Comparing SSA and Explicit Tau-Leaping Stochastic Solvers

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

The following decaying-dimerizing reactions will be constructed and stochastically simulated:

Reaction 1: s1 -> null, with reaction rate constant, c1 = 1.0
Reaction 2: 2 s1 < - > s2, with reaction rate constants, forward: c2f = 0.002 reverse: c2r = 0.5
Reaction 3: s2 -> s3, with reaction rate constant, c3 = 0.04
Initial conditions: s1 = 100000 molecules, s2 = s3 = 0

This example uses parameters and conditions as described in Daniel T. Gillespie, 2001, "Approximate accelerated stochastic simulation of chemically reacting systems," Journal of Chemical Physics, vol. 115, no. 4, pp. 1716-1733.

Create Decaying-Dimerizing Model

model = sbiomodel('Decaying-Dimerizing Reaction Set');

Enter Reactions

r1 = addreaction(model, 's1 -> null');
r2 = addreaction(model, '2 s1 <-> s2');
r3 = addreaction(model, 's2 -> s3');

Set Reactions to be MassAction

kl1 = addkineticlaw(r1, 'MassAction');
kl2 = addkineticlaw(r2, 'MassAction');
kl3 = addkineticlaw(r3, 'MassAction');

Add Rate Constants for Each Reaction

p1  = addparameter(kl1, 'c1',  'Value', 1.0);
p2f = addparameter(kl2, 'c2f', 'Value', 0.002);
p2r = addparameter(kl2, 'c2r', 'Value', 0.5);
p3  = addparameter(kl3, 'c3',  'Value', 0.04);

Set the Kinetic Law Constants for Each Kinetic Law.

kl1.ParameterVariableNames = {'c1'};
kl2.ParameterVariableNames = {'c2f', 'c2r'};
kl3.ParameterVariableNames = {'c3'};

Specify Initial Amounts of Each Species

model.species(1).InitialAmount = 100000;    % s1
model.species(2).InitialAmount = 0;         % s2
model.species(3).InitialAmount = 0;         % s3

Display the Completed Model Objects

model

model = 
   SimBiology Model - Decaying-Dimerizing Reaction Set 

   Model Components:
     Compartments:      1
     Events:            0
     Parameters:        4
     Reactions:         3
     Rules:             0
     Species:           3
     Observables:       0

Display the Reaction Objects

model.Reactions

ans = 
   SimBiology Reaction Array

   Index:    Reaction:  
   1         s1 -> null 
   2         2 s1 <-> s2
   3         s2 -> s3

Display the Species Objects

model.Species

ans = 
   SimBiology Species Array

   Index:    Compartment:    Name:    Value:    Units:
   1         unnamed         s1       100000          
   2         unnamed         s2       0               
   3         unnamed         s3       0

Get the Active Configuration Set for the Model.

cs = getconfigset(model,'active');

Simulate Model Using SSA Stochastic Solver and Plot

tfinal = 30, logging every 10th datapoint.

cs.SolverType = 'ssa';
cs.StopTime = 30;
solver = cs.SolverOptions;
solver.LogDecimation = 10;
cs.CompileOptions.DimensionalAnalysis = false;
[t_ssa, x_ssa] = sbiosimulate(model);

h1 = subplot(2,1,1);
plot(h1, t_ssa, x_ssa(:,1),'.');
h2 = subplot(2,1,2);
plot(h2, t_ssa, x_ssa(:,2:3),'.');
grid(h1,'on'); 
grid(h2,'on');
title(h1,'Decay Dimerizing Reactions');
ylabel(h1,'Amount of S1');
ylabel(h2,'Amount of S2 & S3');
xlabel(h2,'Time');
legend(h2, 'S2', 'S3');

Figure contains 2 axes objects. Axes object 1 with title Decay Dimerizing Reactions contains an object of type line. Axes object 2 contains 2 objects of type line. These objects represent S2, S3.

Simulate Model Using Explicit Tau-Leaping Solver and Plot in the Same Figure

Without closing the figure window, plot the results from using the Explicit Tau-Leaping Solver.

tfinal = 30, logging every 10th datapoint. Acceptable error tolerance for solver, 0.03.

cs.StopTime = 30;
cs.SolverType = 'explTau';
solver = cs.SolverOptions;
solver.LogDecimation = 10;
[t_etl, x_etl] = sbiosimulate(model);

hold(h1,'on'); 
hold(h2,'on');
plot(h1, t_etl, x_etl(:,1),'o');
plot(h2, t_etl, x_etl(:,2:3),'o');
legend(h2, 'S2 (SSA)', 'S3 (SSA)', 'S2 (Exp. Tau)', 'S3 (Exp. Tau)');
hold(h1,'off'); 
hold(h2,'off');

Figure contains 2 axes objects. Axes object 1 with title Decay Dimerizing Reactions contains 2 objects of type line. Axes object 2 contains 4 objects of type line. These objects represent S2 (SSA), S3 (SSA), S2 (Exp. Tau), S3 (Exp. Tau).

Comparison of Number of Steps for SSA and Explicit Tau-Leaping Algorithms

fprintf('Approximate Number of SSA steps: %d\n', (length(t_ssa) * 10));

Approximate Number of SSA steps: 616010

fprintf('Approximate Number of Explicit Tau-Leaping steps: %d\n', ...
        (length(t_etl) * 10));

Approximate Number of Explicit Tau-Leaping steps: 620

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