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| - | <h2 id="titleText" style="color:rgb(137,202,154);">Tsinghua-A::Modeling</h2> | + | <h2 id="titleText" style="color:rgb(137,202,154);">Tsinghua-A::Modeling::<span style="color: rgb(12,117,34);">GILLESPIE Algorithm</span></h2> |
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| - | <h2 class="textTitle" >Introduction</h2> | + | <h2 class="textTitle" >Gillespie algorithm</h2> |
| | <div class="entry-content"> | | <div class="entry-content"> |
| - | <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/> | + | <p>the reverse process of the gene between the two Loxp sites could not be well described by the DDE or ODE equations since after the reverse process, the gene will have chance to flip again. This process is a discrete, stochastic process instead of a continuous, deterministic process. To make the model more convincing, we use Gillespie algorithm, which is a kind of stochastic simulation algorithm to generate a statistically correct trajectory (possible solution) of a stochastic equation.<a class="textLink" href="https://2012.igem.org/Team:Tsinghua-A/Modeling/GILLESPIE/part1">readmore</a> |
| - | 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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| - | <h2 class="textTitle">Mathematical Model:DDE</h2> | + | <h2 class="textTitle" style="font-size:38px;">Our model</h2> |
| | <div class="entry-content"> | | <div class="entry-content"> |
| - | <p> 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. <a class="textLink" href="https://2012.igem.org/Team:Tsinghua-A/Modeling/ DDE">readmore</a></p> | + | <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. |
| | + | 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. |
| | + | <a class="textLink" href="https://2012.igem.org/Team:Tsinghua-A/Modeling/GILLESPIE/part2">readmore</a></p> |
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| - | <h2 class="textTitle" style="font-size:43px;">Mathematical Model:GILLESPIE</h2> | + | <h2 class="textTitle" style="font-size:43px;">A better model</h2> |
| | <div class="entry-content"> | | <div class="entry-content"> |
| - | <p> 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.<a class="textLink" href="https://2012.igem.org/Team:Tsinghua-A/Modeling/GILLESPIE">readmore</a></p> | + | <p> 1000 genes which are in state ‘A’ are seen as a whole in the above model. To make the simulation more convincing, we then simulate the trajectory of every single molecule. After that we synthesize all trajectories to get the final result.<a class="textLink" href="https://2012.igem.org/Team:Tsinghua-A/Modeling/GILLESPIE /part3">readmore</a></p> |
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| - | <h2 class="textTitle">Sensitivity Analysis</h2>
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| - | <p>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.<a class="textLink" href="https://2012.igem.org/Team:Tsinghua-A/Modeling/Sensitivity">readmore</a></p>
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| - | <h2 class="textTitle">Feedforward</h2>
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| - | <p> 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.<a class="textLink" href="https://2012.igem.org/Team:Tsinghua-A/Modeling/Feedforward">readmore</a></p>
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| - | <h2 class="textTitle">Reference</h2>
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| - | <p>[1] MEGERLE J A, FRITZ G, GERLAND U, et al. Timing and dynamics of single cell gene expression in the arabinose utilization system [J]. Biophys J, 2008, 95(4): 2103-15.<br/>
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| - | [2] RUFER A, NEUENSCHWANDER P F, SAUER B. Analysis of Cre-loxP interaction by surface plasmon resonance: influence of spermidine on cooperativity [J]. Anal Biochem, 2002, 308(1): 90-9.<br/>
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| - | [3] VAN DUYNE G D. A structural view of cre-loxp site-specific recombination [J]. Annu Rev Biophys Biomol Struct, 2001, 30:87-104.<br/>
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| - | [4] BONNET J, SUBSOONTORN P, ENDY D. Rewritable digital data storage in live cells via engineered control of recombination directionality [J]. Proc Natl Acad Sci U S A, 2012, 109(23): 8884-9.<br/>
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| - | [5] ZHANG X, REEDER T, SCHLEIF R. Transcription activation parameters at ara pBAD [J]. J Mol Biol, 1996, 258(1): 14-24.<br/>
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| - | [6] BERNSTEIN D. Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm [J]. Phys Rev E Stat Nonlin Soft Matter Phys, 2005, 71(4 Pt 1): 041103.<br/>
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| - | [7] Danlel T. Gillespie. 1977. Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem., 1977, 81 (25):2340–2361.<br/>
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| - | <a class="navigationButtonA" href="#" style="color:rgb(137,202,154);">Introduction</a></li> | + | <a class="navigationButtonA" href="#" style="color:rgb(137,202,154);">Gillespie algorithm</a></li> |
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