Mass Conservation Analysis

Analysis title

File:DAE-models-Mass-Conservation-Analysis-icon.png Mass Conservation Analysis

Provider

Institute of Systems Biology

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 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 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

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