The control of phenotype: connecting enzyme variation to physiology

Metabolic control analysis (Kacser & Burns (1973). Symp. Soc. Exp. Biol. 27, 65-104; Heinrich & Rapoport (1974). Eur. J. Biochem. 42, 89-95) was developed for the understanding of multi-enzyme networks. At the core of this approach is the flux summation theorem. This theorem implies that there is an invariant relationship between the control coefficients of enzymes in a pathway. One of the main conclusions that has been derived from the summation theorem is that phenotypic robustness to mutation (e.g. dominance) is an inherent property of metabolic systems and hence does not require an evolutionary explanation (Kacser & Burns (1981). Genetics. 97, 639-666; Porteous (1996). J. theor. Biol. 182, 223-232). Here we show that for mutations involving discrete changes (of any magnitude) in enzyme concentration the flux summation theorem does not hold. The scenarios we examine are two-enzyme pathways with a diffusion barrier, two enzyme pathways that allow for enzyme saturation and two enzyme pathways that have both saturable enzymes and a diffusion barrier. Our results are extendable to sequential pathways with any number of enzymes. The fact that the flux summation theorem cannot hold in sequential pathways casts serious doubts on the claim that robustness with respect to mutations is an inherent property of metabolic systems.