Team:Tsinghua-A/Modeling/DDE

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<h2 id="titleText" style="color:rgb(137,202,154);">Tsinghua-A::Modeling::<span style="color: rgb(12,117,34);">DDE</span></h2>
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    <h2 class="textTitle" style="margin-top:135px;">Construction of DDE equations</h2>
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    <h2 class="textTitle" >Introduction</h2>
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<p>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.<br/>
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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.
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<p>The ara operon is regulated by the AraC protein. If arabinose is absent, the dimer AraC protein represses the structural gene by binding to araI 1 and araO 2 and the DNA forms a loop. The loop prevents RNA polymerase from binding to the promoter of the ara operon, thereby blocking transcription .When arabinose is present, arabinose binds AraC and prevents AraC from interacting. This breaks the DNA loop. The two AraC-arabinose complexes bind to the araI site which promotes transcription. When arabinose is present, AraC acts as an activator and promotes the translation of Cre. Then we use Cre-Loxp recombination, a site-specific recombinase technology to carry out inversions in the DNA of cells. The description of the system contains the above mass actions as well as some hill kinetics, Henri-Michaelis-Menten. Since concentration of protein is the integrals of its mRNA, we assume that it is proportional to concentration of mRNA in a previous time. Thus we came up a set of DDEs with 12 equations:
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<h2>Parameters</h2>
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<p>The parameters are inherent factors determining the behaviors, properties of a system. Some of our parameters are derived from original ones, some of them are created to describe the new equations, and others are set for further testing.</p>
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<img src="https://static.igem.org/mediawiki/2012/0/0b/THU-A-Parameter.png" width="800px"/><br/>
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<h2>Result</h2>
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<p>We coded the system in MATLAB. The result following shows that the concentration of Cre and the concentration of Cre-Loxp which we use all the paper to denote the Cre protein which binds to Loxp sites grow to a peak and then decline to zero. So we can expect that the inversion of the DNA which is proportional to the concentration of Cre-Loxp happens only in a period when Cre-Loxp exists. </p>
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<p>The concentration of Cre：</p>
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<img src="https://static.igem.org/mediawiki/2012/f/fc/THU-Amodelpart118.png"/><br/>
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<p>The concentration of Cre-Loxp ：</p>
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<img src="https://static.igem.org/mediawiki/2012/6/6f/THU-Amodelpart119.png"/><br/>
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<a href="https://2012.igem.org/Team:Tsinghua-A/Modeling" style="margin-left:40px;font-size:20px;">Return</a>
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Latest revision as of 21:17, 26 September 2012

Tsinghua-A::Modeling::DDE

Construction of DDE equations



The ara operon is regulated by the AraC protein. If arabinose is absent, the dimer AraC protein represses the structural gene by binding to araI 1 and araO 2 and the DNA forms a loop. The loop prevents RNA polymerase from binding to the promoter of the ara operon, thereby blocking transcription .When arabinose is present, arabinose binds AraC and prevents AraC from interacting. This breaks the DNA loop. The two AraC-arabinose complexes bind to the araI site which promotes transcription. When arabinose is present, AraC acts as an activator and promotes the translation of Cre. Then we use Cre-Loxp recombination, a site-specific recombinase technology to carry out inversions in the DNA of cells. The description of the system contains the above mass actions as well as some hill kinetics, Henri-Michaelis-Menten. Since concentration of protein is the integrals of its mRNA, we assume that it is proportional to concentration of mRNA in a previous time. Thus we came up a set of DDEs with 12 equations:

















Parameters

The parameters are inherent factors determining the behaviors, properties of a system. Some of our parameters are derived from original ones, some of them are created to describe the new equations, and others are set for further testing.






Result

We coded the system in MATLAB. The result following shows that the concentration of Cre and the concentration of Cre-Loxp which we use all the paper to denote the Cre protein which binds to Loxp sites grow to a peak and then decline to zero. So we can expect that the inversion of the DNA which is proportional to the concentration of Cre-Loxp happens only in a period when Cre-Loxp exists.

The concentration of Cre：


The concentration of Cre-Loxp ：


Return



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