View source for Mass Conservation Analysis

;Analysis title
:[[File:DAE-models-Mass-Conservation-Analysis-icon.png]] Mass Conservation Analysis
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:[[Institute of Systems Biology]]
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=== Mass conservation analysis ===

The mass conservation analysis involves the decomposition of the stoichiometric matrix ''N'' into the product of two matrixes:

:: ''N = L × N<sub>R</sub>'',

where ''N<sub>R</sub>'' is the reduced stoichiometry consisting of the linearly independent rows of the matrix ''N'' and ''L'' is the link matrix.

To find such decomposition, we use the Gauss-Jordan method detecting the left null space ''Γ'' of the matrix ''N''<sup>1</sup>, so that

:: ''Γ × N ''= 0.

The matrix ''Γ'' specifies the conservation laws of the system, ie. linear combinations of species concentrations which remain constant over time. Generation of the matrix ''Γ'' is based on the premultiplication of ''N'' by a series of elementary matrixes. In particular, rows of this matrix and hence the species order are permutated. Thus, eliminating from the matrix ''N'' all rows corresponding to the species which result in the null space, we find the matrix ''N<sub>R</sub>''. In addition, the matrix ''L'' consists of the identity matrix rows and rows defined by ''Γ'' arranged according to the species order in the matrix ''N''.
==== References ====

# HM Sauro, B Ingalls, "Conservation analysis in biochemical networks: computational issues for software writers". Biophysical Chemistry, 109(1): 1-15, 2004.

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