Low-dimensional sensory feature representation by trigeminal primary afferents

Abstract

In any sensory system, the primary afferents constitute the first level of sensory representation and fundamentally constrain all subsequent information processing. Here, we show that the spike timing, reliability, and stimulus selectivity of primary afferents in the whisker system can be accurately described by a simple model consisting of linear stimulus filtering combined with spike feedback. We fitted the parameters of the model by recording the responses of primary afferents to filtered, white noise whisker motion in anesthetized rats. The model accurately predicted not only the response of primary afferents to white noise whisker motion (median correlation coefficient 0.92) but also to naturalistic, texture-induced whisker motion. The model accounted both for submillisecond spike-timing precision and for non-Poisson spike train structure. We found substantial diversity in the responses of the afferent population, but this diversity was accurately captured by the model: a 2D filter subspace, corresponding to different mixtures of position and velocity sensitivity, captured 94% of the variance in the stimulus selectivity. Our results suggest that the first stage of the whisker system can be well approximated as a bank of linear filters, forming an overcomplete representation of a low-dimensional feature space.

Figure 1.

Primary trigeminal afferent responses to dynamic whisker stimulation. A, Autocorrelation of white noise stimulus, plotted in normalized units. B, Excerpt of white noise stimulus. C, D, Raster plots of spikes evoked by the white noise excerpt in B. E, Autocorrelation of texture-induced whisker motion. F, Excerpt of texture-induced whisker motion. G, H, Raster plots of spikes evoked by texture-induced whisker motion for the same units in C and D.

Figure 2.

Comparison of primary afferent response to texture versus white noise. A, Each point shows the firing rate (averaged over 10 s stimulus presentation) evoked by white noise compared with that evoked by texture, for a given unit. B, Analogous comparison for spike- timing jitter.

Figure 3.

Diverse responses in the population of primary afferents. A, PSTHs (1 ms bins, normalized to each unit's maximum firing rate) of all recorded units evoked by white noise. B, For each unit, correlation coefficient between the PSTH and position, velocity, and acceleration of the white noise. C–E, STAs for ideal position, velocity, and acceleration-sensitive units. F, STAs for each recorded unit. G, STAs classified by fitting to a mixture of Gaussians model (Petersen et al., 2008). P/V denotes position/velocity hybrids (see Materials and Methods).

Figure 4.

Model structure and parameter fitting. A, Schematic of the GLM. The linear filters k⃗ and h⃗ are convolved with the whisker stimulus and spike history, respectively. The resulting coefficients are summed with the constant b and passed through the nonlinear function f(·) to produce the time-dependent probability of a spike. B1, Stimulus filter for an example unit. C1, The stimulus filter convolved with the white noise autocorrelation (black line), compared with the unit's STA (gray line). D1, The unit's spike feedback filter. B2–D2, Corresponding results for a second example unit.

Figure 5.

PSTH prediction performance for the GLM: single-unit examples. A1, PSTH of an example unit (black line) evoked by white noise, compared with PSTH predicted by the GLM model with parameters shown in Figure 4C1–D1 (gray line). B1, Corresponding data for the texture stimulus (same unit as A1). C1, Variance of spike count across trials (20 ms time window) plotted against its mean (same unit as A1). D1, Corresponding data for the GLM model. A2–D2, Analogous results for a second example unit.

Figure 6.

PSTH Prediction performance of the GLM: population data. A, Each point shows the prediction quality (correlation coefficient between actual and predicted PSTH) for white noise compared with that for texture, for a given unit; 1 ms bins. B, Effect of spike feedback term on PSTH prediction: correlation coefficient between actual and predicted PSTH with spike feedback compared with that without spike feedback for a given unit. Results computed for white noise.

Figure 7.

Timing precision of PSTH prediction. A, Correlation coefficient (median across units) between recorded and predicted PSTHs for white noise and texture, as a function of spike time bin size. Data shown both for GLM and LNP models. Bars denote SEM, computed by bootstrap resampling. B, Example of PSTH evoked by white noise (black line above the x-axis) compared with predicted PSTH from GLM (black line below) and LNP model (gray line below).

Figure 8.

Kinetic feature space encoded by the primary afferent population. A, Proportion of variance of stimulus filters explained by 1–4 PCs in order of decreasing eigenvalue. B, The first three PCs. C, Smoothed stimulus filters for each primary afferent plotted at its location in the space spanned by PCs 1 and 2 (gray lines). Superimposed are the stimulus features corresponding to different locations in the space, as detailed in the main text (black). D, Corresponding plot for PCs 1 and 3.