Weakly electric fish generate a periodic electric field as a carrier signal for active location and communication tasks. Highly sensitive P-type receptors on their surface fire in response to carrier amplitude modulations (AM's) in a noisy phase locked fashion. A simple generic model of receptor activity and signal encoding is presented. Its suprathreshold dynamics, memory and receptor noise reproduce observed firing interval distributions and correlations. The model ultimately explains how smooth responses to AM's are compatible with its nonlinear phase locking properties, and reveals how receptor noise can sometimes enhance the encoding of small yet suprathreshold AM's.
We consider the dependence of information transfer by neurons on the Type I vs. Type II classification of their dynamics. Our computational study is based on Type I and II implementations of the Morris-Lecar model. It mainly concerns neurons, such as those in the auditory or electrosensory system, which encode band-limited amplitude modulations of a periodic carrier signal, and which fire at random cycles yet preferred phases of this carrier. We first show that the Morris-Lecar model with additive broadband noise ("synaptic noise") can exhibit such firing patterns with either Type I or II dynamics, with or without amplitude modulations of the carrier. We then compare the encoding of band-limited random amplitude modulations for both dynamical types. The comparison relies on a parameter calibration that closely matches firing rates for both models across a range of parameters. In the absence of synaptic noise, Type I performs slightly better than Type II, and its performance is optimal for perithreshold signals. However, Type II performs well over a slightly larger range of inputs, and this range lies mostly in the subthreshold region. Further, Type II performs marginally better than Type I when synaptic noise, which yields more realistic baseline firing patterns, is present in both models. These results are discussed in terms of the tuning and phase locking properties of the models with deterministic and stochastic inputs.
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.
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