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We use Gillespie algorithm in stochastic modelling. The procedure of this algorithm is shown as follows in the form of pseudocode:<br /><br /> | We use Gillespie algorithm in stochastic modelling. The procedure of this algorithm is shown as follows in the form of pseudocode:<br /><br /> | ||
+ | <ul class="paraUl" style="list-style:none;"> | ||
Step 1: Initialize the reaction system at \(t=0\) with rate constants \(c_1, c_2, ......, c_v\) as initial numbers of molecules \(x_1, x_2, ......, x_u\) corresponding to \(v\) reactions and \(u\) sustances (both reactants and products) involved in the reaction system.<br /><br /> | Step 1: Initialize the reaction system at \(t=0\) with rate constants \(c_1, c_2, ......, c_v\) as initial numbers of molecules \(x_1, x_2, ......, x_u\) corresponding to \(v\) reactions and \(u\) sustances (both reactants and products) involved in the reaction system.<br /><br /> | ||
Step 2: For each \(i=1,2,......,v\), calculate the hazard for the \(i^{th}\) type of reaction, denoted as \(h_i(x,c_i)\) based on current substance number \(x\).<br /><br /> | Step 2: For each \(i=1,2,......,v\), calculate the hazard for the \(i^{th}\) type of reaction, denoted as \(h_i(x,c_i)\) based on current substance number \(x\).<br /><br /> | ||
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Step 9: If \(t\ \text{<}\ T_{max}\), return to step 2. \(T_{max}\) corresponds to the maximum duration of the reaction set by the user.<br /><br /> | Step 9: If \(t\ \text{<}\ T_{max}\), return to step 2. \(T_{max}\) corresponds to the maximum duration of the reaction set by the user.<br /><br /> | ||
Step 10: Plot the result to see the dynamic of the quantity of the substance that you are interested in.<br /><br /> | Step 10: Plot the result to see the dynamic of the quantity of the substance that you are interested in.<br /><br /> | ||
+ | </ul> | ||
Although the algorithm is rather simple, basic mathematical skills is required to understand its theoretical basis. You may consult the book written by <a href="#Ref4">Wilkinson and Darren J.</a> for a thorough understanding. The result is shown in <a href="#Fig5">Fig. 5</a>.<br /><br /> | Although the algorithm is rather simple, basic mathematical skills is required to understand its theoretical basis. You may consult the book written by <a href="#Ref4">Wilkinson and Darren J.</a> for a thorough understanding. The result is shown in <a href="#Fig5">Fig. 5</a>.<br /><br /> | ||
The result demonstrates that recombined P<sub>target</sub>s do occur and two rounds of reverse transcription and recombination can take place in one replication cycle of E. coli (1200 s) (<a href="#Fig5">Fig 5a</a>). On the contrary, no recombined will come out within that period if the initial cDNA is 5 molecules and initial Cre is 3228 molecules (<a href="#Fig5">Fig 5b</a>). This again demonstrates the necessity of putting RT and Cre under different induction setups. The fluctuation of the number of recombined P<sub>target</sub> is due to the backward reaction that Cre can rebind with recombined and reverting the action, making it not counted as recombined P<sub>target</sub> by the algorithm. | The result demonstrates that recombined P<sub>target</sub>s do occur and two rounds of reverse transcription and recombination can take place in one replication cycle of E. coli (1200 s) (<a href="#Fig5">Fig 5a</a>). On the contrary, no recombined will come out within that period if the initial cDNA is 5 molecules and initial Cre is 3228 molecules (<a href="#Fig5">Fig 5b</a>). This again demonstrates the necessity of putting RT and Cre under different induction setups. The fluctuation of the number of recombined P<sub>target</sub> is due to the backward reaction that Cre can rebind with recombined and reverting the action, making it not counted as recombined P<sub>target</sub> by the algorithm. |
Revision as of 22:44, 21 October 2019