Pii: S0025-5564(99)00056-5

The detection of synergisms ± deviations from additive or linear behaviour ± is often an important step in uncovering mechanisms of biochemical processes. Yet, a theoretical background for systemic analysis of synergisms in metabolic networks is lacking. Based on suitable mathematical models, such a theoretical approach should allow predicting synergisms and analysing what mechanistic features contribute to speci®c synergisms. This work presents a conceptual framework and formalism that ful®l these purposes. The synergism between perturbations of a pair of parameters is quanti®ed as the di€erence between the response to the simultaneous perturbation of both parameters and the sum of the individual responses to the perturbations of each parameter. A generalisation measures deviations from multiplicative or power-law behaviour. These deviations were called log-synergisms, as in logarithmic coordinates they are quanti®ed in the same way as the synergisms are in Cartesian coordinates. For small perturbations, synergisms and log-synergisms are approximately proportional to the second derivatives (in Cartesian and logarithmic coordinates, respectively) of the observable to the perturbed parameter(s). These derivatives, here called synergism or log-synergism coecients, measure how steeply the responses diverge from linearity/additivity or power-law/multiplicativity. The formalism now presented allows evaluating (log-)synergism coecients for systemic steady-state responses, and relates these coecients to intrinsic kinetic properties of the underlying processes. A robust homeostasis of metabolite concentrations requires that these have moderate systemic logand relative-synergism coecients. Ó 2000 Elsevier Science Inc. All rights reserved.