Elsevier

Journal of Theoretical Biology

Volume 111, Issue 2, 21 November 1984, Pages 303-321
Journal of Theoretical Biology

Mathematical modelling of dynamics and control in metabolic networks. II. Simple dimeric enzymes

https://doi.org/10.1016/S0022-5193(84)80212-XGet rights and content

The dynamics of enzyme cooperativity are examined by studying a homotropic dimeric enzyme with identical reaction sites, both of which follow irreversible Michaelis-Menten kinetics. The problem is approached via scaling and linearization of the governing mass action kinetic equations. Homotropic interaction between the two sites are found to depend on three dimensionless groups, two for the substrate binding step and one for the chemical transformation. The interaction between the two reaction sites is shown capable of producing dynamic behavior qualitatively different from that of a simple Michaelis-Menten system; when the two sites interact to increase enzymatic activity over that of two independent monomeric enzymes (positive cooperativity) damped oscillatory behavior is possible, and for negative cooperativity in the chemical transformation step a multiplicity of steady states can occur, with one state unstable and leading to runaway behavior. Linear analysis gives significant insight into system dyanmics, and their parametric sensitivity, and a way to identify regions of the parameter space where the approximate quasi-stationary and quasi-equilibrium analyses are appropriate.

References (20)

  • BowenJ.R. et al.

    Chem. Engng. Sci.

    (1963)
  • HammesG.G. et al.
  • HeinekenF.G. et al.

    Math. Biosci.

    (1967)
  • LaneA.N.

    J. theor. Biol.

    (1982)
  • MeiskeW.

    Math. Biosci.

    (1978)
  • PalssonB.O. et al.

    J. theor. Biol.

    (1984)
  • SrereP.A.

    Biochem. Medicine

    (1970)
  • VolkensteinM.V. et al.

    Biochim. biophys. Acta.

    (1966)
  • AdairC.S.

    J. biol. Chem.

    (1925)
  • AtkinsonD.

    Cellular Energy Metabolism and its Regulation

    (1977)
There are more references available in the full text version of this article.

Cited by (0)

View full text