Team:Tsinghua-A/Modeling

Introduction

In our project, we want to use Cre-Loxp recombination, a site-specific recombinase technology to carry out inversions in the DNA of cells which can change the initial ‘AND’ gate to the ‘OR’ gate. Due to the fact that the inversion is invertible, what we expect to achieve is that to a great extent the genes are transferred from initial state to the desired state.
The mathematical model of the whole process can be divided into two parts：Part 1: Construction of DDE equations to describe the process of the generation of Cre protein and Cre protein binding to Loxp sites. The result shows that the concentration of Cre protein and Cre protein binding to Loxp sites grow to a peak and then degrade to zero. Part 2: Using Gillespie algorithm to simulate the stochastic process of the reversal after Cre binds to Loxp sites. We can see from the result of this part that the inversion only happens when Cre protein binding to Loxp sites exists and about 50% of genes flip to the state we want. To analyze the property of this model, we then design the Part 3. Part 3: Sensitivity analysis of several parameters. We analyze three parameters and the third parameter –the degradation rate of Cre protein –have an obvious effect on the final percent of the genes in different state, which inspires us to introduce a feed forward to the system to increase the percent of the genes flip to the state we want, so we have the Part 4. Part 4: The addition of the feed forward part and the analysis of the new model. By introducing a feed forward to the system, we do get the desired result that more genes flip to the state we want.

Mathematical Model:DDE equations

We construct DDE equations to describe the process of the generation of Cre protein and Cre protein binding to Loxp sites. The result shows that the concentration of Cre protein and Cre protein binding to Loxp sites grow to a peak and then degrade to zero. readmore

Mathematical Model:GILLESPIE algorithm

We use Gillespie algorithm to simulate the stochastic process of the reversal after Cre binds to Loxp sites. We can see from the result of this part that the inversion only happens when Cre protein binding to Loxp sites exists and about 50% of genes flip to the state we want.readmore

Sensitivity Analysis

We analyze three parameters and the third parameter –the degradation rate of Cre protein –have an obvious effect on the final percent of the genes in different state.readmore

Feedforward

By introducing a feed forward to the system, we increase the percent of the genes flipping to the state we want.And the system is more stable.readmore

References

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