Biochemical systems theory: operational differences among variant representations and their significance.

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 non-linear character of these interactions. The Power-Law Formalism, an example of such a language, underlies several recent attempts to develop an understanding of integrated biochemical systems. It is the simplest representation of integrated biochemical systems that has been shown to be consistent with well-known growth laws and allometric relationships--the most regular, quantitative features that have been observed among the systemic variables of complex biochemical systems. The Power-Law Formalism provides the basis for Biochemical Systems Theory, which includes several different strategies of representation. Among these, the synergistic-system (S-system) representation is the most useful, as judged by a variety of objective criteria. This paper first describes the predominant features of the S-system representation. It then 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 analyzing biochemical systems, namely Metabolic Control Theory and Flux-Oriented Theory. It is hoped that the comparisons presented here will result in a deeper understanding of the relationships among these variants. Finally, some recent developments are described that demonstrate the potential for further growth of Biochemical Systems Theory and the underlying Power-Law Formalism on which it is based.