Biochemical Systems Theory: Alternative Views of Metabolic Control

Abstract

An appropriate language or formalism for the analysis of complex biochemical systems has been sought for several decades. The necessity for such a formalism results from the large number of interacting components in biochemical systems and the complex nonlinear character of these interactions. The Power-Law Formalism (Savageau, 1969b) is an example of such a language that underlies several recent attempts to develop an understanding of integrated biochemical systems. This formalism provides the basis for a theory, which is called Biochemical Systems Theory. Several different strategies of representation are possible within Biochemical Systems Theory. Among these, the “S-system” representation is the most useful, as judged by a variety of objective criteria (Sorribas and Savageau, 1989abc). This chapter first describes the predominant features of the S-system representation. The mathematical form of the S-system is deduced from the biochemical network in a straightforward fashion. The parameters of the S-system — rate constants and kinetic orders — are readily related to experimental data. The steady-state behaviour is characterized by a set of linear algebraic equations that can be solved symbolically or numerically. The differential equations that characterize the dynamic behaviour can be solved with very efficient numerical techniques. Methods for making well-controlled comparisons of alternative designs have been developed and applied to several classes of biochemical systems. In many cases these applications have led to more specialized theories with strong predictive capabilities. Specific predictions of these theories have been confirmed by experimental results from a number of independent laboratories. This chapter presents detailed comparisons between the S-system representation and other variants within Biochemical Systems Theory. These comparisons are made on the basis of objective criteria that characterize the efficiency, power, clarity and scope of each representation. Two of the variants within Biochemical Systems Theory are intimately related to other approaches for analysing biochemical systems, namely the Metabolic Control Theory of Kacser & Burns (1973) and of Heinrich & Rapoport (1974) and the Flux-Oriented Theory of Crabtree & Newsholme (1987). It is hoped that the comparisons presented here will result in a deeper understanding of the relationships between these variants.