Encoding Carrier amplitude Modulations via Stochastic phase Synchronization

The firings of excitable systems can phase lock to periodic forcing. In many situations however, the firings are separated by a random number of forcing cycles, even though they occur near a preferred phase of the forcing. Also, the associated interspike interval histograms display peaks over a continuous range of integer multiples of the forcing period, and the peak heights are a unimodal function of increasing multiples of the period. This paper focusses on these patterns of stochastic phase synchronization and their alteration by physiologically relevant stimuli that modulate the amplitude of the periodic forcing. Specifically, two regimes of the FitzHugh–Nagumo system exhibiting stochastic phase locking are considered. We discuss how internal noise, originating from e.g. synaptic or conductance fluctuations, must interact with either suprathreshold or subthreshold dynamics, and in some instances with subthreshold chaos, to produce such firing patterns. These responses to constant amplitude “carriers” are then compared to those from carriers with random band-limited amplitude modulations (AM’s). The comparison is based on the mean firing rate, as well as phase synchronization computed using a suitably defined input–output phase difference. Further, using the stimulus reconstruction technique to characterize synchrony between random AM’s and spikes, the internal noise is shown to help transmit information about random carrier AM’s in the subthreshold and slightly suprathreshold cases. This transmission also depends nonmonotonically on the carrier frequency. Our results provide biophysical insight into the dynamics of neural signal encoding that combines a mean rate code on long time scales and a precise temporal code based on phase locking on the shorter time scale of the carrier period.