Time lag in a model of a biochemical reaction sequence with end product inhibition

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Abstract

The model studied is that of Goodwin, in which all but one of the reactions obey linear kinetics, while the end-product inhibits the first reaction in a term of Michaelis-Menten form, with Hill coefficient ϱ: z=−∞txn(T)G(t−T)dtThe results obtained relate to time lag in the off diagonal terms in these equations. The time lag is taken in distributed form, for example replacing xn in the first equation by dxtdt=k1xt−−1−b1xt, i=2, …n.For any non-negative G, time lag in these terms can not destabilize the equilibrium point in the case ϱ = 1. For a particular class of functions G one can obtain some insight into the consequences of time lag by relating the model to that with a longer loop of reactions. Then known results can be used for general ϱ and n.

References (13)

  • B.C. Goodwin

    Adv. Enzyme Regul.

    (1965)
  • N. MacDonald

    J. theor. Biol.

    (1977)
  • D.J. Allwright
  • J.M. Cushing

    S.I.A.M. J. math. Anal.

    (1975)
  • Z. Grossman et al.
  • S.P. Hastings et al.

    J. dif. Egns

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

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