these genes keep the state ‘B’ finally.
To understand the affection of the degradation constant of Cre protein more clearly, we then simulate the process when the degradation constant of Cre protein changes from 0.1 to 1.5. And we can get the following result.

To see the result more clearly, we magnify the above figure and just see a part of it.

The result shows that there is more genes in state ‘B’ which we want when the degradation constant of Cre protein is smaller. So we can expect that if we introduce a feed forward to the system which can accelerate the degradation of Cre protein after a certain time we add arabinose, we can also get more genes in state ‘B’ finally. Based on this idea, we designed a system with feed forward.