Autonomous chaotic behaviour of the slime mould Dictyostelium discoideum predicted by a model for cyclic AMP signalling

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Abstract
How sustained oscillations lose their periodicity and thus give rise to chaos was first analysed in mathematical models, then observed in chemical systems such as the Belousov-Zhabotinsky reaction where chaos is autonomous because it originates from endogenous kinetic mechanisms. In contrast, chaos can also be obtained by periodically forcing an oscillatory system, as shown, for example, in cardiac cells and yeast glycolysis. Biochemical evidence for autonomous chaos has been obtained both in vitro for the peroxidase reaction and in enzymatic models not based directly on experimental systems. We report here the occurrence of autonomous chaos in a realistic model for the cyclic AMP signalling system of the slime mould Dictyostelium discoideum, based on receptor modification. This model is also capable of bursting, a phenomenon characteristic of some pacemaker neurones such as R15 in Aplysia. Whereas bursting has not been observed in D. discoideum, our model suggests that 'aperiodic signalling' in the mutant Fr17 provides the first example of autonomous chaos occurring spontaneously at the cellular level.