Decoding of MSTd population activity accounts for variations in the precision of heading perception

Abstract

Humans and monkeys use both vestibular and visual motion (optic flow) cues to discriminate their direction of self-motion during navigation. A striking property of heading perception from optic flow is that discrimination is most precise when subjects judge small variations in heading around straight ahead, whereas thresholds rise precipitously when subjects judge heading around an eccentric reference. We show that vestibular heading discrimination thresholds in both humans and macaques also show a consistent, but modest, dependence on reference direction. We used computational methods (Fisher information, maximum likelihood estimation, and population vector decoding) to show that population activity in area MSTd predicts the dependence of heading thresholds on reference eccentricity. This dependence arises because the tuning functions for most neurons have a steep slope for directions near straight forward. Our findings support the notion that population activity in extrastriate cortex limits the precision of both visual and vestibular heading perception.

Fig. 1. Heading Discrimination Task and Performance

(A) Schematic illustration of the experimental protocol. Two different reference directions (α=0° and 32°) are shown, along with various comparison directions. (B) Each interval of the motion stimulus has a Gaussian velocity profile (blue), with a corresponding biphasic acceleration profile (black) and sigmoidal position variation (red). (C), (D) Example psychometric functions (vestibular and visual conditions, respectively) from one human subject for three reference headings, 0° (straight-ahead), −32° and 32° (n = 750 trials each). Solid curves illustrate cumulative Gaussian fits in which each data point is weighted according to the number of trials that contribute to it (represented by symbol size). (E), (F) Example data from a macaque monkey. Here the method of constant stimuli was used, thus all data points have the same number of stimulus repetitions (>70).

Fig. 2. Dependence of heading discrimination thresholds on reference eccentricity

(A), (B) Human behavioral thresholds (thin lines: single subjects; thick lines: mean±SE across subjects) as a function of reference heading for the vestibular task (A, N=5 subjects) and the visual task (B, N=3 subjects). (C) Macaque behavioral thresholds, as a function of reference eccentricity, in the vestibular task (blue, 2 animals) and the visual task (pink, 1 animal). Error bars illustrate 95% confidence intervals. (D) Normalized mean thresholds, comparing monkey visual and vestibular thresholds (magenta and blue, respectively) with human visual and vestibular thresholds (red and black, respectively). Data from each subject are normalized to unity at the 0° reference heading before computing the mean and SE across subjects.

Fig. 3. Calculation of Fisher information and discrimination thresholds for an example neuron

(A) Example tuning curve (black) and Fisher information (red). Arrow indicates the direction corresponding to peak Fisher information. (B) Neuronal discrimination thresholds as a function of reference heading direction for the same example cell. See also Figure S2.

Fig. 4. Summary of MSTd population responses

(A), (C) Distribution of the direction of maximal discriminability, showing a bimodal distribution with peaks around the forward (0°) and backward (±180°) directions for vestibular (n=511) and visual conditions (n=882), respectively. (B), (D) Scatter plots of each cell's tuning width at half maximum versus preferred direction. The top histogram illustrates the marginal distribution of heading preferences. A subpopulation of neurons with visual direction preferences within 45° of straight ahead and tuning width <115° are highlighted (open symbols). See also Figure S1.

Fig. 5. Population Fisher information

(A) Comparison between vestibular (blue, n=511 neurons) and visual (red, n=882 neurons) population Fisher information computed from all neurons with significant tuning in the horizontal plane. (B&C) Fisher information for subsets of congruent neurons only (B, n=223) and opposite neurons only (C, n=193). Solid curves: population Fisher information; Error bands: 95% confidence intervals derived from a bootstrap procedure. See also Figure S3.

Fig. 6. Comparison of predicted and measured heading thresholds as a function of reference direction

(A) Vestibular: n=511 neurons; (B) Visual: n=882 neurons; (C&D) For a subset of neurons (vestibular: n=248; visual: n=472), Fisher information was calculated from tuning curves that included two extra headings around straight ahead (±22.5°). Gray symbols with error bars illustrate human behavioral thresholds (replotted from Fig. 2A, B). Black lines illustrate population predictions from Fisher information. See also Figure S4.

Fig. 7. Comparison between predicted thresholds computed from Fisher information and population decoding

(A) Computation of the log likelihood function used for maximum likelihood decoding. (B), (C) Comparison of predicted thresholds from Fisher information (black), maximum likelihood decoding (red), and population vector decoding (green). See also Figure S5.

Fig. 8. Accuracy of heading estimation for maximum likelihood (ML) and population vector decoding schemes

(A), (B) The decoded heading direction from vestibular (A) and visual (B) population activity is plotted as a function of the true heading. Data points represent single-trial estimates for 10° increments of true heading. (C), (D) The error between predicted and actual headings is plotted versus true heading. Data shown are mean ±SD (10 repetitions). Red: ML decoding; green: population vector predictions. See also Figure S6.

Fig. 9. Influence of correlated noise on thresholds predicted from Fisher information

Noise correlations deteriorate heading information encoded by the MSTd population, but this effect is roughly homogeneous across all reference headings for both the vestibular (A) and visual (B) conditions. The overall shape of the threshold dependence on reference heading is similar when assuming independent noise (solid lines) and when incorporating the structure of noise correlations measured in MSTd during heading discrimination (dashed lines, Angelaki et al., 2009).