Strong correlations between sensitivity and variability give rise to constant discrimination thresholds across the otolith afferent population

Abstract

The vestibular system is vital for our sense of linear self-motion. At the earliest processing stages, the otolith afferents of the vestibular nerve encode linear motion. Their resting discharge regularity has long been known to span a wide range, suggesting an important role in sensory coding, yet to date, the question of how this regularity alters the coding of translational motion is not fully understood. Here, we recorded from single otolith afferents in macaque monkeys during linear motion along the preferred directional axis of each afferent over a wide range of frequencies (0.5-16 Hz) corresponding to physiologically relevant stimulation. We used signal-detection theory to directly measure neuronal thresholds and found that values for single afferents were substantially higher than those observed for human perception even when a Kaiser filter was used to provide an estimate of firing rate. Surprisingly, we further found that neuronal thresholds were independent of both stimulus frequency and resting discharge regularity. This was because increases in trial-to-trial variability were matched by increases in sensitivity such that their ratio remains constant: a coding strategy that markedly differs from that used by semicircular canal vestibular afferents to encode rotations. Finally, using Fisher information, we show that pooling the activities of multiple otolith afferents gives rise to neural thresholds comparable with those measured for perception. Together, our results strongly suggest that higher-order structures integrate inputs across afferent populations to provide our sense of linear motion and provide unexpected insight into the influence of variability on sensory encoding.

Figure 1.

Experimental procedures. A, We recorded extracellular single-unit activity from otolith afferents using glass microelectrodes. We measured head acceleration using a three-dimensional linear accelerometer. VN, Vestibular nuclei. B, We determined the PD of each afferent in the following way. First, we applied sinusoidal translation (5 Hz, 0.2 G) along the fore–aft and lateral directions in the horizontal plane (I) and estimated sensitivity in each direction (II, black circles). Second, the sensitivity for an arbitrary direction was estimated by a cosine fit (II, gray curve), and the PD was defined as the direction for which sensitivity was maximal (II, dashed green line). We stimulated each afferent along its PD by rotating the monkey's head (III, dashed arrow) to align the axis of translation (III, black arrow) with PD (III, green arrow).

Figure 2.

Regular and irregular otolith afferents respond differentially to sinusoidal stimuli. A, Time-dependent firing rate (gray) from typical regular (left) and irregular (right) afferents in response to 0.5 Hz (top) and 6 Hz (bottom) sinusoidal linear acceleration stimuli. Superimposed are the firing rate estimates based on Equation 1 (solid black trace). B, Population-averaged neuronal gain (i.e., sensitivity) (left) and phase (right) for regular (blue) and irregular (red) otolith afferents as a function of the stimulus frequency. Note that gain increases with stimulus frequency for both afferent types. However, this increase was more pronounced for irregular afferents. The inset expands the y-axis to illustrate that the gain of regular afferents also increases as a function of frequency. The shaded bands show 1 SEM.

Figure 3.

Regular and irregular otolith afferents display similar detection thresholds. A, Segment of a 5 Hz sinusoidal stimulus (top, left) and the corresponding firing rate response (top, right). We plotted firing rate as a function of linear acceleration (bottom) and used signal-detection theory to compare the distribution of firing rates for a given value of linear acceleration (black Gaussian curve) and that obtained for zero acceleration (gray Gaussian curve) to obtain a plot of d′ as a function of linear acceleration (middle). The detection threshold T_d′ was computed as the lowest absolute value of head acceleration for which d′ = 1 (blue arrow). B, Population-averaged detection threshold values T_d′ for regular (blue, Reg), irregular (red, Irr), and all (black, Total) afferents as a function of stimulus frequency. It is seen that regular and irregular afferents have similar thresholds (t test, p > 0.11 for every stimulus frequency) that do not vary significantly with frequency (ANOVA, p = 0.23 and p = 0.14 for regular and irregular afferents, respectively).

Figure 4.

Comparison between neural thresholds obtained using different methodologies for otolith afferents. A, B, Plots of the instantaneous firing rate as a function of linear acceleration for the same example regular afferent. We compared the firing rate distributions for a given positive value of acceleration Ḧ (black Gaussian curves) and that obtained for zero linear acceleration (i.e., Ḧ = 0) (gray curve in A) or the firing rate distribution when the acceleration has the opposite value (i.e., −Ḧ) (gray curve in B). The insets illustrate the corresponding neurometric functions obtained using ROC analysis. The detection T_max and discrimination T_min−max thresholds were computed as the values of linear acceleration for which the probability of correct detection is equal to 84% (blue arrows in A and B, respectively). C, Top, Population-averaged neural threshold values computed using different methodologies: T_d′exc (black) and T_d′inh (green) were computed using d′ as described in Figure 3 but using only positive or negative values of head acceleration, respectively. T_max (purple) and T_min−max (orange) are also shown for comparison. Bottom, Same measures but normalized such that both T_d′exc and T_d′inh are divided by $\sqrt{2}$ and T_max is divided by 2. It is seen that all curves then coincide (ANOVA, p > 0.54 for all stimulus frequencies), which illustrates that the different methodologies used to compute neural thresholds lead to estimates that differ only by a proportionality constant that is independent of frequency. D, Top, Population-averaged T_min−max values for regular (blue, Reg) and irregular (red, Irr) afferents obtained when the firing rate is estimated using the inverse ISI (dashed) and a Kaiser filter (solid). It is seen that using a Kaiser filter gives rise to significantly lower threshold estimates (t test, p < 0.05 for all frequencies). However, both regular and irregular afferents display thresholds that are not significantly different from one another using either methodology (t test, Kaiser filter, p > 0.05 for all frequencies; 1/ISI, p > 0.05 for all frequencies). The inset illustrates the firing rates estimated by the reciprocal ISI (dashed red) and Kaiser filter (solid red) to a 0.5 Hz sinusoidal head acceleration stimulus (solid black). Bottom, Same quantities as a function of stimulus frequency using a double y-axis plot. The fact that all curves superimpose illustrates that using different methodologies to estimate firing rate will give rise to threshold estimates that only differ by a proportionality constant that is independent of frequency. We found empirically that dividing the threshold values estimated from the inverse ISI by 3.6 gave rise to values that were not significantly different from those obtained using the Kaiser filter (t test, p > 0.13 and p > 0.07 for regular and irregular afferents, respectively, for every stimulus frequency). The shaded bands represent 1 SEM.

Figure 5.

Linear extrapolation significantly underestimates neural threshold values in the PD. A, Illustration showing why linear extrapolation would underestimate the neural discrimination threshold at PD. Left, Schematic of the fore–aft (FA) and lateral (Lat) axes of translation (black arrows) as well as the PD of an example afferent (green line and arrows). Right, Discrimination threshold (T_min−max) of this afferent as a function of direction (i.e., the absolute difference between the axis of translation and the PD of the afferents: |PD − 2D|) calculated using the sensitivity tuning curve (inset). The black circles show measured sensitivities (inset) and corresponding threshold values (main panel). The gray circles were obtained using a cosine fit (solid black line in inset) for sensitivity (inset) and estimating the corresponding threshold values. The predicted threshold at PD (dashed circle) based on a linear extrapolation (dashed line) is much smaller than the actual value measured by direct stimulation along the PD of the afferent (filled green circle, green arrow). Based on the fact that the discrimination threshold is inversely proportional to sensitivity, we would expect that the threshold as a function of direction would be well fit by a 1/cosine function (solid black line in main panel). Extrapolating the discrimination threshold at PD using this fit gives rise to a correct estimate. B, Discrimination threshold values T_min−max as a function of direction for regular (blue) and irregular (red) afferents during 5 Hz sinusoidal stimulation. We used a 1/cosine fit (solid lines; see Materials and Methods) to extrapolate the threshold at PD (red and blue arrows). The R² values quantifying the goodness-of-fit are also shown. We then compared the extrapolated threshold values (open bars in the inset) with the actual measured values (filled bars in the inset) and found no significant differences (t test, p = 0.14 and 0.09 for regular and irregular afferents, respectively). C, Same data as in B except that we instead used a linear fit to extrapolate discrimination threshold values at PD. The best fits are shown (dashed lines) along with goodness-of-fit as quantified by R². We note that fitting a straight line gave rise to lower R² values than using a 1/cosine function. We also compared the linearly extrapolated discrimination threshold values (red and blue arrows, open bars in the inset) with the actual measured values (filled bars in the inset) and found that the former significantly underestimated the latter (t test, p < 0.0001 for both regular and irregular afferents).

Figure 6.

Strong positive correlations between sensitivity and variability lead to discrimination thresholds that are independent of resting discharge regularity and stimulus frequency. A, Response sensitivity as quantified by the slope of the firing rate-head acceleration curve (circles) and variability as quantified by the SD of the firing rate distribution obtained via a Kaiser filter at zero head acceleration (triangles) as a function of CV* for regular (blue, Reg) and irregular (red, Irr) afferents during 5 Hz sinusoidal stimulation. B, Variability as a function of sensitivity for regular (blue) and irregular (red) afferents during 5 Hz sinusoidal stimulation. Both quantities were strongly positively correlated (r = 0.9, p ≪ 10⁻³). The linear fit to the data (dashed line) had a slope of 0.024 ± 0.009 G and an offset of 0.5 ± 2.3 spikes/s. Importantly, the offset was not significantly different from 0 (p = 0.4), indicating that variability is proportional to sensitivity. C, Comparison between discrimination threshold values T_min−max for regular (filled blue rectangles) and irregular (filled red rectangles) afferents as a function of CV*. Also shown are the predicted threshold values based on sensitivity and variability (open black rectangles). The inset shows the predicted discrimination threshold values as a function of the actual measured ones. There is excellent agreement because all data points are scattered close to the identity line (dashed line) (R² = 0.89, the slope of the best-fit straight line is not significantly different from 1, p = 0.44). D, A strong positive correlation between resting rate variability and neuronal sensitivity (r = 0.8, p ≪ 10⁻³): the slope of the best linear regression was 0.025 ± 0.013 G and the offset (0.99 ± 3.18 spikes/s) was not significantly different from 0 (p = 0.4). Note that resting rate variability was estimated as the SD of the Kaiser filtered firing rate in the absence of any stimulus. E, Population-averaged response sensitivity (solid) and variability (dashed) as a function of linear acceleration frequency for regular (blue) and irregular (red) afferents. F, Population-averaged discrimination threshold values T_min−max (solid) did not significantly differ from the predicted values (dashed) over the whole frequency range for both regular (bottom) (t test, p > 0.31 for all stimulus frequencies) and irregular (top) (t test, p > 0.15 for all stimulus frequencies) afferents. The shaded bands represent 1 SEM.

Figure 7.

Pooling the activities of afferent populations of increasing size gives rise to decreasing discrimination threshold values that approach those reported in perceptual studies. A, B, Population-averaged discrimination threshold values (circles) T_min−max as a function of population size N obtained by estimating the firing rate using either a Kaiser filter (A) or the inverse ISI (B). Also shown are a 1/√N fit (green traces in A and B) as well as perceptual threshold values reported by MacNeilage et al. (2010b) (dashed line) and Valko et al. (2012) (dotted line). In both cases, the data are well fit (A, R² = 0.93; B, R² = 0.90), indicating that the discrimination threshold decreases as 1/√N. In both panels, the red and blue arrows give the smallest population sizes that lead to discrimination threshold values that are equal to those reported for perception by MacNeilage et al. (2010b) and Valko et al. (2012), respectively.