Article Figures & Data
Figures
- Figure 1.
Quantifying response gain signatures of LGN neurons. A, B, Contrast response functions of an example M cell (A) and P cell (B). Open points are the F1 response at the temporal frequency of the stimulus. Smooth black lines indicate the fit of a descriptive function (Eq. 8) to these data. Dashed lines indicate the C50 (M cell, 0.21; P cell, 0.50), and the magenta arrows indicate the maximum contrast within the linear range of each cell at which response gain was calculated (M cell, 387 spikes/s/contrast; P cell, 28 spikes/s/contrast). C, Illustration of the method used to calculate a saturation index. The example M cell has a saturation index of 0.38, while the example P cell has a saturation index of −0.04. D, The relationship between the nature of the contrast response function (accelerating, linear, saturating) and the saturation index. E, F, Response gain versus the C50 (E) and saturation index (F). Blue points represent P cells (N = 71), and red points represent M cells (N = 41).
- Figure 2.
Using sweep stimuli to estimate temporal frequency tuning. A, B, The response of an example M cell to the chirp sweep stimulus. At the top of the figure, the black curve indicates the temporal contrast profile of the stimulus. In A, gray curves plot the firing rate of the cell over time, aligned to drift onset, and red curves are the response predicted by the LN model. The two plots in B give the amplitude (left) and phase (right) response of this LN model as a function of temporal frequency. C, D, The response of a different M cell to the stepped sweep stimulus. Plots follow the same conventions as in A and B. The topmost sinusoidal curve in B indicates the temporal contrast profile of the stepped sweep stimulus, and each epoch is shown on a scale from black to green as the temporal frequency increases. Colors indicate periods of constant frequency (each 1.6 s). The open red points in D are the amplitude and phase of the first harmonic response calculated from these spike times.
- Figure 3.
M and P cell temporal frequency tuning as a function of both luminance and contrast. A, B, The responses of one M cell and one P cell at multiple luminances and contrasts. In the main 3 × 3 plot, each subplot is a single set of measurements of temporal frequency tuning at a given contrast and luminance. Contrast values increase left to right, and luminance values increase from bottom to top. Open gray points are measured F1 responses for cells (recorded with the stepped sweep stimulus). Smooth lines through these points plot the amplitude response of the LN model fit to each condition. Filled points indicate temporal frequencies 0 ± 1.5 octaves from the preferred frequency. Colors indicate low (red), medium (gold), and high (teal) temporal frequencies. A, B, The rightmost subplots show the contrast response functions estimated from the LN model at these three temporal frequencies (same color convention) for each luminance. Open points in these subplots are the response of the LN model as a function of contrast. The smooth curves in these subplots show the fit of a descriptive function (Eq. 8) to these data. Temporal frequency tuning curves in the main 3 × 3 plot show only a subset of stimulus contrasts, while the contrast response functions in the subplots indicate the response across all tested contrasts.
- Figure 4.
Diversity of contrast response functions within M and P cell populations. A–F, Contrast response functions from M cells (N = 26) and P cells (N = 37) recorded in the main luminance × contrast experiment. The thin lines in each subplot (A–F) represent data for one cell evaluated at contrasts between 0 and 0.4 at one of three temporal frequencies indicated by the title at the top of each subplot. Blue lines represent P cells, and red lines represent M cells. Thick blue and red lines indicate the population-averaged contrast response function. These data are taken from the midluminance condition (10–12 cd/m2, 282–356 Td). Given an initial characterization of each cell, the tested contrast ranges in the main experiment differed from cell to cell. Therefore, some M cell curves end at a contrast of 0.2.
- Figure 5.
Average contrast response functions as a function of luminance. A–F, The average contrast response function for P cells (A–C) and M cells (D–F) over a contrast range of 0–0.4. The background luminance varies across rows. Low, mid, and high luminance correspond to 3.5, 12.6, and 41 cd/m2 for most cells (100, 356, 1159 Td). The smooth curves through the points give the fit of Equation 8 to the data. Error bars are the SEM across cells. The color of each curve indicates the TF. Gold, Medium TF; red, medium TF – 1.5 octaves; teal, medium TF + 1.5 octaves. Average saturation indices across these conditions are shown in Extended Data Figure 5-1.
- Figure 6.
Change in response saturation as a function of luminance and temporal frequency. A–F, Each line shows the change in saturation index across temporal frequency for P cells (N = 41), and M cells (N = 26). Changes are relative to the average saturation index across frequencies. Open points are the mean (±SEM) saturation index at each TF. The insets in each subplot illustrate the shape of the contrast response function at minimum (dot-dashed), median, and maximum (dot-dashed) saturation indices in each plot. The scale bars marked with asterisks show the difference in saturation index expected by chance for each cell type. Dark lines cross this criterion and show a significant monotonic decrease in saturation as a function of temporal frequency (contrast gain control). Extended Data Figure 6-1 illustrates how chance changes in saturation index were calculated.
- Figure 7.
Change in firing rate as a function of luminance and temporal frequency. A–F, Firing rate at 0.2 contrast as a function of mean luminance and temporal frequency. Each line shows the firing rate of a P cell (blue) or M cell (red) at a contrast of 0.2 as a function of background luminance. Each row corresponds to the variation in firing rate at a different temporal frequency, increasing from left to right. We plot firing rates on a square root axis, showing each cell relative to the mean firing rate across luminance conditions. Asterisks indicate significant differences between conditions (*p < 0.005, **p < 0.001, Wilcoxon rank-sum test). Darker lines indicate cells that show a near-monotonic increase in firing rate. Extended Figure 7-1 illustrates the contrast response functions at (3–4.5 vs 35–40 cd/m2) and the absolute firing rate differences at multiple contrasts.
- Figure 8.
Decomposition of temporal frequency tuning into separable effects of luminance and contrast. A, B, Temporal frequency tuning of example M and P cells for the stepped sweep stimulus and the separable LN model prediction. Gray open points in the area bounded by the shaded boxes are the F1 responses at different temporal frequencies recorded from each cell at a given luminance (row) and contrast (column) condition. These data are those appearing in Figure 3. The solid purple line is the prediction of the separable LN model of the F1 response in each condition. The solid blue and red tuning curves in the shaded boxes are derived using singular value decomposition and represent the independent contribution of contrast and luminance to temporal frequency tuning. The outer product of these tuning curves (purple lines through the data) are the separable function of contrast and luminance that best fit the data.
- Figure 9.
Comparing separable model predictions versus original LN model and F1 responses. A, B, Original and separable LN model predictions for an M cell recorded during a stepped sweep in one stimulus condition. A, B, The gray curves indicate the firing rate of the cell over time and are the same in both panels. The curve at the top of A indicates the change in stimulus contrast over time. As temporal frequency increases, the curve becomes greener. The solid orange and purple curves inset in A and B are the predictions of the original and separable LN models, respectively. The rmse between the original and separable models and the measured response were 15.4 and 15.5 spikes/s, respectively. C, The root mean square error between the original (x-axis) or separable (y-axis) LN models and the firing rate of the cell. Each point indicates a single cell, and colors indicate cell type, as in previous plots. The black line is unity. D, The distribution of rmse differences between data and the separable model, split by cell type. E, Separability index (see Materials and Methods) split by cell type. The bars at the top of the plot are the estimated ranges of the separability index expected because of uncorrelated data variation (black) and for a perfectly separable neuron with P cell noise (blue) or M cell noise (red). F, Variance explained (R2) by SVD on raw F1 response versus variance explained (R2) on F1 responses predicted by the LN model. The data follow the same conventions used in C.
Extended Data
Figure 5-1
Average saturation index across temporal frequencies and luminances. A, B, Saturation indices for M and P cells as a function of temporal frequency. Each error bar is the mean ± SEM of the saturation indices of M cells (n = 26) and P cells (n = 41) as a function of temporal frequency. The color of each line indicates the luminance level. Lines connect conditions that are statistically different from one another (Wilcoxon rank-sum test, p < 0.005). Download Figure 5-1, EPS file.
Figure 6-1
Simulating the expected change in saturation index on a cell-by-cell basis. A, The variability of the F1 response. The open circles are trial-by-trial F1 responses plotted in the real plane versus the complex plane. The closed circle is the mean F1. The length of the dashed line is the amplitude response of this cell, and the angle of the dashed line from the origin indicates the phase. The SD across trials is measured from the euclidean distances between the single trials and their average. B, C, Coefficient of variation as a function of contrast. Each line is the relationship between the CV (SD/mean F1), and the bolder lines are the average CV as a function of contrast per cell class. The dashed line is the fit of a double exponential to these data. D, Simulations of different contrast response functions. Each line is a single contrast response function that passes through the points (sampled at the contrasts used in our experiment). The darkness of the line indicates how saturated the cell is. E, F, Chance-level variations in the saturation index for P and M cells. Each set of points is a single trial, simulated from the mean responses shown in D and the empirically derived relationship between contrast and coefficient of variation. Lines through these points show the median and 95% confidence intervals on these data. For each cell class, the significance criterion we selected was the maximum chance-level change in saturation across all degrees of saturation, according to this simulation. Download Figure 6-1, EPS file.
Figure 7-1
Contrast response functions at low and high luminance levels for M and P cells. A, B, D, E, Individual cell contrast response functions. Each point is the output of the LN model at that temporal frequency and contrast for either P cells (shades of blue, n = 41) or M cells (shades of red, n = 26). The smooth lines through the points are the fit of Equation 8 to the data. C, F, Firing rate saturation for individual cells. Each point is the firing rate of a P cell (C) or an M cell (F) at half-maximum contrast (x) versus the firing rate at max contrast (y) in response to high-temporal frequency stimuli. Points are shaded according to luminance (darker shades = 3.5–4.0 cd/m2; lighter shades = 38–40 cd/m2). The marginal distributions along the top show differences as a function of luminance at each contrast condition. The histograms in the corners show differences in firing rate for each luminance condition. Asterisks indicate when the distributions are significant between conditions (Wilcoxon rank-sum test, p < 0.005). Download Figure 7-1, EPS file.
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