Pii: S0025-5564(99)00057-7

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 bene®ts from the more e€ective 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 ®rst-order sensitivity analysis and new relationships for (log-)synergism coecients 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, ̄uxes and/or parameters. This treatment, which generalises RederÕs 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 ̄ux conservation at steady-state to simplify synergism analysis. Issues of numerical e€ectiveness are brie ̄y 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. Ó 2000 Elsevier Science Inc. All rights reserved.