Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways

Michael A. Savageau

Research output: Contribution to journalArticlepeer-review

73 Scopus citations


Recent evidence has shown that elementary bimolecular reactions under dimensionally-restricted conditions, such as those that might occur within cells when reactions are confined to two-dimensional membranes and one-dimensional channels, do not follow traditional mass-action kinetics, but fractal kinetics. The power-law formalism, which provides the context for examining the kinetics under these conditions, is used here to examine the implications of fractal kinetics in a simple pathway of reversible reactions. Starting with elementary chemical kinetics, we proceed to characterise the equilibrium behaviour of a simple bimolecular reaction, derive a generalised set of conditions for microscopic reversibility, and develop the fractal kinetic rate law for a reversible Michaelis-Menten mechanism. Having established this fractal kinetic framework, we go on to analyse the steady-state behaviour and temporal response of a pathway characterised by both the fundamental and quasi-steady-state equations. These results are contrasted with those for the fundamental and quasi-steady-state equations based on traditional mass-action kinetics. Finally, we compare the accuracy of three local representations based on both fractal and mass-action kinetics. The results with fractal kinetics show that the equilibrium ratio is a function of the amount of material in a closed system, and that the principle of microscopic reversibility has a more general manifestation that imposes new constraints on the set of fractal kinetic orders. Fractal kinetics in a biochemical pathway allow an increase in flux to occur with less accumulation of pathway intermediates and a faster temporal response than is the case with traditional kinetics. These conclusions are obtained regardless of the level of representation considered. Thus, fractal kinetics provide a novel means to achieve important features of pathway design.

Original languageEnglish (US)
Pages (from-to)9-36
Number of pages28
Issue number1-2
StatePublished - Jun 1998
Externally publishedYes

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Biotechnology
  • Drug Discovery


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