A NEW CLASS OF BIOCHEMICAL OSCILLATOR MODELS BASED ON COMPETITIVE-BINDING

It has been noted that single-enzyme systems can undergo strongly damp ed transient oscillations. In this paper, we present a nonlinear dynam ics analysis of oscillations in undriven chemical systems. This analys is allows us to classify transient oscillations into two groups. In th e first group, oscillations arise from rapid oscillatory relaxation to a slower transient relaxation mode. These oscillations are always str ongly damped. In the second group, it is the slowest relaxation mode w hich is implicated in the oscillations so these can be very lightly da mped. This second class of oscillations has not previously been studie d in enzymology. We show that a remarkably simple single-enzyme system , namely competitive inhibition with substrate flow, generates transie nt oscillations which belong to the second class. In an attempt to des ign an experimentally realizable version of this model, we then discov ered a system which is capable of sustained oscillations. In this expe rimentally realizable model, two substrates compete to bind to a macro molecule. 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 dispar ity in rates of binding and dissociation of the two substrates to the macromolecule.