Refractoriness enhances temporal coding by auditory nerve fibers

Abstract

A universal property of spiking neurons is refractoriness, a transient decrease in discharge probability immediately following an action potential (spike). The refractory period lasts only one to a few milliseconds, but has the potential to affect temporal coding of acoustic stimuli by auditory neurons, which are capable of submillisecond spike-time precision. Here this possibility was investigated systematically by recording spike times from chicken auditory nerve fibers in vivo while stimulating with repeated pure tones at characteristic frequency. Refractory periods were tightly distributed, with a mean of 1.58 ms. A statistical model was developed to recapitulate each fiber's responses and then used to predict the effect of removing the refractory period on a cell-by-cell basis for two largely independent facets of temporal coding: faithful entrainment of interspike intervals to the stimulus frequency and precise synchronization of spike times to the stimulus phase. The ratio of the refractory period to the stimulus period predicted the impact of refractoriness on entrainment and synchronization. For ratios less than ∼0.9, refractoriness enhanced entrainment and this enhancement was often accompanied by an increase in spike-time precision. At higher ratios, little or no change in entrainment or synchronization was observed. Given the tight distribution of refractory periods, the ability of refractoriness to improve temporal coding is restricted to neurons responding to low-frequency stimuli. Enhanced encoding of low frequencies likely affects sound localization and pitch perception in the auditory system, as well as perception in nonauditory sensory modalities, because all spiking neurons exhibit refractoriness.

Figure 1.

Auditory nerve responses entrain and synchronize to the acoustic stimulus waveform. The raster plots display the occurrence times of spikes in two auditory nerve fibers. The CF of each fiber is displayed on top along with μ in green. The length of the green line segment at the top of each panel corresponds to the duration of μ on the same time scale as the figures. The top subpanels display the responses of the fibers over all 200 trials and the bottom subpanels magnify the figures to display only five trials. The sinusoidal blue lines depict the shape of the pure tone stimulus waveform at CF.

Figure 2.

Refractoriness outlasts the excitatory phase of the stimulus cycle for most nerve fibers. a, Histogram displaying the distribution of μ across all cells. b, μ plotted as a function of CF for each fiber. Each point is a measurement from one fiber. The curved dashed line depicts the duration of the excitatory phase of the stimulus cycle at each CF (i.e., half a cycle). c, Histogram displaying the distribution of μ/T across all cells.

Figure 3.

The ratio of the refractory period to the stimulus period determines whether neurons fire multiple spikes per cycle. a, The percentage of stimulus cycles in which a fiber fired more than one spike is plotted against CF for each fiber. The horizontal dashed line indicates 2%, the criterion for multiple spikers. b, The percentage in a is plotted against μ/T.

Figure 4.

Examples of removing refractoriness. a, Raster plots of simulated responses (spikes) using a Poisson-with-dead-time model derived from the observed responses in Figure 1. b, Raster plots of simulated responses (excitatory events) using the same model as in a but without refractoriness. Excitatory events can occur in rapid succession, as reflected by the occurrence of tight clusters of events with no apparent space between them. The aligned late-cycle responses in the left panel are due to noise in the calculated excitation function for this fiber. The fiber's observed responses contained a few late discharges (Fig. 1a) that occurred in time bins when the neuron was usually refractory. This caused an overestimate of the excitation function for those time bins, which in turn caused alignment of stochastic events at those time bins. Such overestimates were rare across the population of fibers.

Figure 5.

Entrainment is enhanced when the refractory period is less than the stimulus period. a, EI_S plotted against CF for each cell. b, Difference in EI between observed responses and the model without refractoriness is plotted versus CF. Positive values reflect an enhancement of entrainment by refractoriness. c, Same difference as in b is plotted against μ/T.

Figure 6.

The impact of refractoriness on synchronization of single and multiple spikers. Example period histograms for two neurons are shown. a, Smoothed period histogram depicting the probability of event occurrence at each phase of the stimulus cycle for the fiber in Figure 1, left. The blue dashed line depicts the stimulus waveform. The length of the green double-arrowed line corresponds to the duration of μ in the phase domain. The black histogram shows the phase distribution of spikes in measured responses and the red histogram shows the phase distribution of excitatory events from simulated responses of the model without refractoriness. The inset displays the same histograms normalized so that the area under them is equal. The σ of spike and excitatory event timing is shown below the inset. The period histogram was smoothed by a running average spanning 10% of the stimulus cycle length for clearer presentation. b, Same as a but for the fiber in Figure 1, right.

Figure 7.

Synchronization is enhanced when the refractory period is less than the stimulus period. a, Temporal dispersion of observed spikes is plotted versus CF. Each point is a measurement from one fiber. The curved gold line is the precision of spike times that would be predicted for a completely unsynchronized response (flat period histogram) at each CF, according to the equation 1/(CF * $\sqrt{12}$). Open circles depict the temporal dispersion of all spikes in each cycle (red) or just the first spike in each cycle (black) for cells that fire multiple spikes per cycle. b, Difference in temporal dispersion between the observed spikes and the simulated excitatory events with refractoriness removed. Positive values correspond to an enhancement in precision by refractoriness. Solid black circles correspond to single-spiking cells for which the change in σ_S was not significant as determined by a bootstrap procedure (see Materials and Methods). The gray circles are single spikers that showed a significant enhancement in precision. c, Change in precision plotted as a function of μ/T.

Figure 8.

Enhancements of entrainment and synchronization by refractoriness are correlated. The change in synchronization due to refractoriness is plotted against the respective change in entrainment. Enhancement in synchronization only occurred when there was a large enhancement in entrainment. Open circles represent the first spike per cycle for multiple spikers.