## Determining the Stoichiometry Matrix for a Model

### What Is a Stoichiometry Matrix?

A stoichiometry matrix lets you easily determine:

• The reactants and products in a specific reaction in a model, including the stoichiometric value of the reactants and products

• The reactions that a specific species is part of, and whether the species is a reactant or product in that reaction

A stoichiometry matrix is an M-by-R matrix, where M equals the total number of species in a model, and R equals the total number of reactions in a model. Each row corresponds to a species, and each column corresponds to a reaction.

The matrix indicates which species and reactions are involved as reactants and products:

• Reactants are represented in the matrix with their stoichiometric value at the appropriate location (row of species, column of reaction). Reactants appear as negative values.

• Products are represented in the matrix with their stoichiometric value at the appropriate location (row of species, column of reaction). Products appear as positive values.

• All other locations in the matrix contain a `0`.

For example, consider a `model object` containing two reactions. One reaction (named `R1`) is equal to `2 A + B -> 3 C`, and the other reaction (named `R2`) is equal to `B + 3 D -> 4 A`. The stoichiometry matrix is:

``` R1 R2 A -2 4 B -1 -1 C 3 0 D 0 -3```

### Retrieving a Stoichiometry Matrix for a Model

Retrieve a stoichiometry matrix for a model by passing the ```model object``` as an input argument to the `getstoichmatrix` method.

1. Read in `m1`, a model object, using `sbmlimport`:

`m1 = sbmlimport('lotka.xml');`
2. Get the stoichiometry matrix for `m1`:

```[M,objSpecies,objReactions] = getstoichmatrix(m1) M = (2,1) 1 (2,2) -1 (3,2) 1 (3,3) -1 (4,3) 1 objSpecies = 'x' 'y1' 'y2' 'z' objReactions = 'Reaction1' 'Reaction2' 'Reaction3'```
3. Convert the stoichiometry matrix from a sparse matrix to a `full` matrix to more easily see the relationships between species and reactions:

`M_full = full(M)`
```M_full = 0 0 0 1 -1 0 0 1 -1 0 0 1```
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