Stochastic Simulation in Virtual Cell

 

A quick tour of Virtual Cell stochastic simulation

 

A quick tour of Virtual Cell stochastic simulation

In the following section, we will discuss how to create and run the stochastic simulations and view the results in Virtual Cell. We shall use Michaelis-Menten as an example.

 

·                    To create a stochastic application.

 

To stochastically simulate a system, users have to create a stochastic application based on the physiology. There are four ways to create such an application.

 

a)      Select the “Application” menu and click on the “New” item and choose “Stochastic Application” sub item (Figure 4). This will set up a new stochastic application.

 

b)      Select the model name in the tree and right click and choose “Create Stochastic Application” (Figure 5). This will set up a new stochastic application.

 

c)      Click on the existing application name and right click and choose “Copy As” item and further down choose “Stochastic Application” (Figure 6). This will copy the original application (whatever deterministic or stochastic) to a stochastic application while keeping the original parameters including structure information and initial condition etc.

 

d)      Click on the existing application name and right click and choose “New” item and further down choose “Stochastic Application” (Figure 7). This will set up a new stochastic application.

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


                 Figure 4. Create a stochastic application from “Application” Menu

 

  
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


                   Figure 5. Create a stochastic application from model tree root

 

 

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

       Figure 6. Copy a stochastic application by existing one from “Copy As” menu item

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


                 Figure 7. Create a stochastic application from “New” menu item

 

 

·                    To set up structure size and initial conditions

 

Structure size and initial conditions are required by stochastic simulation. These are created in the same way that structure size and initial conditions are created in deterministic models. Users can follow instructions in the Virtual Cell user guide to set up the structure size and initial conditions. VCell user guide is located at http://www.vcell.org/login/documentation.html.

·                    To set up simulation parameters

 

After creating a simulation (see Virtual Cell user guide for instructions), users are responsible to choose preferred solver and set up the simulation parameters. We list the different parameter sets below according to different solvers. To set up simulation parameters, users just need to click on “Edit” button in the simulation panel.

 

a)      Gibson-Bruck Exact Solver (Figure 8)

 

STARTING TIME: the time when simulation starts.

ENDING TIME: the time when simulation ends.

RANDOM SEED: a random number generated by PC time, which is used to produce a series of uniformly distributed random numbers.

CUSTOMIZED SEED: a user specified number, which is used to produce a series of uniformly distributed random numbers.

NUMBER OF TRIALS: the number of multiple trials to be run.

OUTPUT OPTIONS: use keep every number of samples or output time interval.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


                     Figure 8. Parameters required by exact stochastic solver

      To view simulation results

 

To intuitively display the results, Virtual Cell displays the trajectories for a single stochastic run and histograms for Monte Carlo simulation. When results status becomes “yes” in the simulation list panel, users can click the “Results’ button to view results. The results will be displayed in either plots or table by selecting the “Show plots” and “Show data” buttons respectively.

 

a)      A trajectory for a single stochastic run shows a stochastic variable or probability of a jump process changes against time (Figure 11 and Figure 12).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


                       Figure 11. Trajectories of stochastic variables

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


          Figure 12. Stochastic variables change against time listed in a table

b)      A histogram for Monte Carlo simulation shows the frequency of a stochastic variable being a certain value at a specific time point after multiple trials (Figure 13 and Figure 14).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


              Figure 13. Histogram of a stochastic variable after Monte Carlo simulation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


              

                  Figure 14. Histograms of stochastic variables listed in a table