A new class of biochemical oscillator models based on competitive binding.

It has been noted that single-enzyme systems can undergo strongly damped transient oscillations. In this paper, we present a nonlinear dynamics analysis of oscillations in undriven chemical systems. This analysis allows us to classify transient oscillations into two groups. In the first group, oscillations arise from rapid oscillatory relaxation to a slower transient relaxation mode. These oscillations are always strongly damped. In the second group, it is the slowest relaxation mode which is implicated in the oscillations so these can be very lightly damped. This second class of oscillations has not previously been studied in enzymology. We show that a remarkably simple single-enzyme system, namely competitive inhibition with substrate flow, generates transient oscillations which belong to the second class. In an attempt to design an experimentally realizable version of this model, we then discovered a system which is capable of sustained oscillations. In this experimentally realizable model, two substrates compete to bind to a macromolecule. The flow of one substrate is controlled by a simple feedback device. Sustained oscillations are observed over a very wide range of parameters. In both models, oscillations are favored by a wide disparity in rates of binding and dissociation of the two substrates to the macromolecule.