Periodicity and chaos in the response of Halobacterium to temporal light gradients

Abstract

Halobacteria spontaneously reverse their swimming direction about every 10 s. This periodicity can be altered by light stimuli. We found that temporal exponential changes in light intensity, depending on wavelength and sign, lengthened or shortened the intervals between reversals. Within a limited range of steepness, light gradients enforced a new stable periodicity upon the system. Outside this range, they caused period doubling or induced a sequence of reversal events without any obvious regularity. An analysis of a functional relationship between apparently irregular periods by plotting each period as a function on the preceding one yielded a clearly discernible non-random structure, which shows some similarities to the one obtained by a model calculation for a periodically perturbed limit cycle oscillator. These results indicate that external forcing of the system may generate chaos. When the decay of intracellular sensory signals is delayed by inhibition of protein methylation the transition from periodic to aperiodic behavior occurs at a lower steepness of the gradient. We therefore assume that the generation of either periodic or deterministic chaotic behavior is determined by the relation between the signal lifetime and the frequency of stimulus inputs. The strong indications for transitions from periodic to chaotic behavior can be regarded as a further support of our hypothesis that the behavioral pattern of Halobacterium is controlled by an endogeneous oscillator.