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We use Gillespie algorithm in stochastic modelling. The procedure of this algorithm[7] is shown as follows in the form of pseudocode:<br /><br /> | We use Gillespie algorithm in stochastic modelling. The procedure of this algorithm[7] is shown as follows in the form of pseudocode:<br /><br /> | ||
− | Step 1: Initialize the reaction system at \(t=0\) with rate constants \( | + | 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<sup>th</sup> 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<sup>th</sup> type of reaction, denoted as \(h_i(x,c_i)\) based on current substance number x.<br /><br /> | ||
− | Step 3: Calculate the combined reaction hazard \(h_0(x,c)=\ | + | Step 3: Calculate the combined reaction hazard \(h_0(x,c)=\Sigma_{i=1}^{v}h_i(x,c_i)\).<br /><br /> |
− | Step 4: Simulate the time to the next reaction, \(t^'\) , which is a random quantity that obeys exponential distribution with parameter \(\lambda\).<br /><br /> | + | Step 4: Simulate the time to the next reaction, \(t^{'}\) , which is a random quantity that obeys exponential distribution with parameter \(\lambda\).<br /><br /> |
− | Step 5: Put \(t:=t+t^'\). <br /><br /> | + | Step 5: Put \(t:=t+t^{'}\). <br /><br /> |
Step 6: Simulate the reaction index, \(j\). The probability that the \(j^{th}\) reaction can occur is \(\frac{h_i(x,c_i)}{h_0(x,c)}, i=1,2,......,v.\).<br /><br /> | Step 6: Simulate the reaction index, \(j\). The probability that the \(j^{th}\) reaction can occur is \(\frac{h_i(x,c_i)}{h_0(x,c)}, i=1,2,......,v.\).<br /><br /> | ||
Step 7: Update \(x\) according to reaction \(j\), which means putting \(x:=x+S^{(j)}\), where \(S^{(j)}\) denotes the \(j^{th}\) colomn of the stoichiometry matrix \(S\). The \(j^{th}\) column of denotes the change in substance number caused by the \(j^{th}\) reaction.<br /><br /> | Step 7: Update \(x\) according to reaction \(j\), which means putting \(x:=x+S^{(j)}\), where \(S^{(j)}\) denotes the \(j^{th}\) colomn of the stoichiometry matrix \(S\). The \(j^{th}\) column of denotes the change in substance number caused by the \(j^{th}\) reaction.<br /><br /> |
Revision as of 02:57, 20 October 2019