Stoichiometric Analysis¶

Preliminaries¶

A network of $m$ chemical species and $n$ reactions can be described by the $m$ by $n$ stochiometry matrix $\mathbf{N}$ . $\mathbf{N}_{i,j}$ is the net number of species $i$ produced or consumed in reaction $j$ . The dynamics of the network are described by

$\frac{d}{dt}\mathbf{s}(t) = \mathbf{N} \mathbf{v}(\mathbf{s}(t),\mathbf{p},t),$

where $\mathbf{s}$ is the vector of species concentrations, $\mathbf{p}$ is a vector of time independent parameters, and $t$ is time.

Each structural conservation, or interchangably, conserved sum (e.g. conserved moiety) in the network coresponds to a lineraly dependent row in the stoichiometry matrix $\mathbf{N}$ .

If there are conserved sums, then the row rank, $r$ of $N$ is $< m$ , and the stochiometry matrix $N$ may first be re-ordered such that the first $r$ are linearly independent, and the remaining $m-r$ rows are linear combinations of the first $r$ rows. The reduced stochiometry matrix $\mathbf{N_R}$ is then formed from the first $r$ rows of $N$ . Finally, $N$ may be expressed as a product of the $m \times r$ link matrix $\mathbf{L}$ and the $r \times n$ $\mathbf{N_R}$ matrix:

$\mathbf{N} = \mathbf{L}\mathbf{N_R}.$

The link matrix $\mathbf{L}$ has the form

$\mathbf{L} = \left[ \begin{array}{c} \mathbf{I}_{r} \\ \mathbf{L}_0 \end{array} \right],$

where $\mathbf{I}_{r}$ is the $r \times r$ identity matrix and $\mathbf{L}_0$ is a $(m-r) \times r$ matrix.

Methods¶

The following methods are related to the analysis of the stoichiometric matrix.

`ExecutableModel.getStoichiometryMatrix`()	Returns the current stoichiomentry matrix, a $n \times m$ matrix where $n$ is the number of species which take place in reactions (floating species) and $m$ is the number of reactions.
`RoadRunner.getLinkMatrix`()	Returns the full link matrix, L for the current model. The Link matrix is an m by r matrix where m
`RoadRunner.getNrMatrix`()	Returns the reduced stoichiometry matrix, $N_R$ , which wil have only r rows where r is the rank of
`RoadRunner.getConservationMatrix`()	Returns a conservation matrix $\Gamma$ which is a $c \times m$ matrix
`RoadRunner.getL0Matrix`()	Returns the L0 matrix for the current model. The L0 matrix is an (m-r) by r matrix that expresses
`ExecutableModel.getNumConservedMoieties`()	Returns the number of conserved moieties in the model.
`ExecutableModel.getConservedMoietyIds`([index])	Returns a vector of conserved moiety identifier symbols.
`ExecutableModel.getConservedMoietyValues`([index])	Returns a vector of conserved moiety volumes.
`ExecutableModel.setConservedMoietyValues`(...)	Sets a vector of conserved moiety values.