Example - Determining Conserved Moieties - MATLAB & Simulink Example

Load the Goldbeter Mitotic Oscillator project, which includes the variable m1, a model object:
```
sbioloadproject Goldbeter_Mitotic_Oscillator_with_reactions
```
The m1 model object appears in the MATLAB Workspace.

Display the species information:

m1.Compartments.Species

SimBiology Species Array

Index:  Compartment:  Name:  InitialAmount:  InitialAmountUnits:
 1       unnamed       C        0.01              
 2       unnamed       M        0.01              
 3       unnamed       Mplus    0.99              
 4       unnamed       Mt       1                 
 5       unnamed       X        0.01              
 6       unnamed       Xplus    0.99              
 7       unnamed       Xt       1                 
 8       unnamed       V1       0                 
 9       unnamed       V3       0                 
 10      unnamed       AA       0

Display the reaction information:

m1.Reactions

SimBiology Reaction Array

   Index:    Reaction:
   1         AA -> C
   2         C -> AA
   3         C + X -> AA + X
   4         Mplus + C -> M + C
   5         M -> Mplus
   6         Xplus + M -> X + M
   7         X -> Xplus

Use the simplest form of the sbioconsmoiety function and display the results. The default call to sbioconsmoiety, in which no algorithm is specified, uses an algorithm based on row reduction.
```
[g sp] = sbioconsmoiety(m1)
```
```
g =

     0     1     1     0     0     0
     0     0     0     1     1     0
     0     0     0     0     0     1


sp = 

    'C'
    'M'
    'Mplus'
    'X'
    'Xplus'
    'AA'
```
The columns in g are labeled by the species sp. Thus the first row describes the conserved relationship, M + Mplus. Notice that the third row indicates that the species AA is conserved, which is because AA is constant (ConstantAmount = 1).
Call sbioconsmoiety again, this time specifying the semipositive algorithm to explore conservation relations in the model. Also specify to return the conserved moieties in a cell array of strings, instead of a matrix.
```
cons_rel = sbioconsmoiety(m1,'semipos','p')
```
```
cons_rel = 

    'AA'
    'X + Xplus'
    'M + Mplus'
```
Use the 'link' option to study the dependent and independent species.
```
[SI,SD,L0,NR,ND] = sbioconsmoiety(m1, 'link');
```
Show the list of independent species:
```
SI
```
```
SI = 

    'C'
    'M'
    'X'
```

Show the list of dependent species:

SD

SD = 

    'Mplus'
    'Xplus'
    'AA'

Show the link matrix relating SD and SI by converting the L0 output from a sparse matrix to a full matrix:

L0_full = full(L0)

L0_full =

         0   -1.0000         0
         0         0   -1.0000
         0         0         0

Show the independent stoichiometry matrix, N_R by converting the NR output from a sparse matrix to a full matrix:

NR_full = full(NR)

NR_full =

     1    -1    -1     0     0     0     0
     0     0     0     1    -1     0     0
     0     0     0     0     0     1    -1

Show the dependent stoichiometry matrix, N_D by converting the ND output from a sparse matrix to a full matrix:

ND_full = full(ND)

ND_full =

     0     0     0    -1     1     0     0
     0     0     0     0     0    -1     1
     0     0     0     0     0     0     0

Determining Conserved Moieties

Determining the Adjacency Matrix for a Model

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