Stochastic Simulation of Radioactive Decay

This example shows how to build and simulate a model using the SSA stochastic solver.

The following model will be constructed and stochastically simulated:

Reaction 1: x -> z with a first-order reaction rate, c = 0.5.
Initial conditions: x = 1000 molecules, z = 0.

This model can also be used to represent irreversible isomerization.

This example uses parameters and conditions as described in Daniel T. Gillespie, 1977, "Exact Stochastic Simulation of Coupled Chemical Reactions," The Journal of Physical Chemistry, vol. 81, no. 25, pp. 2340-2361.

Read the Radioactive Decay Model Saved in SBML Format

model  = sbmlimport('radiodecay.xml')

model = 
   SimBiology Model - RadioactiveDecay 

   Model Components:
     Compartments:      1
     Events:            0
     Parameters:        1
     Reactions:         1
     Rules:             0
     Species:           2
     Observables:       0

View Species Objects of the Model

model.Species

ans = 
   SimBiology Species Array

   Index:    Compartment:    Name:    Value:    Units:  
   1         unnamed         x        1000      molecule
   2         unnamed         z        0         molecule

View Reaction Objects of the Model

model.Reactions

ans = 
   SimBiology Reaction Array

   Index:    Reaction:
   1         x -> z

View Parameter Objects for the Kinetic Law

model.Reactions(1).KineticLaw(1).Parameters

ans = 
   SimBiology Parameter Array

   Index:    Name:    Value:    Units:  
   1         c        0.5       1/second

Update the Reaction to use MassAction Kinetic Law for Stochastic Solvers.

model.Reactions(1).KineticLaw(1).KineticLawName = 'MassAction';
model.Reactions(1).KineticLaw(1).ParameterVariableNames = {'c'};

Simulate the Model Using the Stochastic (SSA) Solver & Plot

cs = getconfigset(model,'active');
cs.SolverType = 'ssa';
cs.StopTime = 14.0;
cs.CompileOptions.DimensionalAnalysis = false;
[t,X] = sbiosimulate(model);

plot(t,X);
legend('x', 'z', 'AutoUpdate', 'off');
title('Stochastic Radioactive Decay Simulation');
ylabel('Number of molecules');
xlabel('Time (seconds)');

Figure contains an axes object. The axes object with title Stochastic Radioactive Decay Simulation, xlabel Time (seconds), ylabel Number of molecules contains 2 objects of type line. These objects represent x, z.

Repeat the Simulation to Show Run-to-Run Variability

title('Multiple Stochastic Radioactive Decay Simulations');
hold on;
for loop = 1:20
    [t,X] = sbiosimulate(model);
    plot(t,X);    % Just plot number of reactant molecules
    drawnow; 
end

Figure contains an axes object. The axes object with title Multiple Stochastic Radioactive Decay Simulations, xlabel Time (seconds), ylabel Number of molecules contains 42 objects of type line. These objects represent x, z.

Overlay the Reaction's ODE Solution in Red

cs = getconfigset(model,'active');
cs.SolverType = 'sundials';
cs.StopTime = 20;
[t,X] = sbiosimulate(model);
plot(t,X,'red');
hold off;

Figure contains an axes object. The axes object with title Multiple Stochastic Radioactive Decay Simulations, xlabel Time (seconds), ylabel Number of molecules contains 44 objects of type line. These objects represent x, z.