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  • Title: [The simplest biochemical autogenerator--open enzyme reaction, S in equilibrium with P, with substrate inhibition].
    Author: Kaĭmachnikov NP, Sel'kov EE.
    Journal: Biofizika; 1976; 21(3):428-33. PubMed ID: 963090.
    Abstract:
    Considered is the mathematical model of an open reversible enzymic reaction S equilibrium P with enzyme E inhibited by excess substrate S. The quasi-stationary output characteristic of the reaction, v(p), is shown to be of hysteretic Z-shaped form. It gives the rate of the product formation, v, as a function of of p=P], provided d[S]dt=0. Owing to hysteresis of the characteristic the reaction can exhibit 1 to 3 stationary states of different stability. Under specified conditions there occur self-oscillations in the reaction. Multiple stationary states and self-oscillations take place only with positive v, i.e. when the net flux is from S to P. The reaction considered is the simplest of all biochemical oscillators studied thus far.
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