Self‐Oscillations in Glycolysis 1. A Simple Kinetic Model

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 i