Comparison between the spectral properties of envelope signals recorded during active and passive self-motion.

<p><b>A:</b> Subject-averaged best-fit power law exponents over the low (gray) and high (black) frequency ranges for all six motion dimensions for active self-motion. Also shown for comparison are the subject-averaged best-fit power law exponents for a single power law over the entire frequency range (blue). <b>B:</b> Subject-averaged best-fit power law exponents over the low (gray) and high (black) frequency ranges for all six motion dimensions for passive self-motion. Also shown for comparison are the subject-averaged best-fit power law exponents for a single power law over the entire frequency range (blue). “*” indicates statistical significance at the p = 0.01 level using a one-way ANOVA.</p

Envelope signals deviate from scale invariance.

<p><b>A:</b> Subject-averaged power spectra (red lines) with best-fit power laws over the low and high frequency ranges (black lines) as well as best-fit single power law over the entire frequency range (blue lines). Also shown are the best-fit power law exponents with confidence interval as well as the transition frequency. The dashed gray lines show the “noise floor”, which is the spectrum of the noise in the measurement obtained when the sensor was not moving (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178664#sec002" target="_blank">Methods</a>). Gray bands show 1 STD. <b>B:</b> Subject-averaged best-fit power law exponents over the low (gray) and high (black) frequency ranges for all six motion dimensions. Also shown for comparison are the subject-averaged best-fit power law exponents for a single power law over the entire frequency range (blue). “*” indicates statistical significance at the p = 0.01 level using a one-way ANOVA. <b>C:</b> Subject-averaged frequency at which the power spectrum starts decreasing more sharply for all six motion dimensions.</p

Subject-averaged maximum value, mean, and kurtosis for passive everyday activities.

<p>The maximum and mean values are expressed in mG for the Lateral, Fore-Aft and Vertical linear acceleration while they are expressed in deg/s for the LARP, RALP and Yaw angular velocity.</p

Statistics of environmental signals obtained when the subject is absent.

<p><b>A:</b> Schematic showing the MEMS module (gold box) located on the subject’s head and placed on the seat during passive self-motion. <b>B,C,D,E, F, G:</b> Trial-averaged power spectra of signals in the external environment (green) during passive self-motion for inter aural (<b>B</b>), Fore-Aft (<b>C</b>), Vertical (<b>D</b>), LARP (<b>E</b>), RALP (<b>F</b>), and YAW (<b>G</b>). The power spectra were in general well fit by a single power law over the entire frequency range (blue lines).</p

Well-established models of the vestibular periphery predict that irregular afferents have greater sensitivities to envelopes than their regular counterparts.

<p><b>A:</b> Schematic showing the vestibular end organs as well as regular and irregular vestibular afferents projecting to the vestibular nuclei. <b>B:</b> Sensitivity to the carrier for the regular (dashed black) and irregular (solid red) model afferents. <b>C:</b> Time series showing a segment of the envelope stimulus (solid black) and the responses of the model regular (dashed black) and irregular (solid red) afferents. <b>D:</b> Gain to the envelope as a function of frequency for the regular (dashed black) and irregular (solid red) model afferents. In both cases the gain is relatively independent of frequency but is about twice higher for the irregular model afferent.</p

Central vestibular neurons but not afferents display a nonlinear relationship between output firing rate and input head velocity.

<p>(A) Output firing rate as a function of head velocity. The inset shows the instantaneous firing rate and the head velocity stimulus as a function of time and the various symbols correspond to different values of the head velocity and the corresponding firing rates. If the firing rate is related linearly to the head velocity stimulus, then the curve relating the two should be well fit by a straight line. The slope of this line is then the response gain. (B) Population-averaged firing rate response as a function of head velocity for afferents when stimulated with 0–5 Hz noise alone (solid blue) and concurrently with 15–20 Hz noise (solid black). In both cases, the curves were well fit by straight lines (dashed lines) and largely overlapped (0–5 Hz alone: <i>R</i>² = 0.99, slope = 0.70 (spk/s)/(deg/s), <i>y</i>-intercept = 98 spk/s; 0–5 Hz with 15–20 Hz: <i>R</i>² = 0.99, slope = 0.72 (spk/s)/(deg/s), <i>y</i>-intercept = 98 spk/s). (C) Population-averaged firing rate response as a function of head velocity for afferents when stimulated with 15–20 Hz noise alone (solid red) and concurrently with 0–5 Hz noise (long dashed black). Both curves were again well fit by straight lines (short dashed lines) and largely overlapped (15–20 Hz alone: <i>R</i>² = 0.99, slope = 1.97 (spk/s)/(deg/s), <i>y</i>-intercept = 102 spk/s; 15–20 Hz with 0–5 Hz: <i>R</i>² = 0.99, slope = 2.06 (spk/s)/(deg/s), <i>y</i>-intercept = 102 spk/s). Note, however, the increased slope with respect to panel B. (D) Population-averaged firing rate response as a function of head velocity for central neurons when stimulated with 0–5 Hz noise alone (solid blue) and concurrently with 15–20 Hz noise (solid black). In both cases, the curves were well fit by straight lines (dashed lines) although the solid black curve had a lower slope (i.e., gain) than the solid blue curve (0–5 Hz: <i>R</i>² = 0.98, slope = 1.56 (spk/s)/(deg/s), <i>y</i>-intercept = 67 spk/s; 0–5 Hz with 15–20 Hz: <i>R</i>² = 0.87, slope = 0.83 (spk/s)/(deg/s), <i>y</i>-intercept = 81 spk/s). (E) Population-averaged firing rate response as a function of head velocity for central neurons when stimulated with 15–20 Hz noise alone (solid red) and concurrently with 0–5 Hz noise (long dashed black). While both curves were similar and largely overlapped, they were not well fit by straight lines (short dashed lines) that underestimated the firing rate for head velocities <−10 deg/s (15–20 Hz: <i>R</i>² = 0.64, slope = 2.32 (spk/s)/(deg/s), <i>y</i>-intercept = 79 spk/s; 15–20 Hz with 0–5 Hz: <i>R</i>² = 0.27, slope = 2.78 (spk/s)/(deg/s), <i>y</i>-intercept = 79 spk/s). We note that central neurons did not display rectification since the firing rate was always above zero.</p

Active motion introduces deviation from scale invariance in the envelopes of natural translational self-motion signals recorded along the Inter-Aural and Vertical axes.

<p><b>A:</b> Schematic showing a subject engaged in active self-motion (left) and in passive self-motion (right). <b>B,C,D,E, F, G:</b> Subject-averaged envelope power spectra for active (left panels) and passive (right panels) activities for inter aural (<b>B</b>), Fore-Aft (<b>C</b>), Vertical (<b>D</b>), LARP (<b>E</b>), RALP (<b>F</b>), and YAW (<b>G</b>). In each case, the power spectra were fitted using two power laws over the low and high frequency ranges (black lines) as well as by a single power law over the entire frequency range (blue lines). Also shown are the best-fit power law exponents with confidence interval as well as the transition frequency.</p

The Vestibular System Implements a Linear–Nonlinear Transformation In Order to Encode Self-Motion

<div><p>Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (∼50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways.</p> </div

A linear-nonlinear (LN) cascade model reveals that central vestibular neurons respond nonlinearly to broadband noise stimulation.

<p>(A) Schematic showing the LN model's assumptions. The stimulus (left) is convolved with a filter <i>H(t)</i> that is given by the inverse Fourier transform of the transfer function in order to generate the linear predicted firing rate (middle). This linear prediction is then passed through a static function f (which can be linear or nonlinear) to give rise to the predicted output firing rate (right). (B) Population-averaged function f for afferents. Also shown is the best-fit line (<i>R</i>² = 0.998±0.001, <i>n</i> = 15) (red) whose slope did not significantly differ from unity (<i>p</i> = 0.99, <i>n</i> = 15, pairwise <i>t</i> test). Inset: population-averaged filter <i>H(t)</i> for afferents. (C) Population-averaged function f for central VO neurons. Also shown are the best-fit straight lines for the intervals (0–80 Hz) and (80–160 Hz) (red) whose slopes were significantly different from one another (<i>p</i> = 0.0014, <i>n</i> = 13, pairwise <i>t</i> test). Inset: population-averaged filter <i>H(t)</i> for central VO neurons.</p

Schematic showing how a nonlinear static relationship between input and output can lead to attenuated sensitivity to sums of low and high frequency stimuli.

<p>(A) Input-output relationship showing a vertex (i.e., a sudden change in slope) (black curve). If we assume that the input is normally distributed with low intensity (i.e., standard deviation) such that all the input values are to the right of the vertex (light green distribution on <i>x</i>-axis), then the corresponding output distribution will also be normally distributed (light purple distribution on <i>y</i>-axis). The mean output (light purple circle on <i>y</i>-axis) corresponds to the image of the mean input (dashed purple circle on <i>y</i>-axis; note that the light purple and dashed purple circles were offset for clarity) as both input and output are linearly related. In contrast, for a higher intensity input that extends significantly past the vertex (dark green distribution on <i>x</i>-axis), the corresponding output distribution (dark purple on <i>y</i>-axis) is skewed with respect to the linear prediction (dashed purple on <i>y</i>-axis). The mean output (dark purple circle on <i>y</i>-axis) is thus greater than the linear prediction (dashed purple circle on <i>y</i>-axis). (Note that here and below, we represented the distributions to have the same maximum value in order to emphasize the fact that we are changing the standard deviation.) (B) Increasing the input distribution intensity for a given mean (compare red, yellow, and blue distributions) causes a greater skew in the corresponding output distribution (unpublished data) and thus an increased bias in their means (red, yellow, and blue dots on the <i>y</i>-axis and inset) as compared to the linear prediction (dashed yellow and blue dots on the <i>y</i>-axis). (C) Shifting the mean of the high intensity input distribution to the left (compare points 1, 2, and 3 on the <i>x</i>-axis and the inset) makes it extend to the left of the vertex more and more (compare the green curves on the <i>x</i>-axis), causing greater skewness in the corresponding output distributions (purple curves on the <i>y</i>-axis), which creates a greater bias in the mean (dark purple points on <i>y</i>-axis) with respect to the linear prediction (light purple points on <i>y</i>-axis). As a result, the mean output in response to a given value of the low intensity input (points 1, 2, and 3 on the <i>x</i>-axis) when the high intensity signal is present (dark purple line) has a lower slope (i.e., gain) than when the high intensity signal is absent (light purple line). (D) Shifting the mean of the high intensity input distribution to the left (compare points 1, 2, and 3 on the <i>x</i>-axis and the inset) makes the corresponding distributions of the low intensity input extend to the left of the vertex more and more (green curves on the <i>x</i>-axis), causing greater skewness in the output distribution (purple curves on the <i>y</i>-axis), which creates a greater bias in the mean (dark purple points on <i>y</i>-axis) with respect to the linear prediction (light purple points on <i>y</i>-axis). Note, however, that the bias in the mean will be lower than in (C) since the input distributions now have a lower intensity as explained in (B). Thus, the input-output relationship when the low intensity signal is present (dark purple line) will have a lower slope (i.e., gain) than when the low intensity signal is absent (light purple line) but the effect will be weaker than in (C).</p