7.2 Performing stochastic simulation using Bio-PEPA

An alternative kind of time series which we could generate is the one which interprets the Bio-PEPA model in the discrete, stochastic regime, in which the species variables are subject to discrete change and take integer number values only in each run.

The Bio-PEPA Eclipse Plug-in offers the following algorithms for stochastic simulation:

• Gillespie’s stochastic simulation algorithm

• Gillespie’s Tau-Leap stochastic simulation algorithm

• Gibson-Bruck stochastic simulation algorithm

In order to generate a time series for our Bio-PEPA model we need to set the parameters for the stochastic simulation (see Figure 21). The parameters which need to be set, differ from one simulator to another but the stochastic simulators typically include:

• Start time — the start time of the time series (often 0)

• Stop time — the stop time of the time series (model dependent)

• Number of data points — the number of data points that you would like to record

• Number of independent replications — the number of simulation runs

Gillespie’s Tau-Leap stochastic simulation algorithm also includes the following parameters:

• Step size — the step size parameter is used to determine the frequency of the tau-leap (default value 0.0010). When the step size is increased the tau-leap occurs more frequently, which decreases the accuracy of the simulation results.

• Relative error — the relative error is used to determine the size of the tau-leap (default value 1.0E-4). When the relative error is increased, so does the size of the tau-leap, which decreases the accuracy of the simulation results.

The simulation results are plotted in the Graph view (see Figure 22 for the results of the simple.biopepa model we saw in the previous sections). By allowing you to choose the number of independent replications, the Bio-PEPA Eclipse Plug-in basically gives you the option of running the simulation any number of times, without having to set the parameters again and comparing the results, since each stochastic simulation run usually has slightly different results from the others (see Figure 23).

Figure 39: Setting parameters for the Gillespie Stochastic Simulation Algorithm (SSA)

Figure 40: The results from a simulation are plotted in the Graph view

Figure 41: Two stochastic simulation runs may produce very similar results but they will not usually be exactly the same