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Create a Rate Rule for an Exponential Rate of Change

This example shows how to change the amount of a species similar to a first-order reaction using the first-order rate rule. For example, suppose the species x decays exponentially. The rate of change of species x is:

The analytical solution is:

where is the amount of species at time t, and is the initial amount. Use the following commands to set up a SimBiology model accordingly and simulate it.

m = sbiomodel('m');
c = addcompartment(m,'comp');
s = addspecies(m,'x','InitialAmount',2);
p = addparameter(m,'k','Value',1);
r = addrule(m,'x = -k * x','RuleType','rate');
[t,sd,species] = sbiosimulate(m);
ylabel('Species Amount');

If the amount of a species x is determined by a rate rule and x is also in a reaction, x must have its BoundaryCondition property set to true. For example, with a reaction a -> x and a rate rule , set the BoundaryCondition property of species x to true so that a differential rate term is not created from the reaction. The amount of x is determined solely by a differential rate term from the rate rule. If the BoundaryCondition property is set to false, you will get the following error message such as Invalid rule variable 'x' in rate rule or reaction.

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