Synergism analysis of biochemical systems. II. Tensor formulation and treatment of stoichiometric constraints

The previous paper outlined a conceptual and mathematical framework for synergism analysis of kinetic models. Though the formalism presented there is adequate for studying simple models, the analysis of large-scale models benefits from the more effective formulation achieved in this work. The present formulation is based on simple tensor operations and takes advantage of the analogy between the formalisms for synergism and log-synergism analysis presented before. Well-known relationships of first-order sensitivity analysis and new relationships for (log-)synergism coefficients of various steady-state properties are cast in the new formal setting. The formalism is then extended to models that are subject to constraints between variables, fluxes and/or parameters. This treatment, which generalizes Reder's concept of link matrices, is applied to networks that include moiety conservation cycles [C. Reder, Metabolic control theory: a structural approach, J. Theor. Biol. 135 (1988) 175]. It is also used to take advantage of flux conservation at steady-state to simplify synergism analysis. Issues of numerical effectiveness are briefly discussed, and the theory illustrated with the study of synergistic behaviour in the metabolism of reactive oxygen species and of a scheme of dynamic channelling.