Modeling

Introduction

The project is intended to treat retrovirus diseases. And we take AIDS as an example. In this project, we want to establish a more effective HIV-curing system with less side-effects by integrating CRISPR/Cas9 system into human hemopoietic stem cells, which aims to protect the helper T cells from virus infection.

So we want to know how effective the CRISPR/Cas9 system is for HIV. In this model, we discuss about dynamic changes of different cells in a person’s body using Matlab. And in this model, we can see how the system works. And this model will help us to forecast the future applications of our project.

In our model, we can see the influence the CRISPR/Cas system produces by the change of virus and cells. But there are too many parameters and that makes it impossible to get clear relation of these parameters easily. If the environment doesn't change, we can stimulate the situation in Matlab for a short time.

Derivation of the model

Theoretical analysis

First, stably transfect hematopoietic stem cells with the plasmid which encodes Cas9 protein. To make the question easier, we suppose that the efficiency is constant. As is shown in other part in this project, second, we can construct a plasmid which encodes the gRNA sequence which is a 20bp conserved regions in HIV DNA and has no conservation in human genome. When the human body is infected by AIDS, using non-viral DNA transfecting methods (in our project we choose A-B toxin based shuttle) to deliver the plasmid into human somatic cells (especially CD4+ cells) and the CRISPR/Cas system is activated. The Cas9 protein recognizes viral DNA with the help of gRNA and cut the target sequence, causing double strand break (DSB). The DSB is then repaired by the non-homologous end joining mechanism in the cell but with high error rate (in this model we suppose the rate doesn’t change), causing frame-shift mutation and gene knockout. The viral protein synthesis is stopped and further infection is impossible, but it provides potentiation for eradicating AIDS.

<math>

 \operatorname{erfc}(x) =
 \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt =
 \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}

</math>

Symbol description

Matlab analysis

Reference