Fig 1.
Spatial receptive-field nonlinearities of marmoset retinal ganglion cells.
A: Layouts of receptive fields (shown as 1.5- contours), spike-train autocorrelograms (lower left), and temporal filters (lower right) of four analyzed cell classes, each showing data from one experiment. The Large OFF cells are pooled from three clusters, each shown separately. Scale bars: spatial: 300 μm, temporal filters: 100 ms, autocorrelograms: 25 ms. B: Spatial receptive field (left) and temporal filter (right) of an OFF midget cell (top row) and an OFF parasol cell (bottom row). C: Firing rate profiles of the two sample cells from B (green trace: OFF midget cell; orange trace: OFF parasol cell) in response to reversing gratings (60 μm spatial period, shown on top; ellipses denoting the 1.5-
receptive-field contours). RGI specifies the reversing-grating index of the corresponding cell. D: Distributions of the reversing-grating index for all four cell classes. E: Firing rate histograms with equally spaced bins from the training segments for white-noise (WN, top) and naturalistic-movie (NM, bottom) stimulation, based on mean light intensity (Imean) and local spatial contrast (LSC) for the OFF midget (left) and OFF parasol (right) cells from B. Firing rates are normalized to the histogram maximum, with empty bins shown in gray. F: Firing rate histograms with quantile bins computed for regions corresponding to blue and yellow boxes in E. Data points used to compute the LSC sensitivity are overlaid, along with the linear fit. Right: Firing rate data (solid lines) of three selected histogram rows (marked by arrows of corresponding color) and fitted softplus functions (dashed lines). G: Distribution of LSC sensitivity for all four cell classes under white noise (left) and naturalistic movies (right).
Fig 2.
Examples of the effect of local spatial contrast on responses to natural scenes.
A: Illustration of the stimulus processing to obtain Imean and LSC by applying the filters of a sample OFF parasol cell (1st column) to the stimulus (2nd column, exemplified here by a single frame) to obtain a temporally convolved stimulus (3rd column, overlaid with the 3- contour of the spatial filter), from which the weighted light intensity signal (4th column) and the weighted spatial contrast (5th column) are extracted. The two rows correspond to two separate stimulus segments. The plots of the light-intensity and spatial-contrast signals display the results of the pixel-wise computation as indicated by the formulas at the top (where us denotes the spatial filter and hs the temporally convolved stimulus frame), with the final values given in the lower left of the plots. The time course of the Z-scored light-intensity and spatial-contrast signals (top) along with the corresponding measured firing rates (bottom) of the sample cell are shown in the 6th column, with the light gray region highlighting the time window of presentation of the analyzed stimulus frame for which the Imean and LSC values in columns 4 and 5 were calculated. B: Same as A, but for a sample OFF midget cell. Both cells are the same as in Fig 1B–F. Frames of the stimulus taken from an open-source movie licensed under CC BY 3.0 [28].
Fig 3.
Schematic of the spatial contrast (SC) model.
For a given cell, the incoming stimulus is first convolved with the cell’s temporal filter to yield the effective stimulus frame hs (overlaid here with the 3- contour of the spatial filter). From this, the mean light intensity signal Imean and the spatial contrast signal LSC are computed by using the cell’s spatial filter us as weights. The Imean and LSC are linearly combined with a weight parameter w used to scale the LSC contribution, and the combined signal is transformed by an output nonlinearity to yield the model’s firing rate response. Scale bars: spatial: 300 μm, temporal: 100 ms. Frame of the stimulus taken from an open-source movie licensed under CC BY 3.0 [28].
Fig 4.
Evaluation of model performance by cell type.
A: Responses of sample cells from each of the four cell classes in Fig 1A to 3 s segments of test stimuli (gray) for white noise (left column) and naturalistic movie (right column), together with the predictions from the LN model (orange) and the SC model (blue). The numbers above each plot show the Pearson’s correlation coefficients between model prediction and cell response. B: Comparison of correlation coefficients for the SC model (rSC) and the LN model (rLN) for each cell in the four cell classes (colors corresponding to the labels in A) under spatiotemporal white noise (top row) and naturalistic movie (bottom row). The average correlation coefficients and
are shown next to the corresponding axes. C: Relative improvement in model performance (
) under white noise (top row) and naturalistic movies (bottom row) for each cell versus receptive-field size (left) and the obtained LSC weight w (right). Colors indicate cell class as in B.
Fig 5.
Examples of improved predictions by SC model versus LN model.
A: Firing rate (top, dark gray) and spike raster (bottom) for the sample OFF parasol from Fig 1B to an 8 s segment of the naturalistic movie test stimulus. Overlaid are response predictions for the LN model (orange) and the SC model (blue). B: Examples of episodes from the natural movie test stimulus with substantially better response prediction by the SC model versus the LN model for the same sample cell as in A. The columns are shown in the same way as in Fig 2. The firing rate curves in column 5 are overlaid with response predictions with colors as in A. Frames of the stimulus in B taken from an open-source movie licensed under CC BY 3.0 [28].
Fig 6.
Computation of functional subunits and performance comparison with a subunit model.
A: Filters representing the relevant stimulus subspace computed via spike-triggered covariance (STC) for a sample ON parasol cell. Shown here are the top 8 of the 16 used for modeling. Scale bar: 100 μm. B: Inferred filters of the functional subunits for the sample cell. The optimal number of filters (here 8) was chosen during model training. The relative weight of each filter in the subunit model is displayed at the top-left of each panel as a percentage of the total sum across all filters. Scale bar: 100 μm. C: Eigenvalue spectrum from the STC analysis of the sample cell. Blue circles correspond to filters from A. D: Distribution of the obtained number of subunits for the four cell classes. Colors as in F. E: Firing rate of the sample cell (dark gray) overlaid with predictions from the SC model (blue) and the subunit model (pink) for a 2 s segment of the spatiotemporal white-noise stimulus. Pearson’s correlation coefficient between model prediction and cell response displayed next to model name in legend. F: Comparison of correlation coefficients for the SC model (y-axis, rSC) and the subunit model (x-axis, rsub) for each cell of the four cell classes under spatiotemporal white noise. The average correlation coefficients and
are shown next to the corresponding axes. G: Relative improvement in model performance (
) under white noise for each cell versus the number of spikes in the training segment of the stimulus (left) and the size of the cells’ spatial receptive fields (right). Colors as in F. In panels F and G, the sample ON parasol cell from A–E is highlighted with a black circle.
Fig 7.
Analysis of spatial scale of contrast sensitivity.
A: Schematic of the SC model from Fig 2, modified to include spatial stimulus smoothing before the computation of LSC. B: Spatial smoothing analysis for a sample cell in response to white noise. Gray curve shows the SC model performance for different smoothing scales, normalized to performance without smoothing. The optimal scale is obtained by interpolation (black segment). Sample white-noise frames at different smoothing scales are shown on top, with the red outline marking the approximate optimal scale. C: Spatial smoothing analysis for all cells under white-noise (top) and naturalistic-movie (bottom) stimulation, with the region around the peak shown enlarged in the inset with dashed outline and relative model performance shown as percentage improvements over a model without smoothing. Distributions of spatial scales of nonlinear stimulus integration for each cell class under white noise are shown in the inset histograms. The x-axis here corresponds to the range of the red segment of main plot. D: Radially-averaged power spectral density (RAPSD) curves averaged across frames of white noise (left) and of the naturalistic movie (right) for different scales of spatial smoothing. Spatial scale (x-axis) is here defined as the inverse of spatial frequency. Shaded gray areas mark the range of 40–50 μm, matching approximately the range of spatial scales from C. Note that the RAPSD of the non-smoothed white-noise stimulus falls off for small spatial scales because RAPSD curves were here computed based on monitor-pixel resolution and the stimulus was close to white only for scales beyond the length of two stimulus squares. Frame of the stimulus in A taken from an open-source movie licensed under CC BY 3.0 [28].