Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system.

Abstract

The effect of a coupling between 2 instability-generating mechanisms is analyzed on a model biochemical system. The system considered is that of 2 allosteric enzymes coupled in series and activated by their respective products. In addition to simple periodic oscillations, the system can exhibit a variety of new modes of dynamic behavior: coexistence between 2 stable periodic regimes (birhythmicity), random oscillations (chaos), and coexistence of a stable periodic regime with a stable steady state (hard excitation) or with chaos. The relationship between these patterns of temporal self-organization is analyzed as a function of the control parameters of the model. Chaos and birhythmicity appear to be rare events in comparison with simple periodic behavior. Relevance of these results is discussed with respect to the regularity of most biological rhythms.