Neural representation of orientation relative to gravity in the macaque cerebellum

Abstract

A fundamental challenge for maintaining spatial orientation and interacting with the world is knowledge of our orientation relative to gravity, i.e., head tilt. Sensing gravity is complicated because of Einstein's equivalence principle, in which gravitational and translational accelerations are physically indistinguishable. Theory has proposed that this ambiguity is solved by tracking head tilt through multisensory integration. Here we identify a group of Purkinje cells in the caudal cerebellar vermis with responses that reflect an estimate of head tilt. These tilt-selective cells are complementary to translation-selective Purkinje cells, such that their population activities sum to the net gravitoinertial acceleration encoded by the otolith organs, as predicted by theory. These findings reflect the remarkable ability of the cerebellum for neural computation and provide quantitative evidence for a neural representation of gravity, whose calculation relies on long-postulated theoretical concepts such as internal models and Bayesian priors.

Figure 1. Tilt and translation protocols and responses from example cells

(A) Equivalence principle: the otolith organs are sensitive to the gravito-inertial acceleration (GIA), which is equal to the difference between the gravity vector (GA) and the translational acceleration (TA). (B) Naming conventions of the head’s translation and rotation axes. (C) Representation of the motion protocols used in this study. The GIA stimulus along the LR axis, represented by a swinging pendulum (bottom), is identical during the 3 protocols (translation, tilt, OVAR). (D–O) responses from a translation-selective cell (red) and a tilt-selective cell (green) during (D), (H) left-right (LR) translation, (E), (I) roll tilt, (F), (G), (J), (K) constant velocity off-vertical axis rotation (OVAR). (L), (M), (N) and (O) illustrate the corresponding yaw velocity (detected by horizontal canals, blue), roll velocity (detected by vertical canals, cyan) and GIA along the LR axis (detected by otolith organs, OTO; black). Gray curves: fit to the LR translation response (shown in D, translation cell) or the roll tilt response (shown in I, tilt cell). We compared the cell’s OVAR modulation to the gray response, and computed a gain ratio (see Experimental Procedures): F: G_trans=0.2, ϕ_trans=156°; G: G_trans=0.9, ϕ_trans=12°; J: G_tilt=0.9, ϕ_tilt=−27°; K: G_tilt=0.4, ϕ_tilt=−86°. Note that the two cells were chosen to have a negligible response to pitch and FB translation, such that these components could be ignored (for illustrative purposes only; all data were analyzed using a vectorial approach; see Experimental Procedures). OVAR beginning shows 3–7s after motion onset. OVAR steady-state illustrates 51–55s (translation cell) or 63–67s (tilt cell) after motion onset. Additional response profiles can be found in Figure S1.

Figure 2. Population summary of tilt and translation responses

The scatter plot shows tilt versus translation gain, with each symbol corresponding to a single neuron, color-coded according to cell classification type (green: tilt-selective cells; red: translation-selective cells; black: GIA-selective cells; grey: composite cells). Different symbols are used for different animals (squares: animal V; circles: animal T; triangles: animal K). Open symbols represent putative Purkinje cells and filled symbols represent confirmed Purkinje cells (see Experimental Procedures). Reconstructed positions of recorded cells in stereotaxic coordinates are illustrated in Figure S3. Boxplots on top and side represent geometric mean (numbers and lines inside box), 95% confidence intervals (box) and SD (lines). The histogram on the lower left shows the distribution of the tilt-translation ratio (TTR). The TTR histogram had two peaks and differed significantly from both a uniform (p_uniform < 0.001) and a Gaussian (p_Gaussian = 0.001) distribution, whereas it was not different from a bimodal distribution (p_bimodal = 0.2). The analysis identifying tilt-selective, translation-selective, GIA-selective and composite cells is based on the assumption of linearity (see Experimental Procedures), which is fulfilled (Figure S7). Additional response properties (preferred directions and phases) can be found in Figure S2; the reconstructed position of the cells is shown in Figures S3.

Figure 3. Decomposition of the OVAR stimulus into actual tilt and erroneous translation signals (see also Figure 1)

(A)–(C) real motion (tilt), (D)–(F) corresponding erroneous translation. (A) During OVAR, the head rotates around a tilted axis (left). In an egocentric frame of reference, the gravity vector rotates around the head (right). (B) During OVAR, the head passes though the Left-Ear-Down (LED), Nose-Down (ND), Right-Ear-Down (RED) and Nose-Up (NU) orientations successively. (C) Pitch and roll oscillations corresponding to the head trajectory in B. (D) Forward-backward (FB) and leftward-rightward (LR) oscillations generating the same otolith activation as in C. (E) Erroneous translational acceleration corresponding to the head orientations represented in B. (F) Illusion of translation along a circular trajectory during steady-state OVAR in humans, obtained by following the pattern of acceleration illusions in E (Vingerhoets et al. 2006; 2007).

Figure 4. Comparison of the response during OVAR with the ‘rereference’ response during tilt or translation on a cell-by-cell basis

Modulation amplitude during OVAR at (A) t=2–4s, (B) t=4–6s and (C) t=60–62s after motion onset is plotted versus tilt (for tilt-selective Purkinje cells, n=37, green) or translation (for translation-selective cells, n=27, red) reference amplitude (i.e. the response amplitude expected in response to a tilt or translation stimulus equivalent to OVAR; see Experimental Procedures; e.g., gray lines in Figure 1D–O). Two data points are shown per cell (corresponding to the two rotation directions; see Experimental Procedures). Linear regressions were performed, with the 95% confidence intervals represented by green and red bands. Different symbols are used for different animals (squares: animal V; circles: animal T; triangles: animal K). Phase values are illustrated in Figure S4. Reconstructed positions of recorded cells in stereotaxic coordinates are illustrated in Figure S3.

Figure 5. Time course of the decoded gravitational (GA) and translational (TA) acceleration estimates

Average gain ratio (G_tilt and G_trans) and phase difference (ϕ_tilt and ϕ_trans) of the OVAR responses (relative to the reference) of (A) tilt-selective cells (green, n=37) and (B) translation-selective cells (red, n=27) as a function of time. Responses are shown as bands illustrating 95% confidence intervals (computed using bootstrapping). Note that the steady-state tilt response, G_tilt, is significantly different from zero. These average population responses can be interpreted as decoded internal TA and GA estimates expressed relative to the GIA (GA) or –GIA (TA), such that (G_tilt =1, ϕ_tilt =0) corresponds to a correct perception of tilt and (G_trans =1, ϕ_trans =0) to a complete illusion of translation (see C). The grey bands on panel B show the TA estimate predicted by solving the equation (GIA = GA−TA). Vertical black bands mark the acceleration period when rotation velocity ramps up from 0 to 180°/s (see Experimental Procedures). Data from individual animals are illustrated in Figure S5. (C) Illustration of the predicted TA signal. The upper panels show the GIA (black) and GA (green) estimates in four conditions (1: correct perception of tilt, 2–3: the perception of tilt decreases and lags, similar to OVAR at t=5s and in the steady-state, 4: no perception of tilt). The predicted TA signal (TA = GA-GIA) is shown in the last row (gray). The TA signal in (4), corresponding to a complete illusion of translation, is used as a reference (G_trans =1, ϕ_trans =0) in (B). Note that the predicted TA signal has a phase lead in (2) compared to (4); this is similar to the phase lead of the TA signal at t=5s. This data is shown for each animal separately in Figure S5.

Figure 6. Simplified model of tilt-translation disambiguation

An internal estimate of gravity (tilt) is computed by multisensory integration of canal and otolith cues (details of the central processing of angular velocity, Ω, are not represented in this figure (see Laurens and Angelaki 2011). An important component of this model is a ‘somatogravic’ feedback, which slowly aligns the GA estimate with the GIA and corrects the errors that would otherwise be introduced because of inaccurate rotation estimates. The time course of the simulated rotation (Ω), gravity (GA) and translation (TA) signals are shown in grey, green and red, respectively (bottom traces), using τ_s=0.9s. Vertical black bands mark the acceleration period as in Fig. 5. The model time constant was determined by fitting horizontal eye velocity of the rotational VOR (cyan), averaged across all animals. The model predicts how the initially correct tilt signal decreases (to G_tilt ≈ 0.33) and acquires a phase lag (ϕ_tilt ≈ −70°), as predicted by equation S8 (see Suppl. Materials: Theory), and how the acceleration signal increases during OVAR (to G_trans ≈ 0.94 and ϕ_trans ≈ 20°).

Figure 7. Responses of tilt-selective Purkinje cells during translation at two frequencies and comparison with somatogravic feedback predictions

(A) Somatogravic effect: a constant acceleration is interpreted as tilt. (B) illustration and simulation of the tilt illusion attributable to the somatogravic feedback during sinusoidal translation at 0.16 Hz (top) and 0.5 Hz (bottom). (C), (D) measured normalized response, h_soma = h_trans/h_tilt, shown as polar plots where the radius illustrates its gain and the polar angle its phase (see Experimental Procedures). Green dots: response of individual cells (0.16 Hz: n=18; 0.5 Hz: n = 71 cells). Red cross: average response of the tilt cell population, computed by linear regression (see Experimental Procedures). Black arrow: response predicted by the model. These data are also shown as gain vs. frequency plots in Figure S6.