Self‐Oscillations in Glycolysis 1. A Simple Kinetic Model

Abstract

The paper describes a simple kinetic model of an open monosubstrate enzyme reaction with substrate inhibition and product activation. A comparison between the model and the phosphofructokinase reaction shows a close resemblance between their dynamical properties. This makes it possible to explain qualitatively most experimental data on single‐frequency oscillations in glycolysis. A mathematical analysis of the model has shown the following. In the model, at a definite relationship between the parameters, self‐oscillations arise. The condition of self‐excitation is satisfied more readily with a lower source rate, larger product sink rate constants, lower product‐enzyme affinity and higher enzyme activity. Self‐oscillations exist only in a certain range of values of the parameter determining the degree of substrate inhibition. This range increases with decreasing source rate. Too strong or, conversely, too weak substrate inhibition leads to damped oscillations. The period of self‐oscillations depends on the degree of substrate inhibition, the source rate, the sink rate constant, the enzyme activity, the affinity of the substrate and the product for the enzyme; it decreases with an increase in these values. With an increase in the relative sink rate constant the steady state amplitude of self‐oscillations initially increases until a definite maximum is reached and then drops to zero. A self‐oscillatory state in the phosphofructokinase reaction exists only when the maximum rate of this reaction is essentially higher than the source rate, and lower than the maximum rate of the reactions controlling the sink of the products. An experimental investigation of self‐oscillations in the phosphofructokinase reaction may be considerably simplified by using a reconstituted system consisting of a small number of reactions with an irreversible sink of the products and artificial substrate supply. In this case the above relationship (section 6) should hold.