Stoichiometric Matrix (analysis)

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Analysis title
File:Stoichiometric-Matrix-analysis-icon.png Stoichiometric Matrix
Provider
Institute of Systems Biology
Plugin
biouml.plugins.modelreduction (Model reduction plug-in)

Description

The stoichiometric matrix N provides the linear relationship of the model between the flux rates of the (enzymatic) reactions and the derivatives of the reactant (enzyme) concentrations.

If a reaction network has n reactions and m participating molecular species then the dynamic mass balance equation can be written as

DAE-models-Stoichiometric-Matrix-stoich1.png

where v is the flux vector and S is the concentration vector:

DAE-models-Stoichiometric-Matrix-stoich2.png

Example

Consider the following system of reactions:

DAE-models-Stoichiometric-Matrix-stoich3.png

This systems comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as:

DAE-models-Stoichiometric-Matrix-stoich4.png

where the rows correspond to S1, S2, S3, S4 and S5, respectively. Note that the process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the stoichiometries in the second reaction simplify when included in the matrix.

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