Synergism analysis of biochemical systems. I. Conceptual framework

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 specific synergisms. This work presents a conceptual framework and formalism that fulfil these purposes. The synergism between perturbations of a pair of parameters is quantified as the difference 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 quantified 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 coefficients, measure how steeply the responses diverge from linearity/additivity or power-law/multiplicativity. The formalism now presented allows evaluating (log-)synergism coefficients for systemic steady-state responses, and relates these coefficients to intrinsic kinetic properties of the underlying processes. A robust homeostasis of metabolite concentrations requires that these have moderate systemic log- and relative-synergism coefficients.