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Coding strategies in the otolith system differ for translational head motion vs. static orientation relative to gravity

  1. Mohsen Jamali
  2. Jerome Carriot
  3. Maurice J Chacron
  4. Kathleen E Cullen  Is a corresponding author
  1. Harvard Medical School, Massachusetts General Hospital, United States
  2. McGill University, Canada
  3. Johns Hopkins University, United States
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Cite this article as: eLife 2019;8:e45573 doi: 10.7554/eLife.45573

Abstract

The detection of gravito-inertial forces by the otolith system is essential for our sense of balance and accurate perception. To date, however, how this system encodes the self-motion stimuli that are experienced during everyday activities remains unknown. Here, we addressed this fundamental question directly by recording from single otolith afferents in monkeys during naturalistic translational self-motion and changes in static head orientation. Otolith afferents with higher intrinsic variability transmitted more information overall about translational self-motion than their regular counterparts, owing to stronger nonlinearities that enabled precise spike timing including phase locking. By contrast, more regular afferents better discriminated between different static head orientations relative to gravity. Using computational methods, we further demonstrated that coupled increases in intrinsic variability and sensitivity accounted for the observed functional differences between afferent classes. Together, our results indicate that irregular and regular otolith afferents use different strategies to encode naturalistic self-motion and static head orientation relative to gravity.

https://doi.org/10.7554/eLife.45573.001

Introduction

The otolith system provides vital information about linear head acceleration in three dimensions (i.e., gravito-inertial forces) and the head’s orientation relative to gravity. This essential system is required for control of balance and posture, as well as for our perception of self-motion and spatial orientation. Indeed, during natural everyday activities, the head not only moves with considerable linear acceleration (frequencies up to 20 Hz and amplitudes up to 8G; see Carriot et al., 2014 for human data and Carriot et al., 2017 for monkey and mouse data), but also frequently remains stationary during large periods of time (Carriot et al., 2014; Carriot et al., 2017). This observation raises the fundamental question of how the otolith system provides estimates of both dynamic head motion and static orientation relative to gravity.

Otolith afferent responses have been traditionally characterized using artificial self-motion stimuli such as sinusoids (reviewed in Goldberg, 2000, Cullen, 2012, Yu et al., 2012, and Jamali et al., 2013) or single Gaussian-like trajectories (Yu et al., 2015; Laurens et al., 2017). In the absence of stimulation, otolith afferents display differences in the variability of their resting discharge and can be classified as regular or irregular. Regular and irregular afferents further display different morphological and physiological features (reviewed in Goldberg, 2000, Cullen, 2012 and Eatock and Songer, 2011). In addition, a number of studies have recorded otolith afferent responses to sound and/or bone vibrations that have frequency content that is an order of magnitude above that of the self-motion experienced during everyday activities (Young et al., 1977; Curthoys et al., 2019; Curthoys et al., 2016; Curthoys et al., 2017). Interestingly, irregular otolith afferents show greater phase locking (i.e., firing only during a specific phase range of the sinusoidal stimulus) at higher frequencies (i.e., 200–3,000 Hz). However, how the otolith afferents respond to the naturalistic self-motion stimuli experienced during everyday activities remains unknown. Specifically, studies have not revealed the role played by heterogeneity in the resting discharge variability of otolith afferents in the coding strategies employed by these neurons.

Accordingly, here we directly addressed how otolith afferents encode the gravito-inertial forces experienced during everyday activities. We found that irregular afferents displayed strong response nonlinearities to naturalistic self-motion and transmitted information via both changes in firing rate and precise spike timing. By contrast, regular afferents primarily encoded naturalistic self-motion through changes in firing rate. Mathematical modeling revealed that the increased sensitivity and variability of irregular afferents could account for functional differences between regular and irregular otolith afferents. Our model further predicted that irregular afferents should display temporally precise phase locking in response to sinusoidal stimulation within the behaviorally relevant physiological range. Further experiments using sinusoidal stimuli confirmed this prediction. Finally, we found that regular afferents outperformed their irregular counterparts in their ability to discriminate between different static head orientations. Taken together, our results establish that regular and irregular otolith afferents use different coding strategies in order to provide estimates of both dynamic head motion and static orientation relative to gravity.

Results

We recorded the activities of primary otolith afferents in two alert macaque monkeys (Figure 1A). Resting discharge variability was quantified from interspike interval histograms (upper left and right panels of Figure 1B) using a normalized coefficient of variation CV* (see 'Materials and methods'). We found that the distribution of CV* values for our dataset was bimodal (Figure 1B, p=0.04, Hartigan’s dip test), consistent with previous studies (reviewed in Goldberg, 2000). Our afferent dataset thus comprised N = 18 regular and N = 17 irregular afferents. We then recorded the activities of primary otolith afferents under stimulation. Our experimental protocol comprised: 1) translational self-motion stimuli with frequencies spanning the natural range (0–15 Hz) mimicking natural movements (Carriot et al., 2017) (see 'Materials and methods') and; 2) different head orientations relative to gravity obtained by statically re-aligning the animal’s whole body. We henceforth refer to these two stimuli ‘naturalistic translational self-motion’ and ‘changes in head orientation relative to gravity’, respectively. We note that we applied the latter in order to investigate otolith afferent coding for frequencies <0.1 Hz, as we could only reliably estimate quantities for frequencies ≥0.1 Hz for naturalistic translational self-motion (see 'Materials and methods').

Regular and irregular otolith afferent responses to naturalistic translational self-motion stimuli.

(A) Schematic showing early vestibular pathways and recording sites. (B) Distribution of resting discharge variability as quantified by CV* for our dataset. As detailed in the Materials and methods, CV* is a normalized coefficient of variation that is used to quantify resting discharge variability independently of differences in firing rate (Goldberg et al., 1984). The distribution was clearly bimodal (Hartigan’s dip test, p=0.04). The insets show the interspike interval histograms from example regular (left, blue) and irregular (right, red) afferents with CV*=0.06 and 0.29, respectively. (C) Time varying linear head acceleration (top row) with corresponding spiking and firing rate from example irregular (second row from top) and regular (third row from top) afferents. The linear firing rate predictions for the irregular and regular afferents are shown in red and blue, respectively. The time varying residuals (i.e., difference between the actual and predicted responses) are also shown for each afferent (bottom row). (D) Population-averaged gains for regular (blue, N = 18) and irregular (red, N = 17) afferents as a function of stimulus frequency. Top left inset: Gain at 2 Hz (green arrow in bottom panel) as a function of CV*. Top right inset: Population-averaged power spectra of the residual for regular (blue) and irregular (red) afferents. The shaded bands show 1 SEM.

https://doi.org/10.7554/eLife.45573.002

Irregular afferents display stronger response nonlinearities and transmit more information overall about naturalistic translational self-motion stimuli than their regular counterparts

Figure 1C shows the responses of typical irregular (top) and regular (bottom) otolith afferents to naturalistic translational self-motion stimuli. Notably, changes in firing rate were greater for the irregular afferent (Figure 1C, compare red and blue curves). Further analysis of neuronal responses across our dataset revealed that irregular afferents displayed greater sensitivity to the stimulus than their regular counterparts (Figure 1D and Figure 1D, left inset). Using linear systems identification techniques, we generated an estimate of the time-dependent firing rate in response to stimulation (see 'Materials and methods'). Overall, there was good agreement between this prediction and the actual firing rate for both regular and irregular afferents (compare blue and gray for regular afferents and red and gray for irregular afferents in Figure 1C). In order to quantify the component of the response that could not be explained by our linear model, we computed the residual (i.e., the difference between our estimate and the actual firing rate). Overall, this residual was distributed over a greater range of values for irregular afferents than for their regular counterparts (compare dashed red and blue curves in Figure 1C). Further analysis of the residual power spectrum revealed nearly constant power, which was higher by over an order of magnitude for irregular afferents (Figure 1D, right inset, compare red and blue curves).

This raises the question of why irregular afferents have higher residuals than regular afferents. One the one hand, it is possible that nonlinearities in the response of irregular but not regular afferents contribute to the poor fit of standard linear models. On the other hand, irregular afferents could display larger trial-to-trial variability than their regular counterparts, which would also increase the residual. Thus, to determine which of these alternatives is correct, we investigated otolith afferent responses to repeated stimulus presentations. Responses from example irregular and regular afferents are shown in the top and bottom panels of Figure 2A, respectively. Notably, responses to repeated stimulus presentations were more similar for the example irregular afferent than for the example regular afferent, as can be seen by the spikes being better aligned across repeated presentations of the stimulus (Figure 2A, compare top and bottom raster plots). To test directly for the presence of nonlinearities and to quantify trial-to-trial variability, we computed the response–response (RR) coherence (i.e., the coherence between the responses to repeated stimulus presentations) as well the stimulus-response (SR) coherence (i.e., the coherence between the stimulus and the response). The coherence is equal to one if both signals are identical and to 0 if they are uncorrelated. The RR coherence is a measure of the trial-to-trial variability in the response. Moreover, a difference between the square root of the RR and the SR coherence values indicates the presence of nonlinearities (Roddey et al., 2000).

Irregular otolith afferents display greater response nonlinearity than their regular counterparts.

(A) Time-varying stimulus (top) as well as spiking- and firing-rate responses to repeated stimulus presentations, obtained from the same irregular (middle) and regular (bottom) afferents shown in Figure 1. (B) Population-averaged stimulus–response (SR, dashed red) and square root of the response–response (√RR, solid red) coherence curves for irregular afferents. (C) Population-averaged SR (dashed blue) and √RR (solid blue) coherence curves for regular afferents. (D) The population-averaged nonlinearity index values for regular (blue) and irregular (red) afferents were significantly different from one another (p=0.0002). (E) Population-averaged mutual information density curves for irregular (red) and regular (blue) afferents. Right bar chart: population-averaged mutual information rates for irregular (red) and regular (blue) afferents were significantly different from one another (p=0.04). Note that there is a one-to-one relationship between the mutual information rate density curve and √RR. Moreover, the mutual information rate is obtained by integrating the mutual information rate density over frequency, as detailed in the 'Materials and methods'. '*' indicates statistical significance at the p=0.05 level as determined using a Wilcoxon ranksum test. The shaded color bands around the curves show one SEM.

https://doi.org/10.7554/eLife.45573.003

Overall, the square root of the RR coherence was higher for irregular afferents than for regular afferents (Figure 2B,C, compare solid red and blue curves), confirming our observation that irregular afferents display lower trial-to-trial variability than their regular counterparts. Therefore, the greater residual observed for irregular afferents cannot be due to increased trial-to-trial variability. We further found greater differences between the square root of the RR and SR coherence curves for irregular afferents (Figure 2B, compare dashed and solid red curves) than for their regular counterparts (Figure 2C, compare dashed and solid blue curves), indicating greater nonlinearity for the irregular afferents. To quantify this observation, we computed a nonlinearity index (NI, see 'Materials and methods') that is null when both curves are equal and increases with increasing level of nonlinearity. As expected, the population-averaged NI value was significantly higher for irregular afferents (Figure 2D; irregular: 40.8 ± 2.2%, regular: 20.0 ± 4.1%; p<0.001, Wilcoxon ranksum test). Therefore, we conclude that the greater residual observed for irregular afferents is due to greater response nonlinearity.

We hypothesized that the greater sensitivity and lower trial-to-trial variability displayed by irregular afferents lead to increased information transmission. To test this prediction, we quantified the mutual information between the neural response and the naturalistic translational self-motion stimulus for irregular and regular afferents (see 'Materials and methods'). Overall, the mutual information rate densities of irregular afferents were consistently higher across frequencies than those of regular afferents (Figure 2E, left panel, compare red and blue curves), leading to significantly greater rates of information transmission (Figure 2E, right panel; irregular: 0.37 ± 0.05 bits/spk; regular: 0.24 ± 0.04 bits/spk; p=0.04, Wilcoxon ranksum test). Thus, our results show that irregular afferents display stronger nonlinearities but lower trial-to-trial variability in their responses to naturalistic translational self-motion stimuli, which leads to greater information transmission.

Contributions of spike timing to the encoding of naturalistic translational self-motion stimuli by otolith afferents

Our results above show that irregular afferents displayed lower trial-to-trial variability in their responses to repeated stimulus presentations than their regular counterparts (Figure 2A, top panel). This led us to hypothesize that increased information transmission by irregular afferents is due to precise spike timing (i.e., irregular afferents use a temporal code to transmit information). We therefore tested whether the spiking activities in response to different stimulus waveforms were more discriminable from one another at timescales much shorter than those contained in the stimulus waveform for irregular afferents. Figure 3A shows the responses of example irregular (red) and regular (blue) afferents to repeated presentations of two different stimulus waveforms (left and right panels). Visual inspection revealed that the responses of the example irregular afferent to both stimulus waveforms were more discriminable from one another compared to those of the example regular afferent (Figure 3A, compare red and blue raster plots), which is in part due to their higher sensitivity. Together with the fact that there is lower trial-to-trial variability in the responses of irregular afferents, this implies that the spiking activities that occur in response to different stimulus waveforms are more discriminable from one another at timescales much shorter than those contained in the stimulus waveform for irregular afferents.

Figure 3 with 2 supplements see all
Irregular but not regular otolith afferents reliably discriminate between different stimulus waveforms through precise spike timing.

(A) Raster plots showing the spiking activities from an example irregular afferent (red) and an example regular afferent (blue) to repeated presentations of two different stimulus waveforms (left and right). (B) Discrimination performance as a function of spike-train duration and timescale τ (i.e., 1/q, see 'Materials and methods') for the example irregular afferent (left) and regular afferent (right). (C) Population-averaged discrimination performance for irregular (red) and regular (blue) afferents as a function of timescale. Chance performance is also shown (dashed line). The shaded color bands around the curves show one SEM. (D) Population-averaged discrimination performance for irregular (red) and regular (blue) afferents as a function of frequency (i.e., inverse of timescale). Chance performance (dashed line) as well as the stimulus power spectrum (shaded gray) are also shown. The shaded color bands (red and blue) around the curves show one SEM. (E, F) Discrimination performance (E) and precision of spike timing (F) as a function of baseline variability as quantified by CV* for regular (blue) and irregular (red) afferents. Afferents with higher CV* tended to display greater discrimination performance (R = 0.89, p=1.38E-12) as well as higher spike-timing precision (R = 0.71, p=4.69E-06). Insets: Population-averaged discrimination performance (E) and spike-timing precision (F) for regular (blue) and irregular (red) afferents (performance p=3.92E–06, precision p=9.26E–06). '*' indicates statistical significance at the p=0.05 level using a Wilcoxon ranksum test.

https://doi.org/10.7554/eLife.45573.004

In order to quantify this observation, we used metrics to quantify the distance spiking activities between and across stimulus waveforms (see 'Materials and methods'). We first used the Victor–Purpura metric (Victor and Purpura, 1996) to quantify the performance of a classifier in determining whether a recorded spiking activity could be correctly predicted as having been elicited by a given stimulus across timescales (see 'Materials and methods'). We predicted that, if information is transmitted via precise spike timing, then discrimination performance should be maximum at timescales significantly shorter than those contained in the stimulus (i.e., <50 ms). Our results confirmed this prediction as discrimination performance was indeed maximum for timescales near 7 ms for irregular afferents (Figure 3B (left), Figure 3—figure supplement 1A). Qualitatively different results were observed for regular afferents as discrimination performance was not only much lower but also maximum at a much larger timescale of 37 ms, which is closer to those contained in the stimulus (Figure 3B (right), Figure 3—figure supplement 1B).

Quantification of our dataset revealed qualitatively similar results for regular and irregular afferents. Indeed, the population-averaged discrimination performance of irregular afferents was considerably higher (three-fold) than that of their regular counterparts across timescales (Figure 3C). This difference in performance was not, however, due to differences in firing rates, either during stimulation (regular: 86 ± 5 spk/sec; irregular: 74 ± 7 spk/sec; p=0.16, Wilcoxon ranksum) or at rest (regular: 85 ± 5 spk/sec; irregular: 71 ± 6 spk/sec; p=0.19, Wilcoxon ranksum). Importantly, maximum performance for irregular afferents was observed for timescales of 10 ms (Figure 3C) or, equivalently, frequencies of 100 Hz (Figure 3D, red arrow). This frequency was five-fold greater than those contained in the naturalistic translational self-motion stimulus (<20 Hz; shaded gray area). By contrast, the discrimination performance for regular afferents reached its maximum value for timescales near 50 ms (Figure 3C) or, equivalently, for frequencies at which there is significant stimulus power (~20 Hz; Figure 3D, blue arrow). Discrimination performance (Figure 3E) and spike-timing precision (i.e., the frequency at which discrimination performance is maximum; Figure 3F) were both strongly positively correlated with resting discharge variability, as quantified by CV* (performance: R = 0.89, p<0.001; precision: R = 0.71, p<0.001). Quantitatively similar results were obtained when using a different distance metric (i.e., Van Rossum; Figure 3—figure supplement 2). Thus, our findings demonstrate that irregular but not regular otolith afferents use a temporal code to transmit information about naturalistic translational self-motion stimuli.

Increases in variability and sensitivity lead to greater information transmission and spike-timing precision

To gain understanding as to why regular and irregular otolith afferents exhibited qualitatively different neural coding properties in response to naturalistic translational self-motion stimuli, we built a stochastic mathematical model based on the leaky integrate-and-fire formalism and adjusted parameters so that the spiking output matched the experimental data (Figure 4A, see 'Materials and methods'). Overall, we found that, by co-varying the resting discharge variability and sensitivity parameters such that their ratio remains constant (Figure 4A, right panel), which is consistent with previous experimental findings (Jamali et al., 2013), we were able to reproduce the experimental data from regular and irregular afferents with good accuracy (Figure 4—figure supplement 1A,B). We then analyzed the output of our model in the same way as the experimental data above. Specifically, we computed the information transmitted and quantified discrimination performance as well as spike-timing precision (see 'Materials and methods'). Overall, increasing sensitivity and variability in our model increased the information rate (Figure 4B), discrimination performance (Figure 4C; Figure 4—figure supplement 1C,D), and spike-timing precision (Figure 4D) to values consistent with those observed experimentally. Thus, our model provides an explanation for our experimental findings. Specifically, our model suggests that the combined effects of the greater sensitivity and resting discharge variability for irregular afferents enable greater information transmission via precise spike timing.

Figure 4 with 1 supplement see all
A simple mathematical model based on the leaky integrate-and-fire formalism can reproduce our experimental data by co-varying sensitivity and variability.

(A) ( Left) Example resting (i.e., in the absence of stimulation) spiking activity from our model for parameter values that reproduced data from irregular and regular afferents (CV*=0.06). (Middle) Interspike interval histograms from example irregular (top) and regular (bottom) model afferents with CV*=0.42 and 0.06, respectively. (Right) Variability as a function of sensitivity in our model. Both were co-varied such that their ratio remains unity (dashed line). (B, C, D) Mutual information rate (B), performance (C), and precision (D) as a function of variability. The blue and red dots show the values used (A) or obtained (B, C, D) for the regular and irregular afferent models, respectively. Note that because variability and sensitivity were co-varied in our model, the results obtained in (B), (C) and (D) could be similarly plotted as a function of sensitivity instead of variability.

https://doi.org/10.7554/eLife.45573.007

Irregular otolith afferents display phase-locking to sinusoidal self-motion translational stimuli

As noted above, otolith afferent responses to translational self-motion stimuli have been traditionally characterized using artificial stimuli such as sinusoids. Thus, we next investigated whether our results obtained using naturalistic translational self-motion stimuli also have implications for how otolith afferents encode sinusoidal stimuli. In the auditory system, temporal precision of spiking relative to a sinusoidal stimulus waveform (i.e., a pure tone) is commonly associated with a nonlinear phenomenon termed phase locking. Specifically, phase locking refers to the observation that action potentials will only occur during certain phases of the stimulus cycle (see recent review by Heil and Peterson, 2017). Accordingly, we predicted that irregular otolith afferents will preferentially display phase locking to sinusoidal translational self-motion.

We tested these predictions by recording from both irregular (N = 10) and regular (N = 11) afferents during sinusoidal translational self-motion. Figure 5A illustrates the responses of example irregular (top panel) and regular (bottom panel) otolith afferents. Overall, consistent with our predictions, the spiking activity of the irregular but not the regular afferent was phase locked to the stimulus (compare top and bottom panels of Figure 5A). Indeed, action potentials reliably occurred preferentially during the rising phase of the stimulus for the irregular afferent (Figure 5A, top panel). By contrast, for the regular afferent, spiking occurred during all phases of the stimulus cycle (Figure 5A, bottom panel). We quantified our results using two commonly used phase-locking index (PLI) measures in the auditory system: PLI1 (i.e., vector strength) and PLI2 (which is based on the entropy of the phase distribution). Moreover, we used a third measure that is based on the latency of the first spike, which has been previously applied to the vestibular system PLI3 (see 'Materials and methods'). Notably, all three measures approach zero when spiking occurs with equal probability at all phases of the stimulus cycle (i.e., there is no phase locking) and approach unity when spiking only occurs at a given stimulus phase (i.e., there is perfect phase locking). Computing PLI values revealed much higher PLI1, PLI2, and PLI3 values for the irregular than for the regular example afferent (Figure 5B,C, compare top and bottom panels).

Irregular otolith afferents display greater phase locking to sinusoidal stimulation than their regular counterparts.

(A) Sinusoidal head acceleration stimulus (top) with raster plots showing the responses of example irregular (middle) and regular (bottom) afferents. (B) Plots of cycle histograms showing firing rate as a function of phase for the same example irregular (top) and regular (bottom) afferents, showing the corresponding values of PLI1 (i.e., vector strength) and PLI2 (i.e., entropy-based). (C) Plots of cumulative probability as a function of first spike time normalized by the mean interspike interval (ISI) for the same example irregular (top) and regular (bottom) afferents with the corresponding values of PLI3. (D) Population-averaged values of PLI1, PLI2, and PLI3 for irregular (top) and regular (bottom) afferents (solid). The hollow bars show the values computed from our model irregular (red) and regular (blue) afferents. Overall, no significant differences were observed (irregular PLI1, p=0.73; irregular PLI2, p=0.55; irregular PLI3, p=1; regular PLI1, p=0.83; regular PLI2, p=0.50; regular PLI3, p=1). (E) Phase locking indices PLI1 (left), PLI2 (middle), and PLI3 (right) as a function of stimulus frequency. (F) Spike-timing precision as a function of PLI1 (left), PLI2 (middle), and PLI3 (right) for regular (blue) and irregular (red) afferents. Strong positive correlations were observed in both cases (left: R = 0.84, p=1.88E–06; middle: R = 0.87, p=4.35E–07; right: R = 0.7, p=0.001).

https://doi.org/10.7554/eLife.45573.009

Qualitatively similar results were seen across our dataset as all three PLI measures were significantly higher for irregular afferents than for their regular counterparts (Figure 5D, solid bars; p<0.001 in all cases, Wilcoxon ranksum tests). Furthermore, we simulated our regular and irregular afferent models and found PLI values that were comparable to those obtained experimentally (Figure 5D, compare solid and hollow bars; irregular — p=0.73, p=0.55, and p=1 for PLI1, PLI2, and PLI3, respectively; regular — p=0.83, p=0.50, and p=1 for PLI1, PLI2, and PLI3, respectively; Wilcoxon ranksum tests). Further, we quantified phase locking in our experimental data for different stimulation frequencies. Overall, irregular afferents displayed increased tendency to phase lock with increasing stimulation frequency, and this tendency was consistently larger than that of their regular counterparts (Figure 5E). Finally, to test our prediction that increased spike-timing precision during naturalistic translational self-motion leads to greater phase locking during sinusoidal translational self-motion, we plotted spike-timing precision as a function of phase locking as quantified by PLI measures (Figure 5F). Spike-timing precision was strongly positively correlated with each measure of phase locking (R = 0.84, 0.87, and 0.7 using PLI1, PLI2, and PLI3, respectively; p≤0.001 in all cases). Thus, taken together, our results firmly establish that information transmission through the precise spike timing observed in irregular otolith afferents is tightly linked to their propensity to display phase locking in response to sinusoidal stimulation. We further consider the implications of this finding in the 'Discussion'.

Regular otolith afferents better encode differences in static head orientation relative to gravity than their irregular counterparts

To summarize thus far, we have shown that irregular afferents transmit more information overall about naturalistic translational self-motion stimuli than do their regular counterparts, in part through precise spike timing. Our modeling predicted that this was due to the increased resting discharge variability and sensitivity of irregular afferents, which causes phase locking in response to sinusoidal stimulation. So why have regular afferents at all? We note that, thus far, our analysis only considered dynamic translational self-motion stimuli and not the gravito-inertial forces experienced when the head is stationary at different orientations relative to gravity.

Thus, we next recorded the activities of regular and irregular afferents with the animal’s head initially upright relative to gravity (i.e., the reference orientation) and then with animal’s head positioned stationary at orientations from 3o to 15o, thereby causing changes in the net acceleration that is sensed by otolith afferents (Figure 6A). We then compared the resulting firing rate distributions obtained under the different conditions (see 'Materials and methods'). Figure 6A shows the firing rate distributions for example regular (blue) and irregular (red) afferents when the animal’s head is positioned at 3o (top panel) versus 15o (bottom panel) relative to earth vertical (black). To quantify discriminability between the firing rate distributions obtained when the animal’s head is positioned stationary at different orientations and those obtained for earth vertical, we used signal detection theory (Green and Swets, 1966; see 'Materials and methods'). We found that the example irregular afferent showed poor discriminability at 3o, which only slightly improved at 15o, as quantified by d’ values of 0.3 versus 0.55, respectively (compare top right and bottom right panels of Figure 6A). By contrast, the example regular afferent’s firing rate distribution measured when the head was positioned at 3o was already discriminable from that measured under reference orientation as quantified by a high d’ value of 1.46 (Figure 6A, top center panel). Discriminability further increased when considering a 15o angle as both distributions displayed minimal overlap as quantified by a d’ value of 5.52 (Figure 6A, bottom center panel). This finding was consistent across our population of otolith afferents as discriminability was significantly higher for regular afferents than for irregular afferents across all angles (Wilcoxon Ranksum test, p<0.03 in all cases; Figure 6B). These results show that the activities of regular otolith afferents provide a greater ability to discriminate between different static head orientations than is provided by their irregular counterparts.

Regular otolith afferents better discriminate between different head orientations relative to gravity than do their irregular counterparts.

(A) (Top left) schematic showing the head positioned vertically (i.e., 0o, left) and at a 3o angle relative to gravity (right). (Top center) Firing rate distributions from an example regular afferent when the head is positioned at 0o (black) and at 3o (blue). (Top right) Firing rate distributions from an example irregular afferent when the head is positioned at 0o (black) and at 3o (red). Also shown are the values of discriminability d’. (Bottom) Same as top row but with a head position at a 15o angle relative to gravity. Firing rates were obtained by convolving the spike trains with a Gaussian spike-density function with standard deviation 10 ms. Firing-rate distributions were obtained using a binwidth of 4 spk/sec (as detailed in the 'Materials and methods'). (B) Population-averaged discriminability index d’ values for regular (blue) and irregular (red) otolith afferents as a function of head orientation angle. '*' indicates statistical significance at the p=0.05 level using a Wilcoxon ranksum test.

https://doi.org/10.7554/eLife.45573.010

Discussion

Here we show that heterogeneities in the otolith afferent population give rise to different coding strategies to represent the gravito-inertial forces experienced during dynamic naturalistic translational self-motion and static head orientation relative to gravity. Analysis of responses to naturalistic translational self-motion stimuli revealed that irregular afferents displayed stronger nonlinearities, and transmitted more information than their regular counterparts for frequencies above 0.1 Hz, via both changes in firing rate and precise spike timing. By contrast, regular afferents transmitted less information primarily through changes in firing rate. Mathematical modeling reproduced these experimental findings, and further predicted that irregular afferents will display stronger phase locking in response to sinusoidal stimulation than their regular counterparts. We validated this prediction experimentally, thereby establishing a tight link between the mechanisms underlying precise spike timing in irregular otolith afferents and their propensity to phase lock in response to sinusoidal stimulation. Finally, using signal detection theory, we found that regular afferent spiking activities obtained by statically positioning the head at different orientations relative to gravity were more discriminable from one another than for irregular afferents. Taken together, our findings establish that irregular and regular otolith afferents differentially encode naturalistic translational head motion and static orientation relative to gravity. Specifically, irregular otolith afferents with high sensitivity and resting discharge variability preferentially encode translational head motion over the 0.1–15 Hz frequency range, whereas regular otolith afferents with lower sensitivity and resting discharge variability instead preferentially encode static head orientation relative to gravity.

Role of resting discharge variability in determining coding in the otolith system

Our results show that irregular afferents, which have greater resting discharge variability than their regular counterparts, actually show lower trial-to-trial variability during naturalistic translational self-motion stimulation. We hypothesize that this is due to the observed strong nonlinearities in their responses, which are due at least in part to higher sensitivity. As such, our results show that the coding properties of otolith afferents during naturalistic translational self-motion stimulation are qualitatively different than those observed previously, which solely considered changes in firing rate (Jamali et al., 2013; Yu et al., 2015). Thus, while theory predicts that trial-to-trial variability during stimulation will increase with increasing resting discharge variability for linear systems (Chacron et al., 2003; Risken, 1996), this is not valid when strong response nonlinearities are present, as is the case during naturalistic translational self-motion. Nevertheless, it is important to note that the relatively lower intensity stimuli resulting from statically positioning the head at different orientations relative to gravity do not elicit strong response nonlinearities from either regular or irregular afferents (Fernandez et al., 1972). As a result, the trial-to-trial variability during static stimulation will be proportional to the resting discharge variability, and thus lower for regular afferents relative to their irregular counterparts. Our results show that this lower resting discharge variability offsets the detrimental effects of lower sensitivity, thereby giving rise to greater stimulus discrimination.

Differential encoding of gravito-inertial forces by irregular and regular otolith afferents: implications for perception

Our results show that regular and irregular otolith afferents use different coding strategies to provide estimates of both dynamic head motion and static orientation relative to gravity. Overall, the mutual information rate densities of irregular afferents were consistently higher across almost the entire physiologically relevant frequency range (0.1–15 Hz) than those of regular afferents. However, as we were only able to reliably estimate information for frequencies ≥0.1 Hz (i.e., the inverse of the stimulus duration of 10 s), how regular and irregular otolith afferents respond to naturalistic translational self-motion for frequencies <0.1 Hz remains unknown. Nonetheless, on the basis of our results obtained using static head orientations (i.e., 0 Hz), we predict that the information transmitted by regular afferents will become greater than that transmitted by irregular afferents as the frequency approaches zero (Figure 2E). This implies that regular afferents outperform their irregular counterparts at encoding low-frequency (i.e., <0.1 Hz) head acceleration signals. Further experiments are needed to test this hypothesis. It should be noted that otolith afferents cannot distinguish the forces that result from translational self-motion from those resulting from changes in head orientation, as detailed below. Therefore, we predict that our results will apply equally to stimuli resulting from either condition. Specifically, we predict that irregular otolith afferents will outperform their regular counterparts at encoding dynamic changes in head orientation, provided that their temporal frequency content is high enough (i.e., >0.1 Hz). Moreover, we predict that regular otolith afferents will outperform their irregular counterparts at encoding low frequency (i.e., <0.1 Hz) translational self-motion.

Behavioral studies have shown that humans and monkeys can distinguish translational self-motion direction when the acceleration exceeds ~1 cm/s2 (s MacNeilage et al., 2010, Soyka et al., 2011, Valko et al., 2012 and Bermúdez Rey et al., 2016; whereas those on monkeys include Gu et al., 2007 and Yu et al., 2015). However, neural detection thresholds for single otolith afferents are substantially higher (~10 cm/s2) (Jamali et al., 2013; Yu et al., 2015), indicating that pooling the activities of multiple otolith afferents is required to give rise to perception of translational self-motion. By contrast, when considering differences in static head orientation relative to gravity, our results here have shown that single regular otolith afferents display discriminability values that are similar to those reported in psychophysical studies (~2o) (Clemens et al., 2011; Valko et al., 2012; Karmali et al., 2014; Janssen et al., 2011; Dahlem et al., 2016; Tarnutzer et al., 2013). This suggests that little additional pooling of afferent activities is actually required. We speculate that this exceptional sensitivity to static differences in spatial orientation serves an essential role in the maintenance of posture during everyday life.

An important problem for the vestibular system is how to distinguish the gravito-inertial forces that result from translational self-motion from those that result from changes in head orientation (also commonly referred to as tilts). Einstein’s equivalence principle posits that the forces resulting from both conditions are physically indistinguishable from one another (Angelaki and Cullen, 2008; Guedry, 1974; Young, 2011). Thus, otolith afferents, which sense linear acceleration, cannot be used alone to distinguish between both conditions (see Goldberg, 2012). It is important to note, however, that semicircular canal afferents will be stimulated by the rotations associated with changing head orientation relative to gravity but not by translational self-motion. Accordingly, the brain can theoretically distinguish between these two movement conditions by integrating multi-sensory inputs from both otolith and canal afferents (Guedry, 1974; Young, 2011; Mayne, 1974; Angelaki and Yakusheva, 2009; Merfeld et al., 1999).

To date, the neuronal mechanisms underlying the distinction between the gravito-inertial forces resulting from tilts versus those resulting from translations have been investigated with well-established methods that use stimuli with identical linear accelerations (Laurens et al., 2013; Laurens et al., 2011; Angelaki et al., 2004; Yakusheva et al., 2007; Yakusheva et al., 2008). Notably, Purkinje cells in the caudal vermis integrate otolith and semicircular canal inputs (reviewed in Angelaki and Cullen, 2008), such that one subset preferentially encodes translations (Yakusheva et al., 2007; Yakusheva et al., 2008) while another preferentially encodes tilts (Laurens et al., 2013). Parietoinsular vestibular cortex neurons can likewise discriminate tilts from translations (Liu et al., 2011). Interestingly, translational self-motion at very low frequencies (i.e., <~0.1 Hz) is incorrectly interpreted as a change in head orientation (Glasauer and Merfeld, 1997; Kaptein and Van Gisbergen, 2006; Seidman et al., 1998; Merfeld et al., 2005b; Merfeld et al., 2005a), thereby generating the ‘somatogravic’ illusion, a cause of disorientation that can be extremely dangerous for pilots. The firing rate modulation of tilt-sensitive cerebellar Purkinje cells appears to provide a neural substrate for this perceptual effect (Laurens et al., 2013). Further studies will be needed to investigate whether, and if so how, changes in firing rate and precise spike-timing information from regular and irregular otolith afferents are differentially decoded by downstream pathways to give rise to other attributes of perception and/or behavior. For example, approaches dissociating the contributions of regular and irregular afferents (e.g., silencing of irregular afferents via anodal currents; Minor and Goldberg, 1991) should provide new insights.

Mechanisms underlying spike-timing precision and phase locking in otolith afferents

Our present results further show that the precise spike timing that is preferentially displayed by irregular otolith afferents in responses to naturalistic translational self-motion is strongly correlated with a tendency to phase lock in response to sinusoidal stimulation. In this context, it is important to note that prior studies investigating otolith afferent responses have predominately focused on relatively low frequencies (of <5 Hz) (Fernández and Goldberg, 1976b; Angelaki and Dickman, 2000; Yu et al., 2012; but see Jamali et al., 2013), whereas natural translational self-motion stimuli contain frequencies up to 20 Hz (Carriot et al., 2014; Carriot et al., 2017). Here, we found that irregular otolith afferents show significant phase locking that increases as a function of stimulation frequency within the physiologically relevant range. Interestingly, auditory stimuli can also induce phase locking in otolith afferents, a property that may relate to the otoliths’ evolutionary origin as hearing organs (reviewed in Straka et al., 2016). Specifically, phase locking has been reported in irregular otolith afferents for sound and vibration stimuli (reviewed in Curthoys and Grant, 2015) whose frequency content is much higher (100–3,000 Hz) than that found in natural vestibular stimuli (0–20 Hz; Carriot et al., 2014; Carriot et al., 2017). It has been proposed that such high-frequency stimuli cause fluid pressure waves in vestibular end organs, which in turn activate vestibular hair cells (Eatock and Songer, 2011; Curthoys and Grant, 2015).

The strong correlation between spike-timing precision in response to naturalistic stimulation and phase locking to sinusoidal stimulation seen for otolith afferents suggests that these two processes share common underlying mechanisms. Neurons in the auditory system also display precise spike timing, which is commonly associated with phase locking (see recent review by Heil and Peterson, 2017). Such phase locking is mediated by low-threshold voltage-gated potassium channels that promote hyperpolarization after spiking (Oertel et al., 2000; Day et al., 2008; Kuznetsova et al., 2008; Rothman and Manis, 2003). Interestingly, such channels are also present in vestibular afferents (Goldberg et al., 1984; Kalluri et al., 2010; Highstein and Politoff, 1978; Iwasaki et al., 2008), suggesting that the same mechanism mediates both phase locking and spike-timing precision in the auditory and vestibular systems. Further, morphological differences between regular and irregular afferents could also contribute to the observed differences in phase locking and spike-timing precision. Notably, regular afferents integrate information from multiple hair cells located far away from the spike initiation zone (Goldberg, 1991), whereas irregular afferents integrate synaptic input from relatively few hair cells and have their spike initiation zone located close by (Highstein and Politoff, 1978). The latter configuration probably minimizes spatial and temporal integration and is therefore predicted to lead to more precise action potential firing, consistent with our present findings.

The vestibular system uses different strategies to encode rotational and translational self-motion stimuli

Another important consequence of our results is that they firmly establish significant differences in how the otolith and canal systems encode naturalistic translational and rotational self-motion, respectively. Specifically, canal afferents also display heterogeneities in resting discharge and can also be classified as either regular or irregular (see Goldberg, 2000 for review). However, the greater sensitivity of irregular canal afferents is not sufficient to compensate effectively for their higher resting discharge variability (Sadeghi et al., 2007). Accordingly, irregular canal afferents display lower detection thresholds than their regular counterparts over the entire behaviorally relevant frequency range (Jamali et al., 2016; Massot et al., 2011; Sadeghi et al., 2007), while the detection thresholds of regular and irregular otolith afferents are similar over this range of frequencies (Jamali et al., 2013).

Comparison between the results presented here, which are focused on otolith afferents, and those of prior studies, which are focused on canal afferents, further reveals fundamental differences in information-coding strategies. Specifically, regular canal afferents preferentially encode rotational self-motion through changes in firing rate, whereas irregular canal afferents preferentially encode these through precise spike timing (Jamali et al., 2016). By contrast, our present results show that irregular otolith afferents transmit more information about high frequency (>0.1 Hz) translational self-motion than their regular counterparts through both changes in firing rate and precise spike timing, whereas regular afferents transmit more information about static head orientation relative to gravity through changes in firing rate. In this context, it is important to note that while otolith afferents display sustained responses to static forces (such as gravity) (Angelaki and Dickman, 2000; Fernández and Goldberg, 1976a; Fernandez et al., 1972; Purcell et al., 2003), this is not the case for canal afferents as their sustained responses to rotations at constant angular velocities are minimal (Fernandez and Goldberg, 1971). Taken together, our present results thus highlight the need for further work to understand how the distinctive coding strategies used by peripheral otolith versus canal afferents are decoded by downstream neurons in order to process these different attributes of head motion (e.g., linear motion vs. head orientation).

Materials and methods

All experimental protocols were approved by the McGill University Animal Care Committee (#2001–4096) and were in compliance with the guidelines of the Canadian Council on Animal Care.

Surgical preparation

Two male macaque monkeys (Macaca fascicularis), aged 6 and 8 years old, were prepared for chronic extracellular recording under aseptic conditions. The surgical preparation was similar to that previously described (Dale and Cullen, 2013). Briefly, under isoflurane anesthesia (0.8–1.5%), a stainless steel head post was secured to the animal’s skull with stainless steel screws and dental acrylic, allowing complete immobilization of the head during the experiments. The implant also held in place a recording chamber oriented stereotaxically towards the vestibular nerve where it emerges from the internal auditory meatus. Finally, an 18 mm diameter eye coil (three loops of Teflon-coated stainless steel wire) was implanted in the right eye behind the conjunctiva. After the surgery, buprenorphine was administered as analgesic (0.01 mg/kg IM, every 12 hr for 2–5 days) and cefazolin (25 mg/kg IM) was injected twice daily for 10 days. Animals were given at least 2 weeks to recuperate from the surgery before any experiments began and were housed in pairs on a 12 hr light/dark cycle.

Data acquisition

During experiments, the head-fixed monkey was seated in a primate chair mounted on top of a linear actuator in a dimly lit room. Thus, all vestibular stimulation was passively generated by the linear actuator rather than actively by the animal. The vestibular nerve was approached through the floccular lobe of the cerebellum, as identified by its eye-movement-related activity (Lisberger and Pavelko, 1986; Cullen and Minor, 2002); entry to the nerve was preceded by a silence, indicating that the electrode had left the cerebellum. Extracellular single-unit activity of otolith afferents was recorded using glass microelectrodes (24–27 MΩ) as previously described (Jamali et al., 2009). Head acceleration was measured by a 3-D linear accelerometer (ADXL330Z, Analog Devices, Inc, Norwood, MA) firmly secured to the animal’s head post. During experimental sessions, unit activity, horizontal and vertical eye positions, and head acceleration signals were recorded on digital audiotape for later playback. During playback, action potentials from extracellular recordings were discriminated using a windowing circuit (BAK Electronics, Mount Airy, MD). Eye position and head acceleration signals were low-pass filtered at 250 Hz (eight-pole Bessel filter) and sampled at 1 kHz. Data were imported into Matlab (The MathWorks, Natick MA) for analysis using custom-written algorithms (Jamali et al., 2019).

Experimental design

The otolith afferents included in the present study were characterized on the basis of their response to sinusoidal translational head movements (5 Hz, 0.2 G; G = 9.8 m/s2) applied along the fore-aft (90o) and/or lateral (0o) axes, and the absence of modulation during yaw rotations. Owing to limitations of our experimental setup, afferents that were predominantly sensitive to stimulation along the vertical axis were not included in our dataset.

Once an otolith afferent fiber was isolated, we first determined its preferred direction (PD), which is the axis along which the neuron is maximally responsive (Jamali et al., 2013). First, we applied sinusoidal translation (5 Hz, 0.2 G) along the fore-aft and lateral axes in the horizontal plane, and the sensitivity of the unit was computed in both directions using Spike2 software (CED, Cambridge, UK) and custom-written MATLAB algorithms (Jamali et al., 2019). We then used these measurements to estimate the tuning curve (i.e. the sensitivity as a function of direction) using a cosine fit (Angelaki and Dickman, 2000; Purcell et al., 2003; Fernández and Goldberg, 1976a). The preferred direction was then taken as the orientation for which neuronal sensitivity was maximal.

Each individual afferent was stimulated along its PD using three types of linear self-motion stimuli.

(i) Sinusoidal translations at 10 different frequencies (1–10 Hz) with peak acceleration of 0.2 G, which were used to investigate phase-locking behavior in otolith afferents. 

(ii) Different head orientations relative to gravity obtained by statically re-aligning the whole body at 3o, 6o, 9o, and 15o pitch angles in the direction that increased the afferent’s activity (i.e., nose up or nose down). After a waiting period following the applied change in pitch angle (Fernández and Goldberg, 1976a), we recorded each afferent’s activity for a minimum of 10 s while the head was statically positioned in the new orientation. 

(iii) Naturalistic translational self-motion stimuli that consisted of low-pass filtered Gaussian white noise (20 Hz cutoff) with zero mean and standard deviation of 0.1 G. The same 10 s realization of the stimulus was repeated 10 times on average in order to assess trial-to-trial variability.

We note that, due to the finite duration of the stimulus, we could not reliably estimate information for frequencies below 0.1 Hz (i.e., the inverse of the stimulus duration). Furthermore, estimating the mutual information at lower frequencies (e.g., 0.01 Hz) would require holding the afferent for durations of 1000 s (i.e., >16 min), which is not currently feasible given the vigorous nature of naturalistic self-motion stimuli.

Analysis of neuronal discharges

Resting discharge

The regularity of resting discharge (i.e., in the absence of stimulation) was determined by means of a normalized coefficient of variation (CV*, after Goldberg et al., 1984) of the interspike intervals (ISIs) recorded during spontaneous activity. Afferents with low values of CV* were classified as regular, whereas those high values of CV* (see Figure 1) were classified as irregular as in previous studies (Goldberg et al., 1990; Jamali et al., 2009; Yu et al., 2012).

Information transmission through changes in firing rate

Neural firing rates fr(t) were estimated by convolving the spike trains with a Gaussian spike density function (standard deviation of 10 ms) as previously described (Roy and Cullen, 2001). To estimate the response gain, the time varying firing rate fr(t) and the stimulus S(t) (i.e., linear acceleration) were both sampled at 1000 Hz. A transfer function H(f) was computed using H(f)=PSfr(f)/PSS(f) and the response gain was then computed as the magnitude of the transfer function G(f)=|H(f)|, where PSfr(f) is the cross-spectrum between the stimulus S(t) and the firing rate fr(t), and PSS(f) is the power spectrum of the stimulus S(t). All spectral quantities (i.e. power-spectra, cross-spectra) were estimated using multitaper estimation techniques with eight Slepian functions (Jarvis and Mitra, 2001) as previously described (Sadeghi et al., 2007). We obtained a linear estimate of the firing rates as described previously (Massot et al., 2012). This was done by convolving the transfer function H(t) described above with the stimulus S(t) and adding the baseline firing rate to this in order to form the linear prediction. The residual N(t) was then computed as the difference between the actual firing rate and its linear estimate.

Response nonlinearity and phase locking

We quantified correlations between the spike train and the stimulus. To do so, the spike train of each afferent in response to the noise stimuli was converted into a binary sequence R(t) with a bin width of 1 ms. The value of each bin was set to one if it contained an action potential and 0 otherwise. The stimulus-response (SR) coherence CSR(f) between the binary sequence R(t) and the stimulus S(t) was computed as in previous studies (Roddey et al., 2000):

(1) CSRf=|PSRf|2PSSfPRRf

where PSR(f) is the cross-spectrum between S(t) and R(t), and PSS(f) and PRR(f) are the power spectra of S(t) and R(t). The SR coherence varies between 0 and 1 and quantifies the extent to which S(t) and R(t) are linearly correlated for a given frequency f. To explore the presence of nonlinearity in the responses of otolith afferents, we quantified the coherence between neuronal activities in response to repetitions of the same stimulus. The response–response coherence (RR coherence) between sequences of action potentials was computed by:

(2) CRR(f)=|<PRiRj(f)>ij|2(<PRiRi(f)>i)2

where PRiRjf is the cross-spectrum between binary sequence Ri(t) and Rj(t), and PRiRif is the power spectra of Ri(t), respectively. Note that the average <>i,j is over all possible combinations of i and j where j < i, while <>i is the average over index i. CRRf is also a number between 0 and 1 and signifies the degree to which the responses to repeated presentations of the same stimulus are correlated at frequency f (Roddey et al., 2000). For k repetitions of the stimuli, the equation above becomes:

(3) CRRf=2k(k-1)i=2kj=1i-1PRiRjf2PRRf2

Since in general CRRfCSRf, a linear model is optimal if the SR coherence equals the square root of the RR coherence. A significant difference between these two quantities indicates that a nonlinear model is necessary to explain the relationship between the stimulus S(t) and the response R(t) for a given frequency f (Roddey et al., 2000). To quantify the difference between the SR and RR coherence estimates, we computed a non-linearity index (NI) as previously described (Chacron, 2006):

(4) NI=100×1-0100CSRf df0100CRRf df

A perfectly linear response results in an NI of zero, whereas with increasing non-linearity, NI approaches 100%.

We calculated the mutual information rate density between the stimulus S(t) and R(t) using (Rieke et al., 1996; Sadeghi et al., 2007; Theunissen et al., 1996):

(5) MIdensityf=-log21-CRRf /FR

where FR is the mean firing rate during stimulation. This normalization accounts for the fact that the mutual information rate density increases with firing rate (Borst and Haag, 2001). The mutual information rate was obtained by integrating (i.e., computing the area under the curve) the mutual information rate density over the frequency range 0–15 Hz.

To measure the phase-locking behavior of otolith afferents, we computed the phase-locking index (PLI) at each frequency of sinusoidal translation using methods previously used in the vestibular literature. As our first method, we calculated vector strength or synchronization index according to the following equation (Goldberg and Brown, 1969):

(6) PLI1=i=1ncos(θi)2+i=1nsin(θi)2n

where θi is the phase angle of spike i relative to the modulation cycle of the stimulus, and n is the total number of action potentials in the analysis window. PLI1 can vary between 0 and 1, with one indicating a perfect entrainment between the neuronal response and the modulation phase and 0 signifying no correlation.

We further used a second measure of phase locking that was based on the entropy of the cycle histogram (Kajikawa and Hackett, 2005; Schneider et al., 2011) which, unlike measures of vector strength (Mardia and Jupp, 2000), can quantify the degree of phase locking even in multi-peaked phase histograms, as in our case. The phase-locking index was quantified as:

(7) PLI2=1-E0/Emax
E0=<P(φ)log2P(φ)>
Emax=log2Nbin

where P(φ) is the probability of firing a spike as a function of stimulus phase, E0 is the entropy of the phase probability distribution, and Emax is the maximum entropy that corresponds to a uniform distribution. Note that PLI2 can vary between 0 and 1. When comparing PLI values to spike-timing precision, we used values computed in response to 10 Hz sinusoidal stimulation. We also used a third method based on the latency of the first spike (Ramachandran and Lisberger, 2006). Rasters of action potentials corresponding to each cycle of the stimulus were ordered according to the time at which the first spike was elicited. Then by plotting the time of the first spike as a function of the spike train number in the ordered rasters, the phase-locking index was computed as:

(8) PLI3=1-ρNμISI

where ρ is the slope of the relationship between the time of the first spike and the binary sequence number, N is the number of spike trains in the raster, and μISI represents the mean interspike interval during resting discharge. In essence, this measure determines what fraction of the average ISI (μISI) is covered by the range of first spike times (ρN) from the responses to each cycle of the stimulus. If the times of the first spikes remain relatively constant (negligible ρ), such that their range only extends up to a small fraction of the average ISI, then PLI3 approaches 1, indicating that the neuron exhibits phase-locking. On the other hand, if the range of first spike times expands across the rasters and reaches the average ISI, the value of PLI3 is near zero, which means that the spikes are not phase locked to the stimuli.

Firing rate responses in different spatial orientations

For each afferent, we determined the degree to which an ideal observer can distinguish an arbitrary non-zero acceleration H" from null (i.e, when the animal’s head was upright relative to gravity) using their corresponding empirical firing-rate distributions obtained for different head orientations. Specifically, we removed the first and the last 2 seconds of neural activity recorded while the head was statically positioned in a given orientation and used the time-dependent firing rate fr(t) to compute its probability density using a firing-rate bin-width of 4 spk/sec. We then computed the d' measure from signal detection theory (Green and Swets, 1966):

(9) d'θ=|μθ-μ0|(σ2θ+σ20)/2

where μθ and σ2θ are the mean and variance of the firing-rate distribution at head orientation θ, and μ0 and σ20 are the mean and variance of the firing-rate distribution at an angle of zero (i.e., vertical), respectively. The d' values were then plotted as a function of θ for regular and irregular units.

Spike-timing precision

To study the precision of spike timing in otolith afferents and to quantify the timescales at which these neurons operate to encode linear self-motion, we employed a classification method based on the Victor-Purpura (VP) measure (Victor and Purpura, 1996) as well as the van Rossum spike distance metric (VR) (van Rossum, 2001). First, to avoid non-stationarities in the response, we discarded the first and last 500 ms of each 10s-long epoch of broadband noise stimulus and split the remaining stimulus duration into nine 1s-long segments (i.e., nine different categories of self-motion stimuli). As mentioned earlier, for each neuron, we obtained the spike train during at least 6 (6–30) repetitions of these stimuli. For each category, one spike train was randomly chosen as a template and the remaining spike trains were assigned to one of the nine categories of stimulus based on the spike distance measure (see below). This procedure was repeated 30 times by drawing different template choices, and averages were then computed to construct a confusion matrix (Figure 3—figure supplement 1). The diagonal elements of this matrix correspond to the percentage of correctly classified spike trains (% correct), which was used as a measure of discrimination performance. Note that the chance level for classification accuracy was 11% because the probability that a spike train could be correctly assigned by chance in a discrimination procedure with nine classes is 1/9.

Distances between spike trains were estimated using the van Rossum (van Rossum, 2001) and the Victor-Purpura (Victor and Purpura, 1996) metrics. The van Rossum metric was computed in the following way. The spike train was first convolved with a decaying exponential kernel with time constant τ:

(10) ft=i=1MΘ(t-ti)e-(t-ti)τ

where ti is the ith spike time, M is the total number of spikes, and Θ(t) is the Heaviside step function (Θ(t) = 0 if t < 0 and Θ(t) = 1 if t ≥ 0). The distance between two spike trains Rj(t) and Rk(t) was then defined as the Euclidean distance between their corresponding filtered traces, fRj(t) and fRk(t):

(11) DvanRossum(fRj,fRk)τ=1τ0fRj(t)-fRk(t)2

Note that the parameter τ governs the temporal resolution of the metric; by varying τ (1 ≤ τ ≤2000 ms) and repeating the classification procedure mentioned above, we investigated the impact of different timescales of the neuronal response on discrimination performance. When τ is small, the metric acts as a ‘coincidence detector’ because even minor differences in spike timing contribute to the distance, whereas at larger timescales the difference in total spike count matters and thus the metric becomes more of a ‘rate difference counter’ (van Rossum, 2001).

The Victor-Purpura metric is computed as the minimum total cost of transforming a spike train into another spike train through a series of basic operations. Specifically, insertion and deletion of a single spike have an associated cost of 1 each, whereas shifting a spike in time by an amount Δt has an associated cost of qΔt (Victor and Purpura, 1997; Victor and Purpura, 1996), where q (in units of 1/sec) is a parameter that determines the relative sensitivity of the metric to spike count and spike timing. Note that the quantity 1/q is a measure of temporal resolution in this metric and is related to the time constant τ in the van Rossum metric.

Modeling

We built a leaky integrate-and-fire neuron to model the activity of otolith afferents using equations as follows:

(12) CmdVdt= -gV(t)+Ibias+σsignalSt+σnoiseξt
VtθVt+=0

where Cm is the membrane capacitance (Cm = 1 nF), V(t) is the membrane potential, g is the membrane conductance for the leak current (g = 0.22 µS), Ibias is a bias current (which is used to simulate the resting discharge of otolith afferents), St is the input current, which consisted of a broadband noise current (15 Hz cutoff) similar to the actual head acceleration stimuli applied to stimulate the afferents, and ξ is a Gaussian white noise process with zero mean and standard deviations of σnoise. To account for the known response dynamics of both regular and irregular otolith afferents, the stimulus St used in the model was obtained by filtering the original broadband noise current using the transfer functions of regular and irregular units as in previous studies (Jamali et al., 2016; Schneider et al., 2015). The parameters σnoise and σsignal determine the response variability and the strength of the signal, respectively. When V(t) is greater than or equal to the threshold θ (i.e., –50 mV), V(t) is immediately reset to 0 mV and a spike is said to have occurred at time t. Equation (11) was numerically integrated using an Euler-Maruyama algorithm with a time step of 0.025 ms. The spiking responses from the model were analyzed in the same way as the experimental data.

For the regular model neuron, parameter values were: Ibias = 3.53 nA, σnoise = 0.14 nA, σsignal = 0.14 nA. For the irregular model neuron, parameter values were: Ibias = 3.53 nA, σnoise = 1.9 nA, σsignal = 1.9 nA. Parameter values were set such that the responses of the regular and irregular model neurons mimicked experimental data (resting discharge; regular model, CV*=0.06; irregular model, CV*=0.42). We co-varied both sensitivity (i.e., σsignal) and variability (i.e., σnoise) in our model keeping their ratio constant and computed the information transmitted by firing rate and spike timing as described above for the experimental data.

Statistics

Our sample sizes were similar to those generally employed in the field (Si et al., 1997; Yu et al., 2012; Jamali et al., 2013; Yu et al., 2015; Laurens et al., 2017). All values are expressed as mean ± SEM throughout. Statistical significance was determined by using Wilcoxon ranksum tests at the p=0.05 level.

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Decision letter

  1. Joshua I Gold
    Senior and Reviewing Editor; University of Pennsylvania, United States
  2. Jean Laurens
    Reviewer; Baylor College of Medicine, United States

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

[Editors’ note: this article was originally rejected after discussions between the reviewers, but the authors were invited to resubmit after an appeal against the decision.]

Thank you for submitting your work entitled "Channel specific coding in the otolith system yields robust estimates of head motion and orientation relative to gravity" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Senior Editor.

Our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we feel that the main point in the current manuscript about selective coding of translation and tilt stimulus is interesting and important, but unfortunately it does not get sufficient support from the current data with the current experimental design. Thus, we regret to inform you that your work will not be considered further for publication in eLife.

Reviewer #1:

In the current study, Jamali et al., explored information coding in two subtypes of vestibular otolith afferents under two stimulus conditions: translation of the head/whole body, and static tilt of the head/whole body. The main finding is that the irregular otolith afferents show larger sensitivity to body translation compared to the regular subtypes, due to their distinguished response dynamics embedded in each class. In contrast, this response sensitivity is reversed under the static tilt (relative to gravity) condition, that is, the regular otolith afferents become more sensitive. These results, particularly the responses of the two types of afferents under static tilt condition, is new and worth reporting. However, there are also concerns here:

1) The current data clearly show that the irregular afferents are more sensitive, or carry more information about translation, including both approximate-natural or sinusoidal translation, compared to the regular counterparts. However, this does not necessarily exclude the possibility that the regular class can also encode translation information. Similarly, to static tilt, the irregular afferents are less sensitive compared to the regular counterparts, but again this does not mean that they cannot encode static tilt. Thus the authors' conclusion about irregular and regular respectively dealing with translation and static tilt, lacks sufficient and direct evidence support.

2) More importantly, the authors further implied that the afferents itself can solve the Einstein's Equivalence Principle problem, through the irregular and regular channels. This is wrong. First, it is well known that due to the physical properties, the otolith and its afferents have no way to solve this problem (e.g. Fernandez and Goldberg, 1976). Second, a series of previous studies (e.g. Angelaki and Dickman, 1999; Angelaki et al., 2004; Liu et al., 2011; Yukushiva et al., 2007) have designed delicate experimental paradigm to directly examine whether different brain stages, from the afferents to cerebellum and cerebral cortex, could solve the translation-tilt ambiguity problem. Importantly, this is done by providing sinusoidal translation, and a "matched" tilt stimulus. The key point is to use a "dynamic" tilt stimulus that provides momentary matched acceleration signal that can be perfectly cancelled or superimposed with the translation stimulus, allowing to examine whether the target neuron really prefers translation or tilt. Using this paradigm, previous researchers have found that otolith afferents respond equally under translation and its matched tilt stimulus. It would be nice for the current work, the authors could further examine how the two types of afferents respond under these stimulus condition, and thus can push this filed a step forward. Unfortunately, the authors here adopt static tilt, providing totally unmatched stimulus compared to the translation (either frequency varied or fixed sinusoidal), and thus cannot directly address whether each type of afferents selectively encode translation against (matched) tilt stimulus. In fact, if the authors have performed the correct experiment paradigm using matched dynamic tilt and translation stimulus, they are very likely to find that their results would be reversed, that is, irregular afferents would now become more sensitive to the (dynamic) tilt relative to gravity compared to the regular counterpart.

3) Thus, there is a fundamental difference between using the dynamic and static tilt stimulus. The current results cannot be used to address the classical Einstein's Equivalence Principle problem. To avoid confusions with the general audience, the author should use correct terms in their text. However, so far there is only one place which is in the last sentence in the Introduction part, the authors have used the word of "static", but did not do so for the other key places including the Abstract, Result and Discussion.

4) Even under the static tilt stimulus as used in the current study, the authors did not show clearly about how they provide the stimulus and compute the responses. How fast were the animals rotated from upright to the expected tilted position? What time window (suppose after tilted) was used to compute firing rate to get the d' value? The authors need to present the whole temporal dynamics of their data to show how they do this, as for their translation data.

5) The difference in the firing statistics and coding ability to the translation stimulus between the irregular and regular otolith afferents are well illustrated in the text, from Figure 1-4. However, these results were sort of reported and overlapped in previous studies, for example, in the authors' own group (Jamali et al., 2013, Figure 2). The only significant difference I see here is that they tested the responses to translation under a frequency-varied condition (what they call "natural"). However, this result is sort of expected from their previous results under the frequency-fixed sinusoidal translation condition, and thus may not be novel enough for the journal. Can the authors clearly state the significant progress they made about the irregular and regular afferents coding ability compared to previous results (e.g. Jamali et al., 2013)?

Reviewer #2:

In this manuscript, Jamali and colleagues analyze the information transmitted by regular and irregular otolith afferents of macaque monkeys, recorded during low-frequency tilt and high-frequency translation. They demonstrate that irregular afferent encode high-frequency otolith stimulation better than regular afferent, due to higher response gains and phase locking. In contrast, regular afferent encode static (i.e. low-frequency) otolith stimulus better.

In line with earlier works, Jamali's analysis of afferent spiking is comprehensive, state-of-the art and well presented. The dataset shown here is also impressive, considering the difficulty of recording otolith afferents. Altogether, this study offers a novel and highly informative study of otolith firing, in particular in the high-frequency range.

Unfortunately, the authors draw an incorrect and flawed conclusion from these results, which is that irregular afferent preferentially encode translational motion whereas regular afferent preferentially encode head orientation relative to gravity. Based on Einstein's equivalence principle, linear and gravitational acceleration are physically indistinguishable, and all otolith afferents respond identically to tilt and translations. The author's implied logic is that natural tilt and translation are segregated in the frequency domain, tilt being confined to low frequencies and translations high frequencies. However, the authors make no effort to justify this assumption. Actually, their own studies (Carriot et al. 2014, 2017) show that natural tilt movements extend well into the high frequency range (>1Hz) where irregular afferent respond preferentially. Furthermore, it is accepted that low-frequency translations are infrequent, such that low-frequency otolith stimuli can be interpreted as tilt. However, regular afferents are also sensitive to mid- or high-frequency stimuli, since they have a flat gain curve. Therefore, they can pick up translations. Thus, both types of afferents are expected to carry mixture of tilt and translation signals. None of this is taken into consideration by the authors, who simply restrict their stimuli to low-frequency tilt and high-frequency translation, and therefore wrongly equate low frequency and tilt, and high frequency and translation. Thus, their conclusion that regular/irregular afferents are 'parallel channels that preferentially encode translations and gravity' is simply biased by their choice of stimuli.

The authors also fail to position their study relative to other works in the field. Until the late 90's, there have been two hypotheses about how the brain discriminates tilt from translation. The 'frequency segregation' hypothesis (Paige, Tomko, Telford, Raphan, Cohen…) posits that the brain segregates tilt and translation by frequencies, i.e. interprets low/high frequency otolith stimuli as tilt/translations respectively (and indeed Raphan 2002 suggests that this could be accomplished by weighting regular/irregular otolith inputs). The 'internal model' hypothesis, advanced e.g. by Mayne, Young and Oman, Merfeld and recently Laurens, Karmali, posits that central brain areas merge semi-circular canal and otolith information to separate tilt from translation (this hypothesis also explains that low-frequency otolith stimulation is preferentially interpreted as tilt based on the statistics of natural stimuli). The frequency segregation hypothesis predicts that the brain can't discriminate tilt and translation stimuli if they have identical frequencies. This has been refuted directly multiple times (in particular by Angelaki's group) and the internal model hypothesis has been repetitively validated by neuronal recordings (e.g. Angelaki, Laurens), psychophysics (e.g. Merfeld's group, Hess, McNeilage) and modeling (e.g. Laurens, Karmali, Bos and Bless). Although the authors are well aware of these progresses, they chose to ignore them (citing only one paper from the last 20 years!) and instead essentially resurrect the frequency segregation hypothesis.

This study contains new and important results on how otoliths transmit low and high frequency motion. I would encourage the authors to focus on this. Should they wish to maintain their hypothesis that regular/irregular afferents preferentially encode tilt and translation respectively, they should at least support it by a sound analysis of the statistics of natural stimuli, and place it in the context of current knowledge on tilt/translation discrimination, based on an accurate review of the literature.

To recapitulate:

Abstract fourth and final sentences; subsection “Parallel processing of gravito‐inertial forces: implications for perception” first sentence in first paragraph and final sentence in the second paragaph: These statements are simply false. Neither regular nor irregular afferent transmit tilt or translation preferentially, unless one assumes that tilt and translation occur in distinct frequency ranges. Such assumptions are never explicitly made, quantified or justified in the manuscript. Even if it was the case, each of this statement should be reworded to indicate that they are valid only under this assumption. Otherwise, they could actually mislead the reader to think that otoliths can actually resolve the tilt/translation ambiguity, which is physically impossible.

Subsection “Parallel processing of gravito‐inertial forces: implications for perception”: This part is extremely incomplete and misses all the modern literature (i.e. post year 2000) on tilt/translation discrimination. The authors should discuss the fact that neurons in the vestibulo-cerebellum can distinguish tilt and translation stimuli that have identical frequencies and magnitudes, which is physically impossible to accomplish in the otoliths, and therefore demonstrates the existence of a central process to distinguish tilt from translation.

Reviewer #3:

The authors investigated the type of information encoded by regular and irregular otolith afferents in monkeys during "naturalistic self-motion stimulation" They used appropriate analytical methods. Data analysis suggests that irregular otolith afferents use timing and rate code and are better suited to detect changes in "gravitionertial acceleration" Regular otolith afferents use only rate code and are better suited at estimating "gravitoinertial acceleration" during the steady state (such as static head tilt). Remarkably, their finding may reconcile two "alternative" hypotheses: that the brain uses only otolith‐related signals to generate a prediction of tilt and translation, vs that the brain uses a combination of otolith and canal signal. Likely, both strategies are used by the brain for spatial navigation. The authors also used computer simulations that indicate that the large sensitivity and variability of irregular afferents can explain the functional differences between afferent classes. The major finding of this study, according to the authors, is that irregular and regular afferent represent two information channels. One channel, regular afferents, relays mostly head orientation signal to the CNS. A second channel, irregular afferents, relay mostly translation. I believe, however, that the interpretation of the data is misleading or incorrect, as both regular and irregular afferents detect combined gravitational and translational information, but perhaps at different optimal frequency bands.

The major issue with this manuscript is that the conclusion, which is the major selling point of the manuscript, is misleading. The authors hypothesize that "Regular afferents preferentially transmit information about head orientation while irregular afferents instead preferentially transmit information about translational self‐motion" If true, this would be very relevant for the field because it would provide a novel solution to the ambiguity found in the response of otolith afferents (which carry gravito-inertial information). However, this hypothesis was not tested directly or indirectly in this study. Thus, it is misleading and should be rewritten through the manuscript to represent the data faithfully, starting with changing the title. There are many ways to test the authors' hypothesis. Perhaps, the simplest way would be to compare the response of afferents during translation and tilt stimuli that contain the same dynamics (i.e., stimuli that generate the same gravitoinertial acceleration). What the data show is that regular and irregular afferents show complementary frequency bands to discriminate gravitoinertial information.

Data analysis suggests that irregular otolith afferents use timing and rate code, while regular otolith afferents use only rate code. This is an important finding because it is opposite to the coding found in the semicircular canal afferents by the same group (Sadeghi et al., 2007). What are the implications that canal and otolith afferent show different coding strategies? Could these differences be due to differences in stimuli (e.g., frequency) or analytical methods between this experiment and that of Sadeghi et al., 2007?

It would help to have model simulation results in the last part of the result section (Figure 6).

[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]

Thank you for choosing to send your work entitled "Irregular and regular otolith afferents differentially encode naturalistic translational head motion and static orientation relative to gravity" for consideration at eLife. Your letter of appeal has been considered by a Senior Editor and the original reviewers, and we are prepared to consider a revised submission with no guarantees of acceptance.

Included below are comments from the reviewers, who were asked to comment on your appeal and revised manuscript. I am including them all in full because I think that they will all be useful to you for making revisions. Reviewer #3 suggested additional experiments, but after discussion we concluded that although such experiments would be quite informative, they are not necessary for a revision for eLife.

Reviewer #1:

In the current revised version of the manuscript, it is good to see that the authors have made significant improvements in their description and interpretation about their findings in that irregular and regular afferents are sensitive under different stimulus dynamics. However, some important citations are still missing, and there are still a few places that need to be further improved for publication:

1) As indicated in my comments in the first run, the findings about different neuronal sensitivity for the two types of afferents under high frequency translation and static tilt stimulus do not necessarily imply that the brain is using the strategy as expected by us, or the authors. First of all, irregular afferents are not unresponsive at all in the static tilt case, and the same logic applies to the regular afferents under the dynamic translation stimuli. Second, whether information about dynamic translation and static tilt stimulus is really decoded from the irregular and regular afferents, respectively, remains unknown under lacking of further experiments like the causality manipulation. Thus, the current statement in the Abstract was made to be too strong. Something like this is better: "Together, our results indicate that irregular and regular otolith afferents may use different strategies to encode naturalistic self-14 motion and static head orientation relative to gravity."

2) Subsection “Differential encoding of gravito-inertial forces by irregular and regular otolith afferents: implications for perception” second paragraph: About monkey's discriminability of self-motion direction, Gu and Angelaki, 2007, should be added in addition to Yu and Angelaki, 2015. About the relatively higher neuronal threshold of the otolith afferents compared to the behavior, Yu and Angelaki's work (2015) should be added in addition to Jamali 2013's work.

3) Third paragraph of subsection “Differential encoding of gravito-inertial forces by irregular and regular otolith afferents: implications for perception”: A comparison with the previous experiments, in particular, the difference in the methodology between the current study and the previous ones needs to be further expanded and clarified. As indicated in the first run of the reviewing process, a series of important works (see below) used a well established method by providing matched translation and dynamic tilt stimuli to examine and compare how neurons would respond under these two conditions with identical acceleration. These works are currently missing and should be included:

a) Angelaki et al., 2004, Neurons compute internal models of the physical laws of motion

b) Liu and Angelaki, 2011, Response Dynamics and Tilt versus Translation Discrimination in Parietoinsular Vestibular Cortex

c) Laurens and Angelaki, 2013, Neural representation of orientation relative to gravity in the macaque cerebellum

Reviewer #2:

In my initial review, I have appreciated the quality of the analyses presented in this manuscript, but I had major concerns regarding the study's overall message that regular and irregular afferents preferentially encode tilt and translation, respectively. However, I am glad to re-consider this study, provided that these concerns are addressed. I find that the authors have indeed addressed them, but not completely, and I would encourage them to revise their manuscript further.

Major points:

The major issue, expressed independently by all three original reviewers, is that the manuscript concluded that irregular and regular afferents preferentially encode head translation and tilt, respectively. I am somewhat bewildered by the author's argument that they never meant to imply this (see e.g. 384-388 of their initial manuscript), but I will let it slide. All three original reviewers independently understood that the manuscript made this conclusion, and there is no doubt that the vast majority of readers would have understood it too. One way or another, the manuscript needed to be revised.

In the present version, the authors have largely clarified this point. However, I think that some readers would still get the wrong message and that additional clarifications are needed:

– Results second paragraph: when they first describe their protocol, the authors should explain that it is representative of naturalistic medium/high-frequency translation or tilt, equivalently (and that their conclusions are equally valid for these types of motion).

– They should generally refer this protocol as a "naturalistic self-motion protocol" and not to "naturalistic translation" (as they already do in many instances). For instance, they should change subsection “Contributions of spike timing towards the encoding of translational self-motion by otolith afferents”; “Increases in variability and sensitivity lead to greater information transmission and spike timing precision”; “Irregular otolith afferents display phase-locking to sinusoidal self-motion translational stimuli.”; “Regular otolith afferents better encode differences in static head orientation relative to gravity than their irregular counterparts.” and Discussion, first paragraph.

In conclusion for this point, the authors' manuscript is very informative about how regular and irregular afferents differentially sense naturalistic, mid/high frequencies tilt and translation, e.g. as experienced when moving naturally. It should be made perfectly clear throughout the entire manuscript that this applies to tilt and translation. Regarding low-frequency motion, it is fine to propose that regular afferent may sense preferentially "quasi-static" stimuli, which, under natural circumstances, would mean head tilt.

Another major point, which I raised in the initial review, is that the discussion of how the brain discriminates tilt from translation is extremely incomplete. This has not been improved. Stating that the brain can "theoretically" distinguish tilt and translation by integrating otoliths and canal afferents was fine in 1998, but it is a gross misrepresentation of the current knowledge in the field. It has been demonstrated over and over that the brain discriminates tilt from translation centrally, and the underlying neuronal bases have been largely explored (predominantly Dora Angelaki's group). Therefore, the authors have to provide and short and up-to-date summary of the current knowledge on this topic.

By the way, in paragraph three of subsection “Differential encoding of gravito-inertial forces by irregular and regular otolith afferents: implications for perception”, the authors state that further studies should investigate how the brain processes otoliths afferent to give rise to perception during low frequency motion. They will be glad to learn that this has already been studied. Neuronal correlates of the somatogravic effect, where low-frequency translations are interpreted as tilt, have been identified by Laurens et al., 2013, in the vestibulo-cerebellum. And the cerebellum contributes to self-motion perception (Dahlem et al., 2016).

Reviewer #3:

In this manuscript, Jamali and colleagues show empirical and modeling data supporting the hypothesis that irregular and regular afferents use different coding methods suitable for representing high-frequency and low-frequency gravitoinertial acceleration, respectively. The manuscript has improved significantly from the original version by departing from its previous claim that the tilt/translation ambiguity is solved at the afferent level.

The general strengths of the manuscript remain the same as in the previous version and include: a set of technically challenging experiments, well suited analytical tools and statistics, and the use of modeling work that can explain the results. It remains controversial whether, or to a which degree, the CNS is decoding information from vestibular afferents as proposed here since both regular and irregular afferents inform about translation and static tilt. Thus, the manuscript may not be of sufficient impact to merit publication in this journal. Interestingly, the authors' hypothesis produces testable predictions on the effect of silencing irregular afferents (i.e., using anodal currents) in perceptual thresholds. Addition of these experiments would raise the impact of the manuscript to merit publication in eLife.

https://doi.org/10.7554/eLife.45573.015

Author response

[Editors’ note: the author responses to the first round of peer review follow.]

First, we would like to thank the editors and reviewers for their efforts in reviewing our paper and providing feedback. We note that there is a consensus amongst all 3 reviewers that our study provides a new and significant contribution to the neuroscientific community and is hence worth reporting. Specifically:

Reviewer #1. “These results, particularly the responses of the two types of afferents under static tilt condition, are new and worth reporting”.

Reviewer #2. “This study contains new and important results on how otoliths transmit low and high frequency motion” and “In line with earlier works, Jamali's analysis of afferent spiking is comprehensive, state-of-the art and well presented. The dataset shown here is also impressive, considering the difficulty of recording otolith afferents. Altogether, this study offers a novel and highly informative study of otolith firing, in particular in the high-frequency range.”

Reviewer #3. “Remarkably, their finding may reconcile two "alternative" hypotheses: that the brain uses only otolith‐related signals to generate a prediction of tilt and translation, vs that the brain uses a combination of otolith and canal signal. Likely, both strategies are used by the brain for spatial navigation. What the data show is that regular and irregular afferents show complementary frequency bands to discriminate gravitoinertial information….This is an important finding because it is opposite to the coding found in the semicircular canal afferents by the same group (Sadeghi et al.,

2007).”

Thus, overall, the reviewers acknowledged that our results and analysis are not only rigorous and robust, but also make significant contribution to the literature.

Indeed, our study is the first to have tested the static and dynamic responses of otolith afferents over a broad physiological range up to 15 Hz using naturalistic stimuli. Based on our data and analyses, our findings make numerous novel and important contributions to the literature, including:

– We establish for the first time, the coherence, information content, and coding strategies of otolith afferents during naturalistic stimuli.

– We show for the first time that irregular and regular primate otolith afferents use different strategies to encode naturalistic translational head motion and static orientation relative to gravity.

– We reproduce these results using an integrate and fire model and explore how the interplay between variability and sensitivity influence the coding strategies employed by otolith afferents.

– We predict and then confirm that otolith afferents actually phase lock for sinusoidal stimulation applied over the physiologically relevant frequency range.

These findings are all novel and highly informative for both the vestibular field as well as the neuroscience community in general.

Based on our reading of the editor’s letter and reviews, we believe that the paper was not rejected due to any issues relating to the validity of any of the findings listed above. Instead, it appears that the paper was rejected due to a misunderstanding of our conclusions, due in large part to a single paragraph in the discussion. In particular, the main concerns of reviewers 1 and 2 is that they felt we implied that otolith afferents alone can solve the ambiguity between tilt and translation (i.e., “Einstein's Equivalence Principle problem”). Specifically,

Reviewer #1 “More importantly, the authors further implied that the afferents itself can solve Einstein's Equivalence Principle problem, through the irregular and regular channels..”

Reviewer #2 “Based on Einstein's equivalence principle, linear and gravitational acceleration are physically indistinguishable, and all otolith afferents respond identically to tilt and translations. The author's implied logic is that natural tilt and translation are segregated in the frequency domain, tilt being confined to low frequencies and translations high frequencies.”

However, we never stated or intended to imply that afferents alone can solve the Einstein's Equivalence Principle problem. Our goal in this section of the discussion was simply to review and acknowledge the literature on this topic. In fact, our argument was quite the opposite, and in our original submission, we actually had explicitly stated that “As mentioned above, Einstein’s equivalence principle posits that the forces resulting from both are physically indistinguishable from one another …Thus, otolith afferents transmit ambiguous information to the brain during everyday life”, as they encode both tilt and translation.

Overall, we believe there was a misunderstanding regarding our use of the term “head orientation” in the text that followed. Throughout the text we used the term “head orientation” to refer to “static head orientation” and not changes in head orientation or dynamic tilt. Since, in our original submission, we had always used the term “static head orientation” to introduce results and discussion related to this aspect of our study, we did not think it was necessary to reiterate the word “static” each time since it made the writing seem overly repetitive. However, we now appreciate that this has led the reviewers to misunderstand our interpretation of the results.

Based on these comments, which only required only text editing changes we have revised the manuscript. For example, we now consistently precede any reference to the coding of head orientation with the word static in the revised manuscript.

Furthermore, we have revised the Discussion to more clearly state that otolith afferents alone cannot solve Einstein's Equivalence Principle. Specifically: “Our results show that regular and irregular otolith afferents use different coding strategies in order to provide estimates of both dynamic head motion and static orientation relative to gravity..” and now more clearly make our point that future work is needed to understand how information carried by regular and irregular otolith afferents during natural stimulation gives rise to perception. Additionally, we have revised our title to: “Irregular and regular primate otolith afferents differentially encode naturalistic translational head motion and static orientation relative to gravity.”

Finally, as detailed above and acknowledged by the reviewers, as well as considering the difficulty of recording from otolith afferents, we again emphasize that our study provides significant novel information about the response properties of these neurons.

We strongly believe that our results constitute a major conceptual advance with respect to previous studies, and has high impact not only for the vestibular field but also for those interested in neural coding and a broader group of neuroscientists interested in how the brain processes sensory inputs to ensure accurate behavior.

[Editors’ note: the author responses to the re-review follow.]

Included below are comments from the reviewers, who were asked to comment on your appeal and revised manuscript. I am including them all in full because I think that they will all be useful to you for making revisions. Reviewer #3 suggested additional experiments, but after discussion we concluded that although such experiments would be quite informative, they are not necessary for a revision for eLife.

Reviewer #1:

In the current revised version of the manuscript, it is good to see that the authors have made significant improvements in their description and interpretation about their findings in that irregular and regular afferents are sensitive under different stimulus dynamics. However, some important citations are still missing, and there are still a few places that need to be further improved for publication:

1) As indicated in my comments in the first run, the findings about different neuronal sensitivity for the two types of afferents under high frequency translation and static tilt stimulus do not necessarily imply that the brain is using the strategy as expected by us, or the authors. First of all, irregular afferents are not unresponsive at all in the static tilt case, and the same logic applies to the regular afferents under the dynamic translation stimuli. Second, whether information about dynamic translation and static tilt stimulus is really decoded from the irregular and regular afferents, respectively, remains unknown under lacking of further experiments like the causality manipulation. Thus, the current statement in the Abstract was made to be too strong. Something like this is better: "Together, our results indicate that irregular and regular otolith afferents may use different strategies to encode naturalistic self-14 motion and static head orientation relative to gravity."

We have changed the Abstract as the reviewer suggested.

2) Subsection “Differential encoding of gravito-inertial forces by irregular and regular otolith afferents: implications for perception” second paragraph: About monkey's discriminability of self-motion direction, Gu and Angelaki, 2007, should be added in addition to Yu and Angelaki, 2015. About the relatively higher neuronal threshold of the otolith afferents compared to the behavior, Yu and Angelaki's work (2015) should be added in addition to Jamali 2013's work.

The references were added per reviewer’s suggestion.

3) Third paragraph of subsection “Differential encoding of gravito-inertial forces by irregular and regular otolith afferents: implications for perception”: A comparison with the previous experiments, in particular, the difference in the methodology between the current study and the previous ones needs to be further expanded and clarified. As indicated in the first run of the reviewing process, a series of important works (see below) used a well-established method by providing matched translation and dynamic tilt stimuli to examine and compare how neurons would respond under these two conditions with identical acceleration. These works are currently missing and should be included:

a) Angelaki et al., 2004, Neurons compute internal models of the physical laws of motion

b) Liu and Angelaki, 2011, Response Dynamics and Tilt versus Translation Discrimination in Parietoinsular Vestibular Cortex

c) Laurens and Angelaki, 2013, Neural representation of orientation relative to gravity in the macaque cerebellum

We appreciate reviewer’s concern and have revised the Discussion to provide description of the neural correlates of how the brain can distinguish between tilt and translation and have included the suggested references.

Reviewer #2:

In my initial review, I have appreciated the quality of the analyses presented in this manuscript, but I had major concerns regarding the study's overall message that regular and irregular afferents preferentially encode tilt and translation, respectively. However, I am glad to re-consider this study, provided that these concerns are addressed. I find that the authors have indeed addressed them, but not completely, and I would encourage them to revise their manuscript further.

We thank the reviewer for his/her support and for providing constructive feedback that helped us to improve the quality of the paper. We appreciate the reviewer’s concerns and have further revised the manuscript to clarify this point.

Major points:

The major issue, expressed independently by all three original reviewers, is that the manuscript concluded that irregular and regular afferents preferentially encode head translation and tilt, respectively. I am somewhat bewildered by the author's argument that they never meant to imply this (see e.g. 384-388 of their initial manuscript), but I will let it slide. All three original reviewers independently understood that the manuscript made this conclusion, and there is no doubt that the vast majority of readers would have understood it too. One way or another, the manuscript needed to be revised.

In the present version, the authors have largely clarified this point. However, I think that some readers would still get the wrong message and that additional clarifications are needed:

We have revised the manuscript to improve the clarity of our main conclusions. We have further revised the text to clarify this point throughout the manuscript.

– Results second paragraph: when they first describe their protocol, the authors should explain that it is representative of naturalistic medium/high-frequency translation or tilt, equivalently (and that their conclusions are equally valid for these types of motion).

– They should generally refer this protocol as a "naturalistic self-motion protocol" and not to "naturalistic translation" (as they already do in many instances). For instance, they should change subsection “Contributions of spike timing towards the encoding of translational self-motion by otolith afferents”; “Increases in variability and sensitivity lead to greater information transmission and spike timing precision”; “Irregular otolith afferents display phase-locking to sinusoidal self-motion translational stimuli.”; “Regular otolith afferents better encode differences in static head orientation relative to gravity than their irregular counterparts.” and Discussion, first paragraph.

We appreciate the reviewer’s comment. We have revised the manuscript to improve clarity regarding the actual experimental protocols that were used and the implications of our results. Specifically, we now describe our stimulation protocol in detail at the beginning of the results by clearly defining the different stimuli used and now consistently refer to these using the same denominations throughout the manuscript. We have also expanded the discussion to clearly state the implications of our results: “Specifically, we predict that irregular otolith afferents will outperform their regular counterparts at encoding dynamic changes in head orientation, provided that their temporal frequency content is high enough (i.e., > 0.1 Hz). Moreover, we predict that regular otolith afferents will outperform their irregular counterparts at encoding low frequency (i.e., lower than 0.1 Hz) translational self-motion.”

In conclusion for this point, the authors' manuscript is very informative about how regular and irregular afferents differentially sense naturalistic, mid/high frequencies tilt and translation, e.g. as experienced when moving naturally. It should be made perfectly clear throughout the entire manuscript that this applies to tilt and translation. Regarding low-frequency motion, it is fine to propose that regular afferent may sense preferentially "quasi-static" stimuli, which, under natural circumstances, would mean head tilt.

We now mention in the text that, while our results showing that irregular otolith afferents outperform their regular counterparts for high (i.e., > 0.1 Hz) frequencies were obtained using translational self-motion stimuli, we predict that they will also apply to dynamic changes in head orientation provided that these also contain high (i.e., > 0.1 Hz) frequencies. We also mention in the text, while our results showing that regular otolith afferents outperform their irregular counterparts at distinguishing between different head orientations relative to gravity were obtained using static head orientations, we predict that they will also apply to translational self-motion provided that the frequency content is low enough (i.e. < 0.1 Hz).

Another major point, which I raised in the initial review, is that the discussion of how the brain discriminates tilt from translation is extremely incomplete. This has not been improved. Stating that the brain can "theoretically" distinguish tilt and translation by integrating otoliths and canal afferents was fine in 1998, but it is a gross misrepresentation of the current knowledge in the field. It has been demonstrated over and over that the brain discriminates tilt from translation centrally, and the underlying neuronal bases have been largely explored (predominantly Dora Angelaki's group). I can perfectly understand that (one of) the authors feel(s) in conflict with Dora Angelaki; but this is not a justification for writing a biased discussion in turn. Whether the authors like it or not, their study will raise the question of how the brain distinguishes tilt from translation. Therefore, they have to provide and short and up-to-date summary of the current knowledge on this topic.

We have revised the Discussion to provide a short and up-to-date summary of the current knowledge on the topic of distinguishing between tilt and translation.

By the way, in paragraph three of subsection “Differential encoding of gravito-inertial forces by irregular and regular otolith afferents: implications for perception”, the authors state that further studies should investigate how the brain processes otoliths afferent to give rise to perception during low frequency motion. They will be glad to learn that this has already been studied. Neuronal correlates of the somatogravic effect, where low-frequency translations are interpreted as tilt, have been identified by Laurens et al., 2013, in the vestibulo-cerebellum. And the cerebellum contributes to self-motion perception (Dahlem et al., 2016).

We have revised the Discussion to include these studies.

Reviewer #3:

In this manuscript, Jamali and colleagues show empirical and modeling data supporting the hypothesis that irregular and regular afferents use different coding methods suitable for representing high-frequency and low-frequency gravitoinertial acceleration, respectively. The manuscript has improved significantly from the original version by departing from its previous claim that the tilt/translation ambiguity is solved at the afferent level.

We thank the reviewer for the positive feedback.

The general strengths of the manuscript remain the same as in the previous version and include: a set of technically challenging experiments, well suited analytical tools and statistics, and the use of modeling work that can explain the results. It remains controversial whether, or to a which degree, the CNS is decoding information from vestibular afferents as proposed here since both regular and irregular afferents inform about translation and static tilt. Thus, the manuscript may not be of sufficient impact to merit publication in this journal. Interestingly, the authors' hypothesis produces testable predictions on the effect of silencing irregular afferents (i.e., using anodal currents) in perceptual thresholds. Addition of these experiments would raise the impact of the manuscript to merit publication in eLife.

We agree with the reviewer that such experiments would be quite informative. However, as noted by the editor, these are beyond this scope of this study and have revised the Discussion to point out that future studies should test these predictions.

https://doi.org/10.7554/eLife.45573.016

Article and author information

Author details

  1. Mohsen Jamali

    Department of Neurosurgery, Harvard Medical School, Massachusetts General Hospital, Boston, United States
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-1750-7591
  2. Jerome Carriot

    Department of Physiology, McGill University, Montreal, Canada
    Contribution
    Data curation, Investigation, Methodology
    Competing interests
    No competing interests declared
  3. Maurice J Chacron

    Department of Physiology, McGill University, Montreal, Canada
    Contribution
    Conceptualization, Supervision, Investigation, Methodology, Writing—original draft, Writing—review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-3032-452X
  4. Kathleen E Cullen

    Department of Biomedical Engineering, Johns Hopkins University, Baltimore, United States
    Contribution
    Conceptualization, Resources, Software, Supervision, Funding acquisition, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing
    For correspondence
    kathleen.cullen@jhu.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9348-0933

Funding

Canadian Institutes of Health Research

  • Kathleen E Cullen
  • Maurice J Chacron

Canada Research Chairs

  • Maurice J Chacron

National Institutes of Health (DC2390)

  • Kathleen E Cullen

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

The authors would like to thank Soroush Sadeghi for his contribution to data collection and S Nuara and W Kucharski for excellent technical assistance. This study was supported by the Canadian Institutes for Health Research and the Canada research chairs.

Ethics

Animal experimentation: All experimental protocols were approved by the McGill University Animal Care Committee (#2001-4096) and were in compliance with the guidelines of the Canadian Council on Animal Care. Two male macaque monkeys (Macaca fascicularis) were prepared for chronic extracellular recording under aseptic conditions. The surgical preparation was similar to that previously described (Dale & Cullen, 2013). Animals (aged 6 and 8 years old) were housed in pairs on a 12 hour light/dark cycle.

Senior and Reviewing Editor

  1. Joshua I Gold, University of Pennsylvania, United States

Reviewer

  1. Jean Laurens, Baylor College of Medicine, United States

Publication history

  1. Received: January 28, 2019
  2. Accepted: June 13, 2019
  3. Accepted Manuscript published: June 14, 2019 (version 1)
  4. Version of Record published: June 24, 2019 (version 2)

Copyright

© 2019, Jamali et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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