Expression to determine reaction rate equation or expression of observable object - MATLAB

Description

The Expression property can be a property of KineticLaw (or AbstractKineticLaw) object or an observable object.

For an observable object, the Expression property is a mathematical expression that lets you perform post-simulation calculations. For details, see SimBiology.Observable.

For a KineticLaw object, the Expression property indicates the mathematical expression that is used to determine the ReactionRate property of the reaction object. Expression is a reaction rate expression assigned by the kinetic law definition used by the reaction. The kinetic law being used is indicated by the property KineticLawName. You can configure Expression for user-defined kinetic laws, but not for built-in kinetic laws. Expression is read only for kinetic law objects.

Note

If you set the Expression property to a reaction rate expression that is not continuous and differentiable, see Using Events to Address Discontinuities in Rule and Reaction Rate Expressions before simulating your model.

Kinetic Law Definition

The kinetic law definition provides a mechanism for applying a specific rate law to multiple reactions. It acts as a mapping template for the reaction rate. The kinetic law is defined by a mathematical expression, (defined in the property Expression), and includes the species and parameter variables used in the expression. The species variables are defined in the SpeciesVariables property, and the parameter variables are defined in the ParameterVariables property of the kinetic law object.

If a reaction is using a kinetic law definition, the ReactionRate property of the reaction object shows the result of a mapping from the kinetic law definition. To determine ReactionRate, the species variables and parameter variables that participate in the reaction rate should be mapped in the kinetic law for the reaction. In this case, SimBiology^® software determines the ReactionRate by using the Expression property of the abstract kinetic law object, and by mapping SpeciesVariableNames to SpeciesVariables and ParameterVariableNames to ParameterVariables.

For example, the kinetic law definition Henri-Michaelis-Menten has the Expression Vm*S/(Km+S), where Vm and Km are defined as parameters in the ParameterVariables property of the abstract kinetic law object, and S is defined as a species in the SpeciesVariable property of the abstract kinetic law object.

By applying the Henri-Michaelis-Menten kinetic law to a reaction A -> B with Va mapping to Vm, A mapping to S, and Ka mapping to Km, the rate equation for the reaction becomes Va*A/(Ka+A).

The exact expression of a reaction using MassAction kinetic law varies depending upon the number of reactants. Thus, for mass action kinetics the Expression property is set to MassAction because in general for mass action kinetics the reaction rate is defined as

$r = k \prod_{i = 1}^{n r} {[S i]}^{m_{i}}$

where [Si] is the concentration of the ith reactant, m_i is the stoichiometric coefficient of [Si], n_r is the number of reactants, and k is the mass action reaction rate constant.

SimBiology software contains some built-in kinetic laws. You can also define your own kinetic laws. To find the list of available kinetic laws, use the sbiowhos -kineticlaw command (sbiowhos). You can create a kinetic law definition with the function sbioabstractkineticlaw and add it to the library using sbioaddtolibrary.

Characteristics

Applies to	Objects: abstract kinetic law, kinetic law, observable
Data type	Character vector
Data values	Defined by kinetic law definition
Access	Read-only in kinetic law object. Read/write in user-defined kinetic law.

Examples

Define Michaelis Menten Reaction Kinetics in SimBiology Model

Create a SimBiology model with a reaction.

m1 = sbiomodel("m1");
r1 = addreaction(m1,"A -> B");

Add a kinetic law for the reaction by using the built-in kinetic law (Michaelis Menten). Check the expression of the kinetic law.

kl = addkineticlaw(r1,"Henri-Michaelis-Menten");
kl.Expression

ans = 
'Vm*S/(Km + S)'

Query the parameters and species variables defined in the kinetic law.

kl.ParameterVariables

ans = 2x1 cell
    {'Vm'}
    {'Km'}

kl.SpeciesVariables

ans = 1x1 cell array
    {'S'}

Define Va and Ka as ParameterVariableNames, which correspond to the ParameterVariables Vm and Km defined in the Expression property of the kinetic law. To set these variables, first create the parameter variables as parameter objects (p1, p2) with the names Va and Ka, and then add them to the kinetic law object kl. The species object with the name A is created when the reaction object r1 is created and need not be redefined.

p1 = addparameter(kl,"Va");
p2 = addparameter(kl,"Ka");

Set the variable names for the kinetic law object.

kl.ParameterVariableNames = ["Va","Ka"];
kl.SpeciesVariableNames   = ["A"];

Verified that the reaction rate is expressed correctly in the ReactionRate property of the reaction object

r1.ReactionRate

ans = 
'Va*A/(Ka+A)'

Define Mass Action Reaction Kinetics in SimBiology Model

Create a SimBiology model with a reaction.

m1 = sbiomodel("m1");
r1 = addreaction(m1,"a + b -> c + d");

Add a kinetic law for the reaction by using the built-in kinetic law (Mass Action). Check the expression of the kinetic law.

kl = addkineticlaw(r1,"MassAction");
kl.Expression

ans = 
'MassAction'

Assign the rate constant for the reaction.

kl.ParameterVariableNames = "k";

Check the reaction rate.

r1.ReactionRate

ans = 
'k*a*b'

Expression