conservationMatrix[s] returns the conservation matrix of a system of reactions, given the stoichiometry matrix s.
See also SBMLConservationMatrix.New in MathSBML version 2.5.6.
The equations used in the implementation and given below here are explained and derived in great detail in the following reference which the authors of MathSBML gratefully acknowledge.
Herbert M Sauro & Brian Ingalls, "Conservation analysis in biochemical networks: computational issues for software writers." Biophysical Chemistry 109:1-15 (2004). [publisher's web site]
The stoichiometry matrix is calculated from the stoichiometry values of the reactants and products in a model's reactions. Every species and every reaction in the model is represented in the matrix. The columns represent the reactions, in the order in which they are defined in the model, and the rows represent the species, in order, as they are defined in the model. Verbose listings will identify the species by name in the output.
The mass balance equations are calculated as
The stoichiometry matrix can be partitioned as
Numerically we can compute