Mass Conservation Analysis
- Analysis title
- Mass Conservation Analysis
- Provider
- Institute of Systems Biology
- Class
MassConservationAnalysis
- Plugin
- biouml.plugins.modelreduction (Model reduction plug-in)
Mass conservation analysis
The mass conservation analysis involves the decomposition of the stoichiometric matrix N into the product of two matrixes:
- N = L × N_{R},
where N_{R} 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^{1}, 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_{R}. 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.