Classic and contemporary approaches to modeling biochemical reactions

Recent interest in modeling biochemical networks raises questions about the relationship between often complex mathematical models and familiar arithmetic concepts from classical enzymology, and also about connections between modeling and experimental data. This review addresses both topics by familiarizing readers with key concepts (and terminology) in the construction, validation, and application of deterministic biochemical models, with particular emphasis on a simple enzyme-catalyzed reaction. Networks of coupled ordinary differential equations (ODEs) are the natural language for describing enzyme kinetics in a mass action approximation. We illustrate this point by showing how the familiar Briggs-Haldane formulation of Michaelis-Menten kinetics derives from the outer (or quasi-steady-state) solution of a dynamical system of ODEs describing a simple reaction under special conditions. We discuss how parameters in the Michaelis-Menten approximation and in the underlying ODE network can be estimated from experimental data, with a special emphasis on the origins of uncertainty. Finally, we extrapolate from a simple reaction to complex models of multiprotein biochemical networks. The concepts described in this review, hitherto of interest primarily to practitioners, are likely to become important for a much broader community of cellular and molecular biologists attempting to understand the promise and challenges of "systems biology'' as applied to biochemical mechanisms.