Difference between revisions of "Mass Conservation Analysis"
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Revision as of 16:27, 4 April 2013
Mass conservation analysis
The mass conservation analysis involves the decomposition of the stoichiometric matrix N into the product of two matrixes:
- N = L × NR,
where NR 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 N1, 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 NR. 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.
