Fig 1.
Multiplexing sensory and behavioral signals with gain modulation.
a) Left: a functional neuron model where the gain of a sensory tuning curve is modulated by the running speed. The modulation is applied identically to the entire tuning curve. Right: two example direction-speed tuning curves corresponding to the model in the left. A direction-selective (left) and orientation-selective (right). The behavioral modulator as a function of the running speed is plotted above tuning curves. b) Left: a functional neuron model where the running speed independently modulates the gain of the different parts of the tuning curve (subunits). Right: two example direction-speed tuning curves corresponding to the model in the left. Sensory subunits are marked with vertical lines in different shades of gray to the right of the tuning curve. Their modulators are plotted above the tuning curves in the corresponding color. Mouse image was taken from: https://doi.org/10.5281/zenodo.3925949.
Fig 2.
Analysis of tuning to stimulus direction and running speed in the mouse visual cortex.
a) Example traces of the calcium imaging data (dF/F) and of mouse running speed obtained from the Allen Brain Observatory (top, dark gray lines and bottom, light gray lines respectively). Gray rectangles mark duration of the stimulus whose orientation and temporal frequency are marked with gray text. b) Left panel: example three-dimensional (running speed - stimulus direction - stimulus temporal frequency) tuning curve of a neuron computed using thresholded dF/F signal (see Methods). Right panel: a two-dimensional (running speed - stimulus direction) tuning curve obtained by averaging the three-dimensional tuning curve on the left across the temporal frequency dimension. c) Distribution of seconds of data per bin in all analyzed datasets. The horizontal white line denotes the average (14 s) and the gray rectangle denotes the interval spanned by 5th and 95th percentiles of the distribution. d) Distributions of the horizontal eye positions pooled across raw recordings (left, gray bar) and averaged within bins of the orientation-speed tuning curves (right, green bar). White lines denote the mean (0 deg) and rectangles denote the interval spanned by 5th and 95th percentiles. Data for each animal was standardized independently via z-scoring. The scale of the plot is symlog (i.e., . The eye position data was not available for all analyzed datasets. e) Left panel: orientation tuning curves of four example neurons. Right panel: running-speed tuning curves of the same neurons as in the left panel (marked with corresponding letter and color). f) Joint orientation-speed tuning curves of four example neurons marked with corresponding letters and colors in, e. g) Example neurons that pass the bootstrap test of velocity modulation. Left column: orientation-speed tuning curves of three example neurons (orange frames). Middle column: distributions of the test statistic of the modulation test (see Methods). Vertical dashed line denotes the significance threshold equal to the 95th percentile of the statistic distribution. Orange and gray triangles denote respectively the values of the test statistic of the original tuning curve and five example bootstrapped samples visualized in the right column. Right column: five example bootstrapped orientation-speed tuning curves. h) Example neurons that do not pass the bootstrap test of velocity modulation. Panel is analogous to g).
Fig 3.
Sparse decomposition of direction-speed tuning curves.
a) Conceptual schematic of a neuron where two sensory subunits (orange and gray circles) are modulated independently by the running speed of the animal. Mouse image was taken from: https://doi.org/10.5281/zenodo.3925949 b) Schematic of the statistical model that decomposes stimulus-speed tuning curves (left column) into a sum of subunit basis functions (second and fourth panels from the left) multiplied by speed-controlled gain modulators (third panel from the left and right panel). The subunit basis functions determine sensory tuning of a neuron, while modulators determine modulation of each subunit by the running speed of the animal. c) Distribution of the SNR values of model fits to stimulus-speed tuning curves. The horizontal white line denotes the average (8 dB SNR) and the gray rectangle denotes the interval spanned by 5th and 95th percentiles of the distribution. d) Histogram of the number of subunits fitted to each neuron. Note that not a single neuron had 7 or 8 significant subunits. e) Left panel: example stimulus-speed tuning curve of a direction-selective neuron with a single sensory subunit. Middle panel: reconstruction of the tuning panel from the model fit. The single fitted sensory subunit is marked with a short vertical orange line on the right side. The SNR of the fit is equal to 23 dB. Right panel: speed modulator of the direction-selective subunit. f) Four example direction-selective neurons (gray frames) together with their respective fits (blue frames) marked with fitted subunits (short, vertical orange lines on the right side of each blue frame) and speed-modulators (orange lines). g) Same as e but for an example direction-selective neuron with two sensory subunits. The subunits and their modulators are now marked with gray and orange lines. h) Same as f but for six example orientation-selective neurons.
Fig 4.
Quantification of differential modulation of sensory subunits.
a) Left: tuning curve of an example neuron with differentially modulated subunits. Right: two bootstrap samples with simulated shared modulation corresponding to the neuron on the left. b) Same as a but for an example neuron with shared modulation between subunits. c) Left: modulators fitted to the tuning curve in a (orange and gray lines correspond to marks in panel a). Dashed black line denotes the correlation maximizing fit to both modulators. Note that the fitted curve is identical for both modulators up to a scaling and a shift. The average correlation of the fit with the two modulators is equal to 0.711. Right: the same as on the left but for bootstrap sample I depicted in panel a. b) Same as c, but for the example neuron displayed in b. e) Left: example tuning curve of a neuron with differently modulated subunits. Middle: a null distribution of the test-statistic
, i.e., the average correlation of the correlation-maximizing fit with both modulators, derived from 1000 bootstrap samples with simulated shared modulation. The vertical dashed line denotes significance threshold at p = 0.01 and the orange triangle the value of the test statistic for the tuning curve on the left. Right: three example bootstrap samples with simulated shared modulation. f) Same as e, but of an example neuron whose subunits are not significantly differently modulated. g) Visualization of the test statistic distribution for 150 randomly selected neurons. Gray circles denote the value of the test statistic
averaged across all bootstrap samples (x-axis) and the value for the data
(y-axis). Thin-gray lines denote the range between 1st and 99th percentile. h) Fraction of neurons that pass the significance threshold of the test for differential modulation of sensory subunits as a function of the threshold value. The threshold is computed as a quantile of the null distribution obtained for each neuron individually via bootstrapping. 35 percent of neurons pass the significance threshold at p = 0.01. i) Histogram of the test statistic for the data (orange) and the average across bootstrap samples for each neuron (gray). The distributions are significantly different (KS-test, p-value < 0.001). Inset depicts the same distribution on the log-probability scale. j) Example tuning curves that pass the significance threshold at p-value thresholds of 0.01, 0.05 (top and middle rows respectively) and that do not pass the threshold of 0.1 (bottom row).
Fig 5.
Behavioral modulation of orientation-selective cells.
a) Left panel: joint distribution of stimulus directions preferred by subunits in two-subunit neurons. Right panel: histogram of angular separation (distance) between stimuli preferred by individual subunits in two-subunit neurons. b) Histogram of log-ratios of modulator strength (stronger to weaker). The mean equal to 3.36 was computed before logarithmic transform. c) Histograms of correlations between modulators in two-subunit neurons. Orange, grey and blue correspond to the original data, bootstrap tuning curves without modulation and bootstrap tuning curves with shared modulation respectively. Data distribution is significantly different from both simulated datasets (KS-test, both p-values < 0.001). d) Histograms of correlations between modulators and running speed in stronger and weaker subunits (left and right panels respectively). Orange, grey and blue correspond to the original data, bootstrap tuning curves without modulation and bootstrap tuning curves with shared modulation respectively. Correlation distributions are significantly different from bootstrap without modulation in both panels (KS-test, p-value < 0.001) and not significantly different from bootstrap with shared modulation (KS-test, p-value > 0.1). Correlation distributions for stronger and weaker modulators are not significantly different (KS-test, p-value = 0.24). e) Scatter plot of modulator correlations with running speed. Each gray dot corresponds to a single neuron. Thin black lines within the plot denote 5th (left and bottom line) and 95th (right and upper line) percentiles of modulator-speed correlations computed with bootstrap samples without modulation. Darker points with Roman numerals correspond to identically labeled tuning curves in panel f. f) Example direction-speed tuning curves (grayscale heatmaps) and corresponding fitted modulators of stronger and weaker subunits (orange and gray lines respectively). Correlations of the stronger and weaker modulator with the running speed are denoted as in orange and gray respectively. Roman numerals correspond to points marked in panel, e. g) The same as e but for randomly permuted modulators (left) and simulated joint modulators (right). h) Proportions of cells in different regions of the correlation plane for real data (top row), bootstrap samples without modulation (second row from the top) and bootstrap samples with simulated joint modulators (third row from the top). Color legend of areas on the correlation plane (as in e-f) is depicted in the bottom row.
Fig 6.
Clustering two-subunit neurons shows diverse effects of locomotion on sensory tuning.
a) Twelve clusters of speed modulators in neurons with two subunits. Bold lines correspond to cluster means (centroids) and shaded areas to cluster standard deviations. Weaker modulators are plotted with a lighter color variant. b) Individual modulators in each of the twelve clusters. Each panel corresponds to an identically positioned panel in a, where colors of centroids in a match the color of frames in b. Each panel consists of two parts corresponding to the stronger and weaker modulator of each cell, separated by a thin, vertical line. Colorful dots correspond to the centers of mass of each modulator. Within each cluster neurons are sorted by the center of mass of the weaker modulator. c) Joint distributions of direction selectivity of fitted subunits in four largest clusters. d) Left panel: a schematic of the anatomical division of the mouse visual cortex according to the Allen Brain Observatory (replotted from [21]). Right panel: distributions of cluster memberships in the six areas of the visual cortex. Each vertical bar corresponds to one area, the total bar height corresponds to 100% of neurons in that area (the absolute number of neurons is denoted above each bar). Colors (right panel, color bar) correspond to clusters visualized in panels a and b.
Fig 7.
Clustering single-subunit neurons shows variability of running speed tuning.
a) Nine clusters of speed modulators in neurons fitted with one subunit. Bold lines correspond to cluster means and shaded areas to cluster standard deviations. b) Distributions of preferred directions for single-subunit neurons. Distribution across all cells (left panel) and three example clusters (colored), corresponding to panel a). The clusters generally show no clear tuning bias for specific stimulus directions. c) Proportional distributions of modulator clusters within six areas of the visual cortex. The colored segments in each vertical bar show the percentage of neurons belonging to each cluster (color bar corresponding to panel a), for each visual area. The total number of neurons in each area is given above the bars.
Fig 8.
Computational benefits of differential tuning.
a) Schematic of computation with behavioral and sensory signals. Population of neuron processes the inputs such that down-stream neurons can read-out task-specific quantities (denoted by ). Mouse image was taken from: https://doi.org/10.5281/zenodo.3925949 b) Performance of hypothetical tasks (grayscale) plotted as a function of the accuracy of representation of behavioral and sensory inputs in the population. Left: a difficult sensory task - to achieve high performance sensory input has to be encoded with high accuracy (vertical blue line) while the behavioral input can be represented with low accuracy (horizontal blue line). Middle: same as left but for a difficult behavioral task. Right: Same as left but for a difficult joint task. c) Example tuning curves representative of three different neuron types modulated by running speed. Left: direction selective neurons. Middle: orientation selective neurons with shared modulation of subunits and symmetric tuning curves. Right: orientation selective neurons with differently modulated subunits. d) Left: simulated stimulus decoding from populations of different neuron models. Lines denote errors averaged over multiple random populations and shaded bars denote the standard deviation of the error. Direction-selective cells (gray solid line and shaded area) and differently modulated orientation-selective neurons (orange line and shaded area) models have very similar performance. Orientation-selective neurons with shared modulation (gray dashed line and gray are) has the constant average error of approximately
regardless of population size. Bottom: simulated decoding of the behavioral variable that modulates neuronal activity. Colors and markers the same as above. Direction-selective neurons yield highest decoding error while multiple both types of orientation-selective neurons models show comparable, better performance.
Fig 9.
Hypothetical mechanisms of differential modulation.
a) Top: a schematic of excitatory convergence of two neurons (A and B) on the third neuron (C). Bottom: Example direction-speed tuning curves of neurons A and B (left, smaller panels) - subunits of both neurons share a common speed modulator. Resulting tuning curve of the neuron C (right) shows differential tuning. b) Same as a but for an example excitatory-inhibitory convergence of two orientation-selective neurons with shared modulation of subunits. c) Schematic of a complex tuning. Top: a 3D tuning curve - in addition to direction and speed, the neuron is tuned to a third variable. This other variable could be either sensory (e.g., temporal frequency), or behavioral (e.g., head movements). Different values of the additional variable are denoted by letters A-D. Bottom: direction-speed tuning changes with the third tuning variable (left; small panels, blue frames). Right: the resulting direction-speed tuning curve shows differential modulation. Mouse image was taken from: https://doi.org/10.5281/zenodo.3925949.