Our previous study was the first to investigate how neurons within the first central stage of vestibular processing in macaque monkeys respond to natural self-motion (Mitchell et al., 2018). Specifically, we focused on a class of neurons within the vestibular nuclei, vestibular-only (VO) neurons, that mediate vestibulo-spinal reflexes as well as self-motion perception (Abzug et al., 1974; Shinoda et al., 1988; Gdowski and McCrea, 1999; Meng et al., 2007; Marlinski and McCrea, 2009). Our results revealed that VO neurons optimally encoded naturalistic self-motion stimuli through temporal whitening (i.e., the spike train power spectrum is independent of temporal frequency and thus "white") because both neuronal variability and tuning were matched to effectively complement natural stimulus statistics (Carriot et al., 2014; Carriot et al., 2017; Mitchell et al., 2018). Our previous study was however limited since we only considered a single class of neurons within the vestibular nuclei and further did not take into account the effects of neural heterogeneities.

Importantly, while VO neurons mediate vestibulo-spinal reflexes as well as self-motion perception as mentioned above, two other distinct neuronal classes instead mediate the vestibulo-ocular reflex (VOR) and its adaptation. Specifically, position-vestibular-pause (PVP) neurons make the primary contribution to the VOR, whereas eye-head (EH) neurons receive cerebellar input and are required for VOR adaptation and motor learning (see Cullen, 2012 for review) (Lisberger, 1984; Lisberger, 1994; Lisberger et al., 1994; Ramachandran and Lisberger, 2008). The VOR generates robust compensatory eye movements in response to head movements encountered during everyday life in order to stabilize gaze (Goldberg et al., 2012) and is an attractive model for understanding how information transmitted by sensory neurons is actually decoded downstream to generate behavior. Importantly, the VOR requires that information as to the detailed timecourse of head movements be contained in the spiking activities of sensory neurons and transmitted to motor areas. However, to date, the effects of neural heterogeneities, particularly in terms of variability, within and across all three vestibular neuronal classes (i.e., PVP, EH, and VO) on coding of naturalistic self-motion remains unknown.

Accordingly, here we investigated how differences in variability within and across distinct central vestibular neuronal classes impact coding strategy during naturalistic self-motion. We first establish that, in the absence of stimulation, all three neural classes displayed a similar wide range of variability as quantified by the coefficient of variation (CV) of the resting discharge. To next determine whether neurons optimally encoded naturalistic self-motion stimuli, we computed their response power spectra as well as the mutual information. Specifically, we tested whether the response power spectrum was independent of frequency or, equivalently, whether the mutual information was close to its maximum possible value for a given level of variability as predicted by theory (Shannon, 1948; Rieke et al., 1996). We found that, within each class, neurons displaying high resting discharge variability displayed temporal whitening. In contrast, neurons displaying lower resting discharge variability did not display temporal whitening but instead faithfully encoded the stimulus’s detailed timecourse as assessed by linear stimulus reconstruction. Interestingly, our results show that faithful encoding was greatest for PVP neurons, suggesting that this coding strategy is necessary to generate the compensatory VOR eye movements observed during naturalistic self-motion stimulation. Using a well-established model of VOR pathways, we validated this prediction. Our findings suggest a novel functional role for variability toward establishing different coding strategies as required for different vestibular functions.

In order to investigate the effects of differences in variability on coding strategy for naturalistic self-motion by central vestibular neurons, single-unit recordings were made from PVP (N = 20), EH (N = 15), and VO (N = 17) neurons within the vestibular nuclei of macaque monkeys (Figure 1A, top). PVP, EH, and VO neurons were identified using standard methodology (reviewed in Cullen, 2012) that characterized a given neuron’s responses to rotational vestibular stimulation in the yaw axis (1 Hz, 40°/s peak velocity) and eye movements (Figure 1—figure supplement 1; see Materials and methods). Specifically, each neuron’s sensitivity to sinusoidal vestibular stimulation was recorded in the dark and while monkeys cancelled their VOR by fixating a target that moved with the vestibular turntable (VOR cancellation). Neuronal sensitivity to eye movements was assessed during steady fixation, saccades, and smooth pursuit (see Materials and methods). The vestibular and eye movement sensitivities of PVP, EH, and VO neurons in our dataset are shown in Figure 1—figure supplement 2 and agreed with previously published values (Roy and Cullen, 2002; Roy and Cullen, 2003; Massot et al., 2011; Mitchell et al., 2018). In particular, we note that PVP and EH neurons can be distinguished based on their differential sensitivities to eye and head movements during smooth pursuit and VOR cancellation, respectively (Figure 1—figure supplement 1).

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During stimulation, there is a component of the variability in the neural response that can be explained by the stimulus and a component that cannot (Stein et al., 2005). The latter component contributes to what is known as trial-to-trial variability in the neural response to repeated presentations of a given stimulus. Such trial-to-trial variability is largely determined by the variability of the resting discharge for vestibular neurons (Sadeghi et al., 2007; Massot et al., 2011; Jamali et al., 2013; Mitchell et al., 2018). This is because, in order to be detected, head movements must sufficiently perturb the resting discharge. As such, it is much easier to detect stimulation when the resting discharge is more regular (i.e., less variability) than when it is more irregular (i.e., more variability) (reviewed in Cullen, 2012).

Effects of variability on central vestibular neuronal coding of naturalistic self-motion

We next investigated the effects of variability on coding strategy during naturalistic self-motion stimulation. To do so, we recorded each neuron’s activity during the application of yaw rotations whose time course closely mimicked those experienced during natural conditions (i.e., the naturalistic self-motion stimulus; Figure 2A,B, see Materials and methods). The time-dependent firing rates in response to naturalistic self-motion stimulation of two example PVP neurons displaying high (left panel) and low (right panel) variability are shown in Figure 2C. Similar graphs for both high and low variability EH and VO example neurons are shown in Figure 2—figure supplement 1. These examples were typical in that all neurons responded to the head motion stimulus, although EH neurons typically responded with less modulation in firing rate than PVP and VO neurons (compare Figure 2—figure supplement 1 to Figure 2C). To quantify optimized coding via temporal whitening, we computed the spike train power spectrum during naturalistic stimulation (see Materials and methods). Our analysis revealed that the power spectra of PVP, EH, and VO neurons displaying high variability were independent of frequency (Figure 2D, solid curves) as they did not deviate from the Poisson confidence interval with the exception of low (<1 Hz) frequencies for the example EH neuron (Figure 2D, gray bands). As mentioned above, the fact that the spectral power was independent of frequency is indicative of temporal whitening. In contrast, spectral power for PVP, EH, and VO neurons displaying low variability decayed similarly to the stimulus power spectrum with increasing frequency and was thus not independent of frequency (Figure 2D, compare dashed curves to solid black). As such, these power spectra strongly deviated from the Poisson confidence interval (Figure 2D, gray bands), indicating that these neurons did not display temporal whitening.

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To quantify differences in temporal whitening, we computed the same whitening index measure that was used in our previous study (Mitchell et al., 2018). Overall, we found that the whitening index similarly depended on CV for all neuronal classes (Figure 2E, left panel). Further, we found that the whitening index was independent of resting discharge firing rate (Figure 2—figure supplement 2A) and the whitening index computed from neurons whose resting discharge firing rates were within a narrow range (45–55 sp/s) strongly depended on CV (Figure 2—figure supplement 2B). These results, together with the fact that neural sensitivity was independent of variability (Figure 2—figure supplement 3), suggest that the differences in whitening are primarily due to differences in variability and, as such, are universal for central vestibular neurons. To test that changes in whitening index were primarily due to changes in CV, we first built a simple model (see Materials and methods) in which changes in variability were explored systematically. Overall, this model correctly fits data from PVP, EH, and VO neurons across all levels of resting discharge variability (Figure 2E, left panel, red curve). Second, to further test our hypothesis, we built a linear-nonlinear cascade model (see Materials and methods and Figure 2—figure supplement 4A) that included the effects of variability in order to predict the spike train power spectrum during naturalistic stimulation for individual neurons. Overall, this model accurately predicted the response power spectra of the same six example neurons (Figure 2—figure supplement 4B). As such, there was excellent agreement between predicted and actual whitening index values for our dataset (Figure 2—figure supplement 4C; Student’s t-test, PVP: F₍₁₉₎ = 0.44, p=0.66; EH: F₍₁₄₎ = 0.98, p=0.34; VO = F₍₁₆₎=0.96, p=0.35). We note that the power spectrum of the resting discharge variability was not different from that of the trial-to-trial variability during stimulation for our dataset (Figure 2—figure supplement 5). Thus, it is reasonable to model the noise/variability during stimulation by adding the variability from the resting discharge. On average, whitening index values for PVP and EH neurons were comparable to those obtained for VO neurons (Figure 2E, right panel). While consistent with our previous finding that, at the population level, VO neurons tend to optimally encode the stimulus via temporal whitening, our current findings emphasize that there are important differences in optimal coding at the individual neuron level both within and across neuronal classes. Specifically, central neurons with low variability tend to not display temporal whitening.

We note that, unlike VO neurons, PVP and EH neurons are sensitive to eye as well as head movements. Thus, we next tested that our results for PVP and EH neurons were not due to patterning of quick phases and/or systematic changes in eye position that occurred throughout vestibular stimulation. To do so, we first compared results obtained on data where spiking activity during vestibular quick phases was removed and the remaining slow phase epochs concatenated (i.e., was is shown in Figure 2) to the entire dataset. Overall, no differences were observed (data not shown). Next, we compared results obtained by restricting our analysis to epochs during which the eye position was relatively constant (i.e., within + / - 5°; see Materials and methods) to those obtained using the full dataset (i.e., when eye position was not restricted). No significant differences were observed (Figure 2—figure supplement 6; Student’s t-test, F₍₃₄₎ = 1.3, p=0.2). Thus, our analysis indicates that differences in whitening observed for PVP and EH neurons are not due to differences in quick phase generation and/or changes in eye position during stimulation.

Finally, we investigated the relative contributions of variability vs. tuning toward determining temporal whitening for all central vestibular neural classes. Our previous results have shown that variability within the VO neuron population was essential toward determining temporal whitening (Mitchell et al., 2018). Here we extended this analysis to all three central vestibular neuron classes and investigated the effects of different levels of resting discharge variability within each class (Figure 2—figure supplement 7). Overall, central neurons with lower variability as quantified by the CV of the resting discharge displayed lower noise power than their counterparts with higher variability. However, there were no significant differences in the amount of signal power transmitted. As such, the signal-to-noise ratio (SNR) decreased with increasing variability. This latter result is important as it suggests that central vestibular neurons with lower variability actually transmit more information than those with higher variability. To test this, we computed the mutual information rate (see Materials and methods) for our dataset and found a significant decrease with increasing CV, thereby confirming our hypothesis (Figure 2—figure supplement 7). Finally, we quantified optimality of coding (i.e., the mutual information divided by its maximum possible value for a given level of variability) and found a significant increase with increasing CV (Figure 2—figure supplement 7), thereby confirming results obtained using the whitening index. Thus, while central vestibular neurons with high variability transmit less information in absolute terms than their counterparts with low variability, they are more optimal in the sense that the mutual information is closer to the maximum possible value.

Neurons with lower variability faithfully encode the detailed time course of naturalistic self-motion stimuli

Our results so far have shown that central vestibular neurons with low variability did not optimally encode naturalistic self-motion stimuli via temporal whitening but transmitted more information than their counterparts with high variability. This raises the question as to what is the functional role of such neurons? Our results showing that the spike train power spectrum of these neurons decayed with increasing frequency like that of the naturalistic self-motion stimulus, together with higher mutual information rates, suggest that these neurons faithfully relay information about the detailed time course of self-motion signals. Indeed, inspection of their time-dependent firing rate responses to naturalistic self-motion stimulation suggests a strong linear relationship between their responses and the stimulus (Figure 2C and Figure 2—figure supplement 1, bottom panels). To test this hypothesis, we quantified the fraction of variance in the stimulus that could be correctly reconstructed from the spiking activity by using a linear decoder that minimizes the mean-squared error between the original and reconstructed stimulus waveforms. Specifically, the reconstructed stimulus was obtained by convolving the spiking activity with a filter whose shape was chosen such as to minimize the mean-squared error between the reconstructed and original stimulus waveforms (see Materials and methods and Figure 3A). The left panel of Figure 3B shows the original naturalistic self-motion stimulus (black) together with the reconstructed stimulus (red) for an example PVP neurons with high variability. The right panel of Figure 3B shows the same but for an example PVP neuron with low variability. These examples were typical in that there was a much better match between the original and reconstructed stimuli for the PVP neuron with low variability (Figure 3B, compare left and right panels). Qualitatively similar results were obtained for EH and VO neurons (Figure 3—figure supplement 1). We quantified these results by computing the coding fraction (CF), which is the fraction of variance in the stimulus that is correctly reconstructed (see Materials and methods). Overall, we found a strong negative correlation between CF and variability as quantified by CV (Figure 3C; All data: R = −0.53, p=10⁻⁴; PVP: R = −0.51; p=0.02; EH: R = −0.07, p=0.8; VO: R = −0.65,p=4.5×10⁻³). Further, we found that CF was independent of the resting discharge firing rate (Figure 3—figure supplement 2A: All data: R = 0.13, p=0.34; PVP: R = 0.05, p=0.82; EH: R = 0.01, p=0.96; VO: R = −0.06, p=0.81). Moreover, CF computed from neurons whose firing rates were within a narrow range (45–55 sp/s) also strongly depended on CV (Figure 3—figure supplement 2B: All data: R = −0.54, p=0.03; PVP: R = −0.96, p=0.03; EH: R = −0.20, p=0.7; VO: R = −0.87, p=0.02). These results strongly suggest that changes in CF were primarily due to changes in the resting discharge CV.

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Importantly, the fact that low values of CF were obtained for neurons with high variability was not trivially due to a lack of response. This is because, as mentioned above, there was no significant correlation between neural sensitivity and variability (Figure 3D). Moreover, as noted above, there was no significant correlation between neural sensitivity to sinusoidal stimulation at different frequencies and variability (Figure 2—figure supplement 2). Overall, PVP neurons displayed the largest coding fraction, followed by VO neurons, and EH neurons displayed the lowest coding fractions overall (Figure 3E). These results demonstrate that neurons with low variability more faithfully represented the stimulus’ detailed time course in their spiking activities than their counterparts with high variability. Thus, together with our results above showing that neurons with low variability do not display temporal whitening, we conclude that variability establishes a trade-off between faithful stimulus encoding and temporal whitening.

Faithful encoding of the time course of naturalistic self-motion stimuli by neurons with low variability is best matched to the known decoding properties of VOR pathways in order to generate the VOR.

Our results show that, across all classes, PVP neurons most faithfully represented the stimulus’ detailed time course in their firing activities. Nevertheless, a significant fraction of PVP neurons displayed temporal whitening. Importantly, information is only useful to the organism if it is decoded by downstream brain areas. As mentioned above, VOR pathways are an attractive model for understanding how information transmitted by sensory neurons is actually decoded downstream to generate behavior because of their relatively simple and well-understood neural circuitry. We first tested whether the VOR evoked in response to naturalistic self-motion stimulation was in fact compensatory. We found that indeed both animals generated robust compensatory eye movements characterized by gains approaching unity, such that the eye velocity was essentially the opposite of head velocity (Figure 4A). This brings the important question as to how these compensatory eye movements are generated. Specifically, which of faithful encoding or temporal whitening by PVP neurons is most appropriate to generate compensatory VOR eye movements during naturalistic self-motion stimulation.

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To answer this question, we used well-established models of VOR pathways in which the head velocity input elicits responses from peripheral vestibular afferents that project to VOR neurons. The output of VOR neurons is in turn decoded by the neural integrator as well as by extraocular motoneurons and the oculomotor plant in order to generate compensatory eye movements (Figure 4B, top; see Materials and methods). Our simulations show that, when the naturalistic head velocity stimulus was used as input, the model generated a robust VOR consistent with that observed experimentally (Figure 4—figure supplement 1). Next, we used the spiking activities of PVP neurons during naturalistic stimulation as input to downstream decoders (i.e., the neural integrator, extraocular motoneurons, and the oculomotor plant) in order to predict compensatory VOR eye movements (Figure 4B, bottom). The predicted eye velocity was then compared to the actual eye velocity (i.e., that computed from measured eye movements) for each PVP neuron in our dataset. Figure 4C shows the predicted (red) and actual (black) eye velocity time series (inset) and power spectra (main panels) when the spiking activities from example PVP neurons with low (left) and high (right) variability were used as input. We found that there was much better agreement between the predicted and actual eye velocity signals when the input from an example PVP neuron with low variability was used (compare right and left panels in Figure 4C). The agreement between predicted and actual eye velocity signals was quantified using a matching index that ranged between 0 (no agreement) and 1 (perfect agreement; see Materials and methods). There was a strong negative correlation between the matching index and variability (R = −0.64, p=2.4×10⁻³; Figure 4D, magenta), suggesting that PVP neurons with lower variability that faithfully represent the detailed time course of head movements make the primary contribution to generate compensatory VOR eye movements. To further test this proposal, we compared the performance at stimulus reconstruction from neuron pairs with varying levels of variability. Overall, we found that the performance of neuron pairs with low variability was overall greater than that obtained when considering pairs with low and high variability (Figure 4—figure supplement 2), which confirms our proposal. For completeness, we also tested which of faithful encoding or temporal whitening by EH neurons, which are required for VOR adaptation and motor learning, is most appropriate to generate compensatory VOR eye movements. Overall, results for EH neurons were qualitatively similar to those obtained for PVP neurons (Figure 4—figure supplement 3 and Figure 4D, blue; R = −0.64, p=0.01). Thus, taken together, our results point to an important functional role for VOR neurons with low variability that faithfully represent the detailed time course of head movements. Specifically, the activities of these neurons are best matched to the known dynamics of downstream decoders in order to generate compensatory VOR eye movements.

The data is available on figshare http://doi.org/10.6084/m9.figshare.12594803.

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Thank you for submitting your article "Neural variability determines coding strategies for natural self-motion: implications for perception and behavior" for consideration by eLife. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Joshua Gold as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

As the editors have judged that your manuscript is of interest, but as described below that substantial additional analyses and clarifications are required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv (if it is not already there) along with this decision letter and a formal designation that the manuscript is "in revision at eLife". Please let us know if you would like to pursue this option. (If your work is more suitable for medRxiv, you will need to post the preprint yourself, as the mechanisms for us to do so are still in development.)

The dichotomy between faithful and efficient coding neurons received a good deal of attention in the consultation among the reviewers. All of the reviewers felt that more needed to be done to clarify and to test this distinction. For example, it is not clear how the decoding errors could be larger for the efficient coding neurons if they really are efficient. Related to this point is whether the efficient coding neurons are simply noisier, and if the whitening comes at the expense of higher noise. Several additional specific points raised in the individual reviews are related to this point. I should emphasize that in consultation the reviewers felt more strongly about this point than is reflected in the individual reviews, and whether you are able to deal with it clearly and effectively will be critical to a re-evaluation of the paper.

Reviewer #1:

This paper follows a previous paper from some of the same authors exploring coding of naturalistic inputs in the vestibular system. The previous paper showed that the combination of stimulus power spectrum, neural filtering and noise led to spectrally-flat ("whitened") responses in one class of vestibular neuron. The present paper extends this analysis to two other types of vestibular neurons, concluding that they show considerable heterogeneity in the degree of whitening. I had several concerns about the analysis/presentation:

Filter calculations and non-Gaussian stimuli:

The paper relies on naturalistic head movement stimuli and uses these for the coding analyses. Some of the calculations presented, however, are valid only for gaussian stimuli. This is particularly true of the linear-nonlinear model and more broadly the construction of the transfer functions. Thus, it seems that the filters extracted could be impacted by the correlation structure of the stimulus. This is a key issue for interpretation of the paper.

Adding noise and optimality:

Neurons that whiten the stimulus are referred to as optimal, while other neurons that encode the stimulus faithfully are referred to as non-optimal. If much of the whitening comes from noise in the resting discharge, however, it does not seem that the "optimal" neurons are really optimal – i.e. they would encode better with non-white responses and less noise. This issue recurs throughout the paper and bears on the tradeoff of optimal vs faithful coding.

How does coding in low and high noise neurons differ:

It would be very useful to see a separation of differences in encoded signal and noise to differences in response power spectra. For example, in Figure 2D, how much of the power spectrum in the high variability neurons is due to noise and how much is due to signal? Related, is the spectrum of the encoded signal similar in high and low variability neurons?

Related to this point, in subsection “Neurons with lower variability faithfully encode the detailed time course of naturalistic self-motion stimuli”: the observation that neurons with low variability encode the stimulus more faithfully than those with high variability is not too surprising. It would help to analyze the nature of the coding – e.g. are there systematic errors or bias in encoding in the case of the high variability neurons? Or are both low and high variability neurons encoding the same temporal frequencies, just with different signal to noise ratios?

Reviewer #2:

This is a very nice extension of previous work, now including more classes of vestibular neurons (PVP/EH/VO), whereas only VO were published on in the earlier work. Some excellent hypotheses are outlined about how different types of signals (faithful stimulus encoders versus efficient whitened outputs) are used in different behaviors. This work nicely connects input statistics to encoding with an eye on behavior.

I have just a few main points that I think would enhance the presentation of these results in the manuscript:

1) A main claim of the paper relies on the dissection of neurons in to high and low CV cells, but it really doesn't seem like the data support a statistical distinction between classes, Figure 1D. Specific questions and comments are:

a) Something else needs to be shown here in Figure 1, like the overall histogram of CV, and the accompanying text should not state that there were significant differences amongst these classes of neurons, then point to a figure in which almost all group comparisons are not significant. This just needs to be made crystal clear throughout: this is a hard-fought-and-won dataset that shows some differences amongst neurons, but there aren't enough data to make claims about broad differences between PVP/EH/VO classes, except for the CF result for PVP vs. EH/VO. The result that the PVP class has a lower CV than EH seems like a very small effect size.

b) This appears to be mostly a paper about high versus low baseline variability (though it would be nice to make rate-matched comparisons, next comment), not about differences in response classes. Put another way, it seems like all classes contain neurons that follow the stimulus and some that perform temporal whitening. The first figure could be reformatted to highlight that more clearly.

c) What is the main claim about subtypes, if the above true? Is it that each type needs a "faithful encoder" channel and a "whitened" channel? It seems that this is exactly what is presented in the Discussion, but then the claims about differences in the EH population and a longer discussion about the VO subtype seems out of place, if that's true. Perhaps PVP can be separated by CF, but the distinction between VO and EH neurons in these data seem more tenuous.

2) Do these results hold if high/low variability neurons are compared in pairs that have similar firing rates?

Reviewer #3:

The authors record from three classes of central vestibular neurons (PVP, EH, VO), which project to different areas. They show that functionally, neurons in each of the classes can be divided into "high variability" (HV) and "low variability" (LV) neurons based on characteristics such as CV of the ISI. HV neurons perform decorrelation (=whitening) consistent with efficient coding, while LV neurons perform "faithful encoding", i.e., permit a precise linear reconstruction of the stimulus. The suggested implication is that this division makes sense in the light of downstream computations: e.g., control of eye velocity in VOR favors LV type encoding, as they show computationally.

I find the paper well-written and well-argued, and would support publication after revisions. I do not see any major technical flaws, but recommend one extra analysis as detailed below.

1) I was confused in how precisely the authors define "High variability" and "Low variability" classes. They look at the FR and CV statistics, and also at the power in the natural frequency band, and all these statistics can be done on natural stim or in the resting state. I presume the classification is based only on the CV in the resting state. If that is true, this should be said explicitly (and if you use any thresholds to decide what is "high" and what "low", please specify). Please clarify.

But if the variability is "continuously distributed", then the HV and LV neurons (used as the examples) are only at the extreme ends of that CV distribution. Can you mark where the example neurons of 1B are in Figure 1C (and perhaps in other relevant figures)? For how many of all your neurons do you then see such clear differences between two encoding schemes, what are the neurons in the middle of the CV distribution doing and what is your functional expectation for them? Figures 2E and 3C show the "interpolation" as a function of CV in terms of whitening and CF, showing this continuum of behaviors, but the story seems to tend to much towards a black and white dichotomy between the two extreme behaviors. I would suggest rewording to make clearer that this is not a dichotomy.

2) Figure 2E and 3C show a pretty strong dependence of WI and CF on CV. If the baseline firing rate (that the authors also quantified in Figure 1) is included as an additional explanatory variable for CF in addition to CV, do you see a much better prediction of CF or WI? For example, are low-CV neurons that have a high CF in Figure 3C the ones that have higher firing rates?

3) When the authors interpret the function of HV / LV neurons in Figure 3 and 4, suggesting that LV neurons are better for VOR, they imply that the system is choosing to use one or the other class. But I imagine the population, which is mixed and has a full CV spectrum, is input to the neural integrator. In fact, it would make lots of sense if I look at Figure 3A, to interpret LV neurons as tracking the slower changes in the stimulus well, whereas HV neurons emphasize faster modulation. A system that reads out both types of neurons (or the full heterogenous population) is thus expected to perform much better in reconstructing the stimulus and controlling the eyes.

I suggest that the authors test this hypothesis by linearly decoding from two or more neurons. In the easiest scenario, they could take one LV and one HV neuron (maybe examples in Figure 3B) and jointly linearly decode the stimulus. This could be compared with the decoding based on two LV and two HV neurons, to see if the major benefit comes from combination of the two classes. One could reconstruct from even more neurons if that is feasible, to see how the reconstruction depends on the number / type of neurons (cf. Marre et al., 2015), but I don't consider necessary for resubmission. If, however, it turns out that the authors discover a large benefit to decoding really from two classes (LV + HV) jointly, I think the interpretation and discussion needs to be modified: heterogeneity is beneficial since it permits precise full stimulus reconstruction, and so VOR control should not only be done with low variability neurons.

An additional discussion point that the authors may want to consider is that LV neurons can be decoded with more instantaneous filters, whereas decoding from neurons (like HV) that decorrelate requires decoding filters that are extended in time; this may cause delays in the reconstruction and is possibly detrimental if the sensory-motor loop in VOR needs to be fast?

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Neural variability determines coding strategies for natural self-motion in macaque monkeys" for further consideration by eLife. Your revised article has been evaluated by Joshua Gold (Senior Editor) and Fred Rieke (Reviewing Editor).

The manuscript has been improved but there are some remaining issues that need to be addressed before we can make a final decision, as outlined below:

As you will see below, reviewer #3 has some remaining substantial concerns. In consultation, both reviewers and the Reviewing Editor agreed that these points are quite important and dealing with them fully will be essential if we are to proceed with the paper.

Reviewer #2:

I feel that the paper is much improved after revision. Many of my claims were addressed, as were several of the other reviewers. The Gaussian shape of the naturalistic inputs to this system were clearly a point that needed more emphasis and explanation. I'm glad that's been addressed fully.

The distinction amongst classes of neurons is now much clearer, as is, I believe the Abstract and Results section.

Reviewer #3:

The authors have addressed many of my concerns and their additional analyses have clarified the situation. Especially important are the new quantifications that make it clear that low-CV neurons actually transmit more information (thus better stimulus reconstruction) but do not whiten, whereas high-CV neurons transmit less information due to higher noise power, but their output spectra are white.

I have a two outstanding comments:

1) The authors respond that the self-motion marginal PDF is ~Gaussian with low skew. Even small skew can cause distortions in RF estimates (Meyer et al., 2016); more importantly, the necessary condition for the consistency of RF estimates is spherical symmetry, i.e., P(s) = P(-s) where s is the full stimulus waveform, not just a single marginal value (which is what they report). I understand the authors are faced with the empirical issue of a naturalistic stimulus, so I just ask to clarify precisely the conditions for consistent estimation.

2) Perhaps most importantly, although it may appear nitpicking, I would like the authors to go through the text and be very careful about the interchangeable use of "optimal coding" and "whitening", for their high-CV class neurons. I agree that these neurons produce, to a good approximation, a whitened output. I also agree that there is a regime of efficient coding theory, but by no means the only operating regime, where the theory predicts as optimal a match between stim statistics, noise, and the neural filter that generates white outputs (van Hateren, 1992a): specifically, this happens at high SNR, where the "input noise" Np (in van Hateren paper) is vanishing (Equation 25). But this is not the only regime of optimality. When input noise is high, filters are proportional to (sqrt of) signal spectrum (Equation 30), in this case neurons would not whiten but still be optimal.

In your analysis, you have access to channel noise (Nc in van Hateren notation) which you empirically equate by resting discharge spectrum. But I am not sure if you have direct access to the input noise, Np (I am not familiar enough with the system to know what this would constitute). While the traditional regime of application of efficient coding theory is the regime where channel noise dominates over input noise and thus the optimal prediction is whitening, there are cases where the system is not in this regime (retina at low light, or processing of higher order spatial textures beyond V1).

As a consequence, it could be that low-CV neurons are or are not optimal even in the sense of efficient coding, depending on noise constraints we do not know; but they for sure don't whiten.

I would thus recommend being very precise about the claims, e.g., in the Abstract, instead of saying that the neurons did not optimally encode…, I would say they do not whiten. I think it is fair to point out in the paper that the typical regime of efficient coding predicts whitening (van Hateren et al.), but it may be going beyond what you can demonstrate to claim that absence of whitening means non-optimal coding in low-CV neurons. I think that these world-level corrections, to focus on non-whitening vs whitening rather than optimal vs. non-optimal encoding, should not detract from the main message of the paper, and provide an interesting discussion point about optimality.

The dichotomy between faithful and efficient coding neurons received a good deal of attention in the consultation among the reviewers. All of the reviewers felt that more needed to be done to clarify and to test this distinction. For example, it is not clear how the decoding errors could be larger for the efficient coding neurons if they really are efficient. Related to this point is whether the efficient coding neurons are simply noisier, and if the whitening comes at the expense of higher noise. Several additional specific points raised in the individual reviews are related to this point. I should emphasize that in consultation the reviewers felt more strongly about this point than is reflected in the individual reviews, and whether you are able to deal with it clearly and effectively will be critical to a re-evaluation of the paper.

We understand and appreciate your and the reviewers’ comments regarding optimality vs. faithfulness and agree that this is an important point. To directly address this point in the current manuscript, we have first defined our terms (i.e., optimal vs. faithful coding) in the Introduction. Specifically, optimal coding refers to the fact that the mutual information is at its maximum possible value for a given level of variability or, equivalently, that the output power spectrum is independent of frequency (Shannon, 1946; Rieke et al., 1996). Further, we defined faithful encoding as the spike train containing information as to the detailed timecourse of the stimulus and quantified it by comparing the reconstructed stimulus to the original through the coding fraction (i.e., the relative variance of the stimulus that is correctly reconstructed).

Second, in order to directly address the relationship between faithful encoding and optimal coding in our current dataset, we have performed additional analysis which is shown in Figure 2—figure supplement 7. Specifically, we have separated the response power spectra into their noise and transmitted signal power components and now show these as requested by reviewer 1 in panel A. Further, as requested, we have computed the signal-to-noise ratio and show a strong decrease with increasing variability. As such, the high variability neurons are in fact “noisier” than their low variability counterparts. Further, to clarify what is meant by optimal coding, we computed the mutual information between the stimulus and the spike train and compared it to its maximum possible value for a given level of variability. Our results show that, while the absolute mutual information decreases with increasing CV (Panel B, middle), the relative mutual information (i.e., the ratio of the mutual information to its maximum possible value) actually increases (Panel B, right). Thus, neurons with higher CV, while transmitting less information in absolute terms, are more optimal because the mutual information is closer to its maximum possible value for that level of variability. In contrast, neurons with lower CV transmit more information as to the stimulus’ detailed timecourse (i.e., faithful encoding). These new results are now described and discussed in the revised manuscript. In addition, we address the specific reviewers’ comments below.

Reviewer #1:

This paper follows a previous paper from some of the same authors exploring coding of naturalistic inputs in the vestibular system. The previous paper showed that the combination of stimulus power spectrum, neural filtering and noise led to spectrally-flat ("whitened") responses in one class of vestibular neuron. The present paper extends this analysis to two other types of vestibular neurons, concluding that they show considerable heterogeneity in the degree of whitening. I had several concerns about the analysis/presentation:

Filter calculations and non-Gaussian stimuli:

The paper relies on naturalistic head movement stimuli and uses these for the coding analyses. Some of the calculations presented, however, are valid only for gaussian stimuli. This is particularly true of the linear-nonlinear model and more broadly the construction of the transfer functions. Thus, it seems that the filters extracted could be impacted by the correlation structure of the stimulus. This is a key issue for interpretation of the paper.

We understand the reviewer’s comment and had previously directly addressed this important issue in the original paper (Mitchell et al., 2018 ). Specifically, we have shown that the naturalistic self-motion probability distribution is well-fit by a Gaussian (see Figure 1—figure supplement 1B of Mitchell et al., 2018). We further note that the stimulus probability distribution is symmetric with respect to zero, as evidenced by a low skewness of 0.24. As such, there are no inconsistencies or biases in our transfer function and LN model estimates (Chichilnisky, 2001; Paninski, 2003; see Meyer et al., 2016 for review). This is now mentioned in the Materials and methods.

Adding noise and optimality:

Neurons that whiten the stimulus are referred to as optimal, while other neurons that encode the stimulus faithfully are referred to as non-optimal. If much of the whitening comes from noise in the resting discharge, however, it does not seem that the "optimal" neurons are really optimal – i.e. they would encode better with non-white responses and less noise. This issue recurs throughout the paper and bears on the tradeoff of optimal vs. faithful coding.

We understand and appreciate the reviewer’s comment regarding optimality and faithfulness. We agree that this is a major point as mentioned above in our response to the editor’s comments. To directly address this point, we have first clearly defined our terms (i.e., optimal vs. faithful coding) in the revised Introduction. Specifically, optimal coding refers to the fact that the mutual information is close to its maximum possible value for a given level of variability, while faithful encoding refers to the fact the neuron transmits high levels of information about the stimulus, such that the stimulus’ detailed timecourse can be recovered from its spiking activity. Second, we have performed additional analysis of our data to directly demonstrate that neurons with high variability (i.e., HV neurons) are more optimal than neurons with low variability (i.e., LV neurons; see Figure 2—figure supplement 7B, right panel). Indeed, our new results show that the mutual information is closer to its maximum possible value when variability increases. However, the absolute mutual information decreased with increasing variability (Figure 2—figure supplement 7B, middle panel), implying that LV neurons more faithfully encode the stimulus than their HV counterparts. We have revised the text to include description of these new results.

How does coding in low and high noise neurons differ:

It would be very useful to see a separation of differences in encoded signal and noise to differences in response power spectra. For example, in Figure 2D, how much of the power spectrum in the high variability neurons is due to noise and how much is due to signal? Related, is the spectrum of the encoded signal similar in high and low variability neurons?

We now show both signal and noise power in Figure 2—figure supplement 7A. The noise power was higher for high variability neurons than for low variability neurons, thereby leading to a signal-to-noise ratio that decreases with increasing variability (Figure 2—figure supplement 7B, left panel). However, both low and high variability neurons displayed similar signal power (Figure 2—figure supplement 7A).

Related to this point, in subsection “Neurons with lower variability faithfully encode the detailed time course of naturalistic self-motion stimuli”: the observation that neurons with low variability encode the stimulus more faithfully than those with high variability is not too surprising. It would help to analyze the nature of the coding – e.g. are there systematic errors or bias in encoding in the case of the high variability neurons? Or are both low and high variability neurons encoding the same temporal frequencies, just with different signal to noise ratios?

As mentioned above, the fact that the stimulus probability distribution is symmetric implies that there are no systematic biases or errors in our estimates. Moreover, as mentioned for the previous comment, our new analysis shows that low and high variability neurons encode the same range of temporal frequencies with similar tuning functions, but that the signal-to-noise ratio is lower for the latter (Figure 2—figure supplement 7B, left panel).

Reviewer #2:

This is a very nice extension of previous work, now including more classes of vestibular neurons (PVP/EH/VO), whereas only VO were published on in the earlier work. Some excellent hypotheses are outlined about how different types of signals (faithful stimulus encoders versus efficient whitened outputs) are used in different behaviors. This work nicely connects input statistics to encoding with an eye on behavior.

I have just a few main points that I think would enhance the presentation of these results in the manuscript:

1) A main claim of the paper relies on the dissection of neurons in to high and low CV cells, but it really doesn't seem like the data support a statistical distinction between classes, Figure 1D. Specific questions and comments are:

a) Something else needs to be shown here in Figure 1, like the overall histogram of CV, and the accompanying text should not state that there were significant differences amongst these classes of neurons, then point to a figure in which almost all group comparisons are not significant. This just needs to be made crystal clear throughout: this is a hard-fought-and-won dataset that shows some differences amongst neurons, but there aren't enough data to make claims about broad differences between PVP/EH/VO classes, except for the CF result for PVP vs. EH/VO. The result that the PVP class has a lower CV than EH seems like a very small effect size.

We now plot the firing rate and CV distribution for all three classes pooled in Figure 1 as requested. We have furthermore rewritten the Results to emphasize that the distributions of resting discharge variability and firing rate were similar for all neural classes. Finally, we agree with the reviewer and we now emphasize throughout that variability is distributed along a continuum for our dataset, and that we are showing examples within the lower and higher parts of the range of variability displayed by each class.

b) This appears to be mostly a paper about high versus low baseline variability (though it would be nice to make rate-matched comparisons, next comment), not about differences in response classes. Put another way, it seems like all classes contain neurons that follow the stimulus and some that perform temporal whitening. The first figure could be reformatted to highlight that more clearly.

We agree with the reviewer and we have rewritten this sentence to state that: “Thus, while central vestibular neurons displayed a wide range of resting discharge firing rate and variability within each class, both quantities were similarly distributed for all three classes.”. Thus, while there are strong differences in resting discharge variability within each cell class, there are no major differences across cell classes. Further, we now make rate-matched comparisons as described below in answer to comment 2.

c) What is the main claim about subtypes, if the above true? Is it that each type needs a "faithful encoder" channel and a "whitened" channel? It seems that this is exactly what is presented in the Discussion, but then the claims about differences in the EH population and a longer discussion about the VO subtype seems out of place, if that's true. Perhaps PVP can be separated by CF, but the distinction between VO and EH neurons in these data seem more tenuous.

The reviewer raises an interesting point. Based on our dataset, we show that faithful encoding by PVP neurons is necessary to generate compensatory VOR eye movements as it is best matched to the oculo-motor plant requirements. In contrast, we speculate that the larger integration time window needed to decode temporally whitened information is better suited for VOR adaptation, as seen for EH neurons which displayed poor faithful encoding as compared to the other two classes. For VO neurons, we speculate that temporal whitening is better suited to the mechanical demands of the head-neck system (i.e., head inertia) for vestibulo-spinal reflexes. Further, we propose that faithful encoding by a subset of VO neurons serves to improve perception. To make these points clearer in the revised manuscript, we have rewritten the discussion about PVP/EH neurons. Further, we have shortened the discussion about VO neurons as requested.

2) Do these results hold if high/low variability neurons are compared in pairs that have similar firing rates?

We thank the reviewer for raising this important point. To address it, we have added 2 supplementary figures (Figure 2—figure supplement 2 and Figure 3—figure supplement 2). Our new analysis shows that there is no significant correlation between either of whitening index (Figure 2—figure supplement 2A) or coding fraction (Figure 3—figure supplement 2A) and firing rate. Next, we show that, if we only take neurons whose firing rates are within a restricted range (i.e., 45 to 55 sp/s), there is still a positive correlation between the whitening index and CV (Figure 2—figure supplement 2B), and a significant negative correlation between the coding fraction and CV (Figure 3—figure supplement 2B).

Reviewer #3:

The authors record from three classes of central vestibular neurons (PVP, EH, VO), which project to different areas. They show that functionally, neurons in each of the classes can be divided into "high variability" (HV) and "low variability" (LV) neurons based on characteristics such as CV of the ISI. HV neurons perform decorrelation (=whitening) consistent with efficient coding, while LV neurons perform "faithful encoding", i.e., permit a precise linear reconstruction of the stimulus. The suggested implication is that this division makes sense in the light of downstream computations: e.g., control of eye velocity in VOR favors LV type encoding, as they show computationally.

I find the paper well-written and well-argued, and would support publication after revisions. I do not see any major technical flaws, but recommend one extra analysis as detailed below.

1) I was confused in how precisely the authors define "High variability" and "Low variability" classes. They look at the FR and CV statistics, and also at the power in the natural frequency band, and all these statistics can be done on natural stim or in the resting state. I presume the classification is based only on the CV in the resting state. If that is true, this should be said explicitly (and if you use any thresholds to decide what is "high" and what "low", please specify). Please clarify.

We understand the reviewer’s comment. The quantification of variability is based solely on the CV of the resting discharge activity and this is now clearly mentioned in the results. Further, to avoid confusion, we now refer to “resting discharge variability” throughout the manuscript. We have also emphasized that the distribution of CV is continuous and that we are looking at exemplar neurons whose CV values were within the lower and higher range of this distribution.

But if the variability is "continuously distributed", then the HV and LV neurons (used as the examples) are only at the extreme ends of that CV distribution. Can you mark where the example neurons of 1B are in Figure 1C (and perhaps in other relevant figures)? For how many of all your neurons do you then see such clear differences between two encoding schemes, what are the neurons in the middle of the CV distribution doing and what is your functional expectation for them? Figures 2E and 3C show the "interpolation" as a function of CV in terms of whitening and CF, showing this continuum of behaviors, but the story seems to tend to much towards a black and white dichotomy between the two extreme behaviors. I would suggest rewording to make clearer that this is not a dichotomy.

We understand the reviewer’s comment. First, we now mark the example neurons in Figures 1C, 2E, 3C using open symbols as requested. Further, we have emphasized throughout the results that the variability is distributed continuously and that we are looking at example neurons within the lower and higher range of variability throughout. We also now emphasize that both faithful encoding and optimal coding are distributed continuously in our dataset in the discussion in order to stress that this is not a dichotomy, as requested.

2) Figure 2E and 3C show a pretty strong dependence of WI and CF on CV. If the baseline firing rate (that the authors also quantified in Figure 1) is included as an additional explanatory variable for CF in addition to CV, do you see a much better prediction of CF or WI? For example, are low-CV neurons that have a high CF in Figure 3C the ones that have higher firing rates?

We thank the reviewer for raising this important point. To address it, we have added 2 supplementary figures where we show that there is no significant correlation between either of whitening index (Figure 2—figure supplement 2A) or coding fraction (Figure 3—figure supplement 2A) and baseline firing rate. Next, we show that, if we only take neurons whose baseline firing rates are within a restricted range (i.e., 45 to 55 sp/s), there is still a positive correlation between whitening index and CV (Figure 2—figure supplement 2B), and a significant negative correlation between coding fraction and CV (Figure 3—figure supplement 2B).

3) When the authors interpret the function of HV / LV neurons in Figure 3 and 4, suggesting that LV neurons are better for VOR, they imply that the system is choosing to use one or the other class. But I imagine the population, which is mixed and has a full CV spectrum, is input to the neural integrator. In fact, it would make lots of sense if I look at Figure 3A, to interpret LV neurons as tracking the slower changes in the stimulus well, whereas HV neurons emphasize faster modulation. A system that reads out both types of neurons (or the full heterogenous population) is thus expected to perform much better in reconstructing the stimulus and controlling the eyes.

I suggest that the authors test this hypothesis by linearly decoding from two or more neurons. In the easiest scenario, they could take one LV and one HV neuron (maybe examples in Figure 3B) and jointly linearly decode the stimulus. This could be compared with the decoding based on two LV and two HV neurons, to see if the major benefit comes from combination of the two classes. One could reconstruct from even more neurons if that is feasible, to see how the reconstruction depends on the number / type of neurons (cf. Marre et al., 2015), but I don't consider necessary for resubmission. If, however, it turns out that the authors discover a large benefit to decoding really from two classes (LV + HV) jointly, I think the interpretation and discussion needs to be modified: heterogeneity is beneficial since it permits precise full stimulus reconstruction, and so VOR control should not only be done with low variability neurons.

We thank the reviewer for raising this important point. To address, we have split our PVP dataset into neurons with “low variability” and “high variability” as suggested, keeping in mind that variability is actually distributed along a continuum. Specifically, we took the 5 neurons with the lowest values of CV as the “low variability” group and the 5 neurons with the highest values of CV as the “high variability” group. Next, we compared the coding fraction values from all possible pairings between low variability neurons (LVLV), high variability neurons (HVHV), and all possible pairings between low and high variability neurons (HVLV). Overall, the pair-averaged coding fraction for LVHV was significantly lower than that obtained from LVLV pairs (Figure 4—figure supplement 2A). Moreover, the pair-averaged change in coding fraction (i.e., the coding fraction computed from the pair minus the maximum value obtained for individual neurons within that pair) for HVLV was significantly lower than that obtained for LVLV pairs (Figure 4—figure supplement 2B). These results suggest that there is no net advantage in considering mixed neural populations as opposed to populations consisting only of LV neurons for reconstructing the stimulus.

An additional discussion point that the authors may want to consider is that LV neurons can be decoded with more instantaneous filters, whereas decoding from neurons (like HV) that decorrelate requires decoding filters that are extended in time; this may cause delays in the reconstruction and is possibly detrimental if the sensory-motor loop in VOR needs to be fast?

We thank the reviewer for raising this important point and have revised the Discussion accordingly.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

As you will see below, reviewer #3 has some remaining substantial concerns. In consultation, both reviewers and the Reviewing Editor agreed that these points are quite important and dealing with them fully will be essential if we are to proceed with the paper.

Reviewer #3:

The authors have addressed many of my concerns and their additional analyses have clarified the situation. Especially important are the new quantifications that make it clear that low-CV neurons actually transmit more information (thus better stimulus reconstruction) but do not whiten, whereas high-CV neurons transmit less information due to higher noise power, but their output spectra are white.

I have a two outstanding comments:

1) The authors respond that the self-motion marginal PDF is ~Gaussian with low skew. Even small skew can cause distortions in RF estimates (Meyer et al., 2016); more importantly, the necessary condition for the consistency of RF estimates is spherical symmetry, i.e., P(s) = P(-s) where s is the FULL stimulus waveform, not just a single marginal value (which is what they report). I understand the authors are faced with the empirical issue of a naturalistic stimulus, so I just ask to clarify precisely the conditions for consistent estimation.

We understand the reviewer’s comment and agree that the necessary condition for the consistency of RF estimates is spherical symmetry. Our original intent in providing the skewness value was to illustrate that, while non-Gaussian, the distribution of natural head velocities was symmetric with respect to zero. In this revised version, we now explicitly test symmetry by performing a triples test (Randles et al., 1980) and found that we could not reject the null hypothesis (p=0.33). This is now reported in the Materials and methods.

2) Perhaps most importantly, although it may appear nitpicking, I would like the authors to go through the text and be very careful about the interchangeable use of "optimal coding" and "whitening", for their high-CV class neurons. I agree that these neurons produce, to a good approximation, a whitened output. I also agree that there is a regime of efficient coding theory, but by no means the only operating regime, where the theory predicts as optimal a match between stim statistics, noise, and the neural filter that generates white outputs (van Hateren, 1992a): specifically, this happens at high SNR, where the "input noise" Np (in van Hateren paper) is vanishing (Equation 25). But this is not the only regime of optimality. When input noise is high, filters are proportional to (sqrt of) signal spectrum (Equation 30), in this case neurons would not whiten but still be optimal.

In your analysis, you have access to channel noise (Nc in van Hateren notation) which you empirically equate by resting discharge spectrum. But I am not sure if you have direct access to the input noise, Np (I am not familiar enough with the system to know what this would constitute). While the traditional regime of application of efficient coding theory is the regime where channel noise dominates over input noise and thus the optimal prediction is whitening, there are cases where the system is not in this regime (retina at low light, or processing of higher order spatial textures beyond V1).

As a consequence, it could be that low-CV neurons are or are not optimal even in the sense of efficient coding, depending on noise constraints we do not know; but they for sure don't whiten.

I would thus recommend being very precise about the claims, e.g., in the Abstract, instead of saying that the neurons did not optimally encode…, I would say they do not whiten. I think it is fair to point out in the paper that the typical regime of efficient coding predicts whitening (van Hateren et al.), but it may be going beyond what you can demonstrate to claim that absence of whitening means non-optimal coding in low-CV neurons. I think that these world-level corrections, to focus on non-whitening vs whitening rather than optimal vs. non-optimal encoding, should not detract from the main message of the paper, and provide an interesting discussion point about optimality.

We agree that this is an important point. To address it, we have made the requested word changes throughout: specifically, we now make it clear that, when we refer to optimal coding, we mean temporal whitening explicitly. We have furthermore added a new paragraph to the discussion to address the case mentioned by the reviewer for which the input signal-to-noise ratio is low. Specifically, in the vestibular system, input noise to central neurons would come from vestibular afferents. Our previous studies have shown that the trial-to-trial variability displayed by these afferents is low during naturalistic stimulation, as their responses can be predicted solely by considering their tuning (Figure 4—figure supplement 3 of Mitchell et al., 2018), which implies that the input signal-to-noise ratio is high. As such, it is unlikely that the deviation from whitening observed is a signature of optimized coding based on a low input signal-to-noise ratio as seen elsewhere. This argument is made in the Discussion.

Author details

1. Isabelle Mackrous

   Department of Physiology, McGill University, Montreal, Canada

   Contribution

   Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

2. Jérome Carriot

   Department of Physiology, McGill University, Montreal, Canada

   Contribution

   Formal analysis, Validation, Investigation, Visualization, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

3. Kathleen E Cullen

   1. The Department of Otolaryngology- Head and Neck Surgery, Johns Hopkins University School of Medicine, Baltimore, United States
   2. The Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, United States
   3. The Department of Neuroscience, Johns Hopkins University School of Medicine, Baltimore, United States
   4. Kavli Neuroscience Discovery Institute, Johns Hopkins University, Baltimore, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Validation, Methodology, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-9348-0933

4. Maurice J Chacron

   Department of Physiology, McGill University, Montreal, Canada

   Contribution

   Conceptualization, Resources, Software, Supervision, Funding acquisition, Validation, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   maurice.chacron@mcgill.ca

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-3032-452X

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