Temporal self-organization in biochemical systems: periodic behavior vs. chaos.

The patterns of temporal self-organization in regulated biochemical systems are examined. Simple periodic oscillations are the most frequent type of such organization, as exemplified by glycolytic oscillations in yeast and muscle and by the periodic synthesis of adenosine 3',5'-cyclic monophosphate in Dictyostelium discoideum amoebas. These phenomena originate, respectively, from the periodic operation of the product-activated phosphofructokinase and adenylate cyclase reactions. The analysis of a model for a multiply regulated biochemical system shows more complex oscillatory phenomena, e.g., the coexistence between two stable periodic regimes for the same set of parameter values (birhythmicity) and chaos. The latter phenomenon of aperiodic oscillations occurs in a narrow range of parameter values and is much less frequent than simple or complex periodic behavior. It is suggested that a sufficient condition for the occurrence of birhythmicity and chaos in a regulated biological system subjected to a constant environment (i.e., in the absence of periodic forcing) may be the simultaneous presence and interaction of two mechanisms capable of producing oscillations.