The spatial structure of a nonlinear receptive field

Journal name:
Nature Neuroscience
Volume:
15,
Pages:
1572–1580
Year published:
DOI:
doi:10.1038/nn.3225
Received
Accepted
Published online

Abstract

Understanding a sensory system implies the ability to predict responses to a variety of inputs from a common model. In the retina, this includes predicting how the integration of signals across visual space shapes the outputs of retinal ganglion cells. Existing models of this process generalize poorly to predict responses to new stimuli. This failure arises in part from properties of the ganglion cell response that are not well captured by standard receptive-field mapping techniques: nonlinear spatial integration and fine-scale heterogeneities in spatial sampling. Here we characterize a ganglion cell's spatial receptive field using a mechanistic model based on measurements of the physiological properties and connectivity of only the primary excitatory circuitry of the retina. The resulting simplified circuit model successfully predicts ganglion-cell responses to a variety of spatial patterns and thus provides a direct correspondence between circuit connectivity and retinal output.

At a glance

Figures

  1. Receptive fields of On alpha-like RGCs have heterogeneous structure and nonlinear subunits.
    Figure 1: Receptive fields of On alpha-like RGCs have heterogeneous structure and nonlinear subunits.

    (a) Image of an RGC superimposed on the spatial component of the linear receptive field derived from white-noise stimulation. Ellipse shows the 2 standard deviation boundary of the best-fit Gaussian profile. (b) One-dimensional profile of a slice of the receptive field denoted by the red line in a. (c) Average temporal filter from the pixels inside the ellipse in a. (d) Excitatory input currents (Resp.) elicited by a stimulus (Stim.) consisting of temporally modulated discs (top) or 44 μm bars (bottom; Online Methods). (e) Frequency-doubled (F2) response power as a function of bar width. Error bars, s.e.m. (n = 4 trials).

  2. Nonlinear and heterogeneous receptive-field properties cause unique responses to stimuli with fine spatial structure.
    Figure 2: Nonlinear and heterogeneous receptive-field properties cause unique responses to stimuli with fine spatial structure.

    (a) Texture stimuli with different spatial scales (top; see Online Methods for stimulus construction) and firing rate of an example cell in response to the presentation of each texture stimulus shown above it (bottom). Textures were flashed for 0.5 s with 1 s blank between trials with a maintained light level throughout. Gray bars indicate texture presentation. (b) Mean spike count as a function of the spatial scale of the texture. Error bars, s.e.m. (n = 7 cells). Arrowhead indicates spatial scale used for the stimuli in ce. (c) Examples of two texture stimuli generated with different random seeds (top). Responses of two different On alpha-like RGCs to texture stimuli generated with eight random seeds (middle and bottom). (d) Stimulus examples and responses elicited by the same texture stimulus translated 33 μm in eight different directions; '–' indicates original position, and 'SW', 'S' and so on indicate the direction of translation. (e) Stimulus examples and responses elicited by the same texture stimulus presented at eight different rotation angles. Error bars (c–e), s.d. across 10–20 trials.

  3. Excitatory inputs and spike responses have similar sensitivity to rotation.
    Figure 3: Excitatory inputs and spike responses have similar sensitivity to rotation.

    (a) Average firing rate and excitatory input current measured from the same cell in response to a texture stimulus presented at two different rotation angles. Gray bars indicate texture presentation. (b) Spike count (top) and charge transfer in excitatory input currents (bottom) at each rotation angle for the cell in a. Error bars, s.d. across 10 trials at each rotation angle. (c) Normalized spike count versus normalized charge transfer of excitatory input current in response to rotations of a texture stimulus (n = 4 cells 32 total angles). Dashed line is unity. (d) Maximum linear Fisher information about rotation angle across different texture scales for spike counts or charge transfer (Online Methods). Dashed lines connect points from the same cell.

  4. Type 6 bipolar cells contact the majority of excitatory postsynaptic sites on the On alpha-like RGC.
    Figure 4: Type 6 bipolar cells contact the majority of excitatory postsynaptic sites on the On alpha-like RGC.

    (a) On alpha-like RGC expressing tdTomato (blue) with labeled putative postsynaptic sites identified by puncta of postsynaptic density protein PSD95-CFP (green). Type 6 bipolar cell axon terminals are labeled with an antibody to Syt2 (red). All On bipolar cells were labeled by Grm6-YFP (not shown here). Boxed region is magnified in ce. (b) Putative postsynaptic sites from a colored according to whether they were apposed to a type 6 bipolar cell or a different On bipolar cell (BC). (c) Top and side views of a stretch of the RGC dendrite. All On bipolar cells are labeled by Grm6-YFP (red). (d) Same region as in c with only the type 6 bipolar cell label (Syt2) shown in red. (e) Synapse identification for the region in c,d. (f) Fraction of type 6 bipolar cell synaptic contacts as a function of distance from the soma for three cells. (g) A different On alpha-like RGC labeled as in a, in a genetic background with type 7 bipolar cells labeled (Gus-GFP; red). Boxed region is magnified in i,j. (h) Identification of type 7 synaptic contacts. Blue shows regions lacking type 7 cone bipolar labeling. (i) Magnified view of a stretch of RGC dendrite. (j) Synapse identification for the region in i.

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  5. Nonlinear spatial interactions in the receptive field are aligned to the locations of type 6 bipolar cells.
    Figure 5: Nonlinear spatial interactions in the receptive field are aligned to the locations of type 6 bipolar cells.

    (a) Maximum intensity projection fluorescence image of the RGC dendrites (green) and genetically labeled bipolar cells (red). (b) Side view of the RGC and bipolar cells in a. (c) Magnification of the boxed region in a showing the interaction between a type 6 bipolar cell and the RGC dendrites in a 1.5-μm plane of the image stack. (d) Projection of the type 6 bipolar cell from the axon terminal to the dendrites where the stimuli were aligned (Online Methods) in the same region as in c. (e) Average excitatory input currents (top) to an RGC in response to small spots presented individually (solid black traces) or simultaneously (red traces). The dashed traces are linear sums of the individual spot responses. Nonlinearity index (bottom; Online Methods) as a function of the distance between the centers of the stimulus spots. Error bars, s.e.m. (n = 291 total spot pairs in 17 RGCs). (f) Schematic of the logic of the experiment to determine whether type 6 bipolar cells provided nonlinear input to RGCs. We tested the nonlinear interaction between spots that were located either within or across the presumed boundary of a type 6 bipolar cell receptive field. (g) Nonlinearity index plotted in a color scale for each pair of spots (n = 170) with distance between spots either 18 μm or 29 μm. Locations of points along the ordinate and abscissa indicate the distance of each of the two spots from the labeled bipolar cell center (Online Methods). Dotted lines indicate the value of the bipolar cell receptive-field radius yielding the most significant difference (P < 10−3) between 'within' and 'across' regions. (h) Significance of the statistical test (P value of one-tailed t-test) that the nonlinearity index for 'within' bipolar spot pairs exceeds that for 'across' bipolar spot pairs (that is, within > across) plotted as a function of the assumed radius of the bipolar-cell receptive field (RF). (i) Mean nonlinearity index in each region of g for a bipolar cell receptive-field radius of 22 μm.

  6. Construction of the bipolar cell weight map from anatomical measurements.
    Figure 6: Construction of the bipolar cell weight map from anatomical measurements.

    (a) Image of RGC dendrites (blue), PSD95-YFP (green) and type 6 bipolar cell (red). Putative synapses between the bipolar cell and RGC were counted as in Figure 3. (b) RGC dendrites were traced and the length of dendrite in the convex polygonal axonal territory of the bipolar cell axon terminal was measured (thin white lines). (c) Number of putative synapses as a function of RGC dendritic length in the bipolar cell axon territory (n = 28 bipolar cell–RGC pairs; raw data from ref. 27). Dashed line indicates best fit line through the origin (slope = 0.39 synapses μm−1). (d) Histogram of the bipolar cell axon area (mean = 227 ± 51 μm2). (e) Model of bipolar cell weights based on the anatomical measurements in c and d. Tracing of RGC dendrites (green) and model of bipolar cell synaptic weights. Model bipolar cells with nonzero weights are outlined in black, and darker fill colors correspond to larger weights (Online Methods).

  7. A predictive model of RGC responses to two-dimensional patterns of light.
    Figure 7: A predictive model of RGC responses to two-dimensional patterns of light.

    (a) Schematic of the model (Online Methods). The stimulus is sampled by the receptive field of each bipolar cell subunit (see b). The resulting input is passed through the nonlinear output function of the bipolar cell (see c). The bipolar cell outputs are each weighted by the anatomical model and summed at the RGC. (b) Measurement of the receptive field of a type 6 bipolar cell in one dimension. Charge transfer in response to 0.5 s steps of a bright bar (top) at different positions were fit by a one-dimensional Gaussian (bottom). (c) Contrast-response function measurement. Uniform 300 μm discs of light were presented to the RGC while excitatory input currents were measured. The charge transfer, normalized to its maximum, is plotted as a function of the contrast of the stimulus. (d) Response profiles of two RGCs to a texture stimulus at different rotation angles along with model predictions based on the measured nonlinear transfer function and imaged dendrites of each cell. Texture scale was 36 μm. Data points are charge transfer, normalized to the mean, of RGC excitatory input currents. Error bars, s.d. across 10 trials at each rotation angle. The model prediction was calculated for each degree of rotation. Solid purple line is the mean and shaded region is the s.d. over 10 choices of random seed in the jittering of the bipolar cell grid (Online Methods).

  8. Tests of the predictive power of simplified receptive-field models.
    Figure 8: Tests of the predictive power of simplified receptive-field models.

    (a) Bipolar cell weight maps based on the anatomical model (as in Fig. 6) or a circular two-dimensional Gaussian (top). Weight maps are normalized so that the darkest colors represent maximal weight, but the sum of the weights was constant across models. Examples of a measured output nonlinearity and a linear function replacing the output nonlinearity. (b) Data from a single cell and predictions from models using the two different bipolar cell weight maps in a. The dashed line shows the prediction for an optimized Gaussian model with a free parameter to shift the stimulus relative to the Gaussian weight profile. The orange line shows the prediction for a Gaussian model where the stimulus is perfectly centered (a flat line by construction since the Gaussian weight map was radially symmetric). Error bars, s.d. across 10 trials at each rotation angle. (c) Measured responses versus predictions from the anatomical, Gaussian and centered Gaussian bipolar weights models for a population of cells. (d) Data points from b along with predictions for a model with linear bipolar cell output and anatomically estimated bipolar cell weights (purple). (e) Measured responses versus predictions from the nonlinear (filled symbols) and linear (open symbols) bipolar cell output models for the same population as in c. Both models used the anatomically defined bipolar cell weights. For population data in c and e, n = 10 cells at 80 total rotation angles.

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Author information

Affiliations

  1. Department of Physiology and Biophysics, University of Washington, Seattle, Seattle, Washington, USA.

    • Gregory W Schwartz,
    • Haruhisa Okawa,
    • Felice A Dunn,
    • Rachel O Wong &
    • Fred Rieke
  2. Department of Molecular and Cell Biology, Harvard University, Cambridge, Massachusetts, USA.

    • Josh L Morgan
  3. Department of Ophthalmolgy and Visual Sciences, and Department of Anatomy and Neurobiology, Washington University, St. Louis, Missouri, USA.

    • Daniel Kerschensteiner
  4. Howard Hughes Medical Institute, Seattle, Washington, USA.

    • Fred Rieke

Contributions

G.W.S. performed ganglion cell recordings, analysis and designed receptive-field models. H.O. performed imaging experiments and analyses (Figs. 4 and 6). F.A.D. performed bipolar cell recordings (Fig. 7b). J.L.M. and D.K. performed imaging experiments analyzed in Figure 6. G.W.S., R.O.W. and F.R. conceived of experiments and analyses. G.W.S., H.O., F.A.D., R.O.W. and F.R. wrote the paper.

Competing financial interests

The authors declare no competing financial interests.

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Supplementary information

PDF files

  1. Supplementary Text and Figures (4M)

    Supplementary Figures 1–6, Supplementary Tables 1–3, Supplementary Discussion

Movies

  1. Supplementary Movie 1 (18M)

    Identifying appositions of PSD95 puncta with type 6 bipolar axon terminals. The dendritic segment shown in Figure 4c–e is zoomed in and rotated in three dimensions to demonstrate the identification of appositions with type 6 bipolar axon terminals. PSD95-CFP puncta, tdTomato filled alpha-like On RGC dendrites, On bipolar axons labeled by YFP and Syt2 immunoreactivity are shown in green, blue, red and white, respectively. The first set of flashing white dots represent all the identified PSD95 puncta and the second set show those apposed to On bipolar axon terminals. The red flashing dots represent PSD95 puncta classified as apposed to type 6 bipolar cells.

  2. Supplementary Movie 2 (16M)

    Identifying appositions of PSD95 puncta with type 7 bipolar axon terminals. The identification of the apposition of PSD95 puncta with type 7 bipolar cells is demonstrated in three dimensions in the same way as in Supplementary Movie 1 using the dendritic segment enlarged in Figure 4i,j. PSD95-CFP puncta, tdTomato filled alpha-like On RGC dendrites, type 7 bipolar axons labeled by GFP are shown in green, blue and red, respectively. The first set of flashing white dots represents all the identified PSD95 puncta and the second set represents those apposed to type 7 bipolar cells.

Additional data