Allosteric and related phenomena: An analysis of sigmoid and non-hyperbolic functions

https://doi.org/10.1016/0022-5193(75)90023-5Get rights and content

Abstract

The graphs of rational polynomial functions are of considerable importance in enzyme kinetics but a full analysis of the turning points and inflexions is only possible for 2 : 2 functions due to the complexity of the first and second derivatives for 3 : 3 and higher degree functions. This paper describes a simple method which can be applied to rational functions of any degree in order to discover the relationship between the coefficients necessary for the curve to have an initial sigmoid inflexion and a final inflexion (which implies a maximum in the graph). This technique is then applied to the current allosteric models. In addition, a full analysis of the 2 : 2 function with a maximum is given together with a method of separating this type of behaviour (partial substrate inhibition) from the 1 : 2 function (dead-end substrate inhibition).

References (28)

  • G.S. Adair

    J. biol. Chem

    (1925)
  • S. Ainsworth

    J. theor. Biol

    (1968)
  • S. Cha

    J. biol. Chem

    (1968)
  • W.W. Cleland

    Biochim. biophys. Acta

    (1963)
    W.W. Cleland

    Biochim. biophys. Acta

    (1963)
    W.W. Cleland

    Biochim. biophys. Acta

    (1963)
  • W. Ferdinand

    Biochem. J

    (1966)
  • E.T. Harper

    J. theor. Biol

    (1971)
  • A.V. Hill

    J. Physiol., Lond

    (1910)
  • E.L. King et al.

    J. phys. Chem

    (1956)
  • R.B. Parker et al.

    J. Pharmac

    (1971)
  • W.D. Paton
  • J. Wyman

    J. Am. chem. Soc

    (1967)
  • G.R. Ainsle et al.

    J. biol. Chem

    (1972)
  • E.J. Ariens
  • D.E. Atkinso

    Rev. Biochem

    (1966)
  • Cited by (21)

    View all citing articles on Scopus
    View full text