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

Michael A. Savageau

Research output: Contribution to journalArticle

66 Citations (Scopus)

Abstract

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
JournalBioSystems
Volume47
Issue number1-2
DOIs
StatePublished - Jun 1998
Externally publishedYes

Fingerprint

Fractals
Kinetic theory
enzymatic reactions
Kinetic Theory
biochemical pathways
Fractal
Pathway
Enzymes
Kinetics
enzyme
kinetics
Reversibility
State Equation
Design
Chemical Kinetics
closed loop systems
Reaction kinetics
Power Law

ASJC Scopus subject areas

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

Cite this

Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways. / Savageau, Michael A.

In: BioSystems, Vol. 47, No. 1-2, 06.1998, p. 9-36.

Research output: Contribution to journalArticle

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