Team:Tsinghua-A/Modeling/GILLESPIE/part2

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	FENG Zili & GUO Mingzhou, Tsinghua-A Team, iGEM
	2012.09.08
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		<h2 id="titleText" style="color:rgb(137,202,154);">Tsinghua-A::Modeling::<span style="color: rgb(12,117,34);">Part2</span></h2>
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     		<h2  style="margin-top:135px; font-size:38px;">Our model</h2>
<p>In our model , we use Gillespie algorithm to simulate the process of inversion. Here we use  
Markov chain to describe the process of inversion.</br>
We assume that the state ‘A’ , ‘B’ , ‘C’ , ‘D’ , is the original state , the state after inversion , the 
Intermediate state when A forms holiday junction, the Intermediate state when B forms holiday 
junction respectively.
</p>
<img src="https://static.igem.org/mediawiki/2012/0/09/THU-AMGP21.png"/>
<p style="margin-left:300px;"><b>(VAN DUYNE G D, 2001)</b></p>
 <img src="https://static.igem.org/mediawiki/2012/8/80/THU-AMGP22.png"/>
<p style="margin-left:300px;"><b>(VAN DUYNE G D, 2001)</b></p>
<p>The following are the reactions which are related to the process of inversion. </p>
<img src="https://static.igem.org/mediawiki/2012/d/d3/THU-AMGP24.png"/>
<p>Then we get the following Markov chain.</p>
<img src="https://static.igem.org/mediawiki/2012/4/46/THU-AMGP23.png"/>
<p>Here,<img src="https://static.igem.org/mediawiki/2012/2/2b/THU-AMGP25.png"/>are the probabilities of the reaction in an 
Infinitesimal time. According to the property of the Markov chain , we can get:</p>
<img src="https://static.igem.org/mediawiki/2012/d/db/THU-AMGP26.png"/>
<p>In the model,<img src="https://static.igem.org/mediawiki/2012/1/16/THU-AMGP27.png"/>is proportional to the concentration of Cre-Loxp and<img src="https://static.igem.org/mediawiki/2012/d/d7/THU-AMGP28.png"/>are much larger than<img src="https://static.igem.org/mediawiki/2012/1/11/THU-AMGP29.png"/>
Here we see 1000 genes which are in state ‘A’ as a whole and we get the following results. </br>
The concentration of Cre-Loxp ：
</p>
<img src="https://static.igem.org/mediawiki/2012/d/d4/THU-AMGP210.png"/>
<p>The number of the genes which are in the original state and in the state after inversion:</p>
<img src="https://static.igem.org/mediawiki/2012/6/6f/THU-AMGP211.png"/>
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