# ReactionRate

Reaction rate equation in reaction object

## Description

The ReactionRate property defines the reaction rate equation. You can define a ReactionRate with or without the KineticLaw property. KineticLaw defines the type of reaction rate. The addkineticlaw function configures the ReactionRate based on the KineticLaw and the species and parameters specified in the kinetic law object properties SpeciesVariableNames and ParameterVariableNames.

The reaction takes place in the reverse direction if the Reversible property is true. This is reflected in ReactionRate. The ReactionRate includes the forward and reverse rate if reversible.

You can specify ReactionRate without KineticLaw. Use the set function to specify the reaction rate equation. SimBiology® software adds species variables while creating reactionObj using the addreaction method. You must add the parameter variables (to the modelObj in this case). See the example below.

After you specify the ReactionRate without KineticLaw and you later configure the reactionObj to use KineticLaw, the ReactionRate is unset until you specify SpeciesVariableNames and ParameterVariableNames.

For information on dimensional analysis for reaction rates, see How Reaction Rates Are Evaluated .

Note

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

## Characteristics

 Applies to Object: reaction Data type Character vector Data values Character vector defining the reaction rate. Default is '' (empty character vector). Access Read/write

## Examples

### Add a Reaction Defined by Michaelis-Menten Kinetic Law

Create a model, add a reaction, and assign the expression for the reaction rate equation.

1. Create a model object, and then add a reaction object.

modelObj = sbiomodel('my_model');
reactionObj = addreaction(modelObj, 'a -> c + d');
2. Create a kinetic law object for the reaction object of the type 'Henri-Michaelis-Menten'.

reactionObj KineticLaw property is configured to kineticlawObj.

3. The 'Henri-Michaelis-Menten' kinetic law has two parameter variables (Vm and Km) and one species variable (S) that you should set. To set these variables, first create the parameter variables as parameter objects (parameterObj1, parameterObj2) with names Vm_d and Km_d and assign them to kineticlawObj.

4. Set the variable names for the kinetic law object.

set(kineticlawObj,'ParameterVariableNames', {'Vm_d' 'Km_d'});
set(kineticlawObj,'SpeciesVariableNames', {'a'});
5. Verify that the reaction rate is expressed correctly in the reaction object ReactionRate property.

get (reactionObj, 'ReactionRate')

MATLAB® returns:

ans =

Vm_d*a/(Km_d + a)

### Add a Reaction without a Kinetic Law

Create a model, add a reaction, and specify ReactionRate without a kinetic law.

1. Create a model object, and then add a reaction object.

modelObj = sbiomodel('my_model');
reactionObj = addreaction(modelObj, 'a + b -> c + d');
2. Specify ReactionRate and verify the assignment.

set (reactionObj, 'ReactionRate', 'k*a');
get(reactionObj, 'ReactionRate')

MATLAB returns:

ans =

k*a
3. You cannot simulate the model until you add the parameter k to the modelObj.

SimBiology adds the parameter to the modelObj with default Value = 1.0 for the parameter.

### Define a Custom Hill Kinetic Law that Works with Dimensional Analysis

This example shows how to define a custom reaction rate for the Hill kinetics that is compatible with DimensionalAnalysis feature of SimBiology.

This example is useful especially if you are using the built-in Hill kinetic law, but have the kinetic reaction with a non-integer exponent and cannot verify the model because dimensional analysis failed. The built-in Hill kinetic law has the following expression: $\frac{{V}_{m}*{S}^{n}}{{K}_{p}+{S}^{n}}$. Suppose ${K}_{p}={K}_{h}{}^{n}$, then you can rewrite the equation as follows: $\frac{{V}_{m}}{{\left(\frac{{K}_{h}}{S}\right)}^{n}+1}$. The redefined Hill kinetic equation is compatible with Dimensional Analysis and allows you to have a non-integer exponent.

Create a SimBiology model.

m1 = sbiomodel('m1');

Add a compartment, two species, and a reaction.

r1 = addreaction(m1, 'a -> b');

Add a predefined a Hill kinetic law for the reaction.

Display the rate expression of the built-in kinetic law.

k1.Expression
ans =

Vm*S^n/(Kp + S^n)

Define parameters, values, and units.

set(k1, 'ParameterVariableNames', {'Vm','n','Kp'});
set(k1, 'SpeciesVariableNames', {'a'});
set(s1, 'InitialAmount', 2.0);

set(s1, 'InitialAmountUnits', 'mole/liter');
set(s2, 'InitialAmountUnits', 'mole/liter');
set(c1, 'CapacityUnits', 'liter');
set(p1, 'ValueUnits', 'mole/liter/second');
set(p2, 'ValueUnits', 'dimensionless');
set(p3, 'ValueUnits', 'mole/liter');

Verify the model.

verify(m1)
Error using SimBiology.Model/verify
--> Error reported from Dimensional Analysis:
Dimensional analysis failed for reaction 'a -> b'.
When using the power function, both the base and exponent must be dimensionless or the exponent must be an explicit
integer constant (for example 2 in 'x^2').

You are seeing the error message because SimBiology only allows exponentiation of any dimensionless quantity to any dimensionless power.

Redefine the reaction rate so that it is compatible with dimensional analysis and allows a non-integer exponent.

r1.ReactionRate = 'Vm / ( (Kh/a)^n + 1 )';
k1.KineticLaw = 'Unknown';

Define the value and units for Kh parameter.

set(p4, 'ValueUnits', 'mole/liter');

Verify the model.

verify(m1)

You no longer see the error message.

Simulate the model.

[t,x,names] = sbiosimulate(m1);

Plot the results.

plot(t,x);
xlabel('Time');
ylabel('Amount');
legend(names);