Determining the Stoichiometry Matrix for a Model

What Is a Stoichiometry Matrix?

A stoichiometry matrix provides stoichiometric information about reactants and products in model reactions. It 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.

Read in m1, a model object, using sbmlimport:
```
m1 = sbmlimport('lotka.xml');
```

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'

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
```