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What is the location of the center-surround receptive fields of retinal ganglion cells?

What is the location of the center-surround receptive fields of retinal ganglion cells?

I have read wikipedia article about receptive fields of visual system and it states the following:

The receptive field is often identified as the region of the retina where the action of light alters the firing of the neuron. In retinal ganglion cells (see below), this area of the retina would encompass all the photoreceptors, all the rods and cones from one eye.

I understand the part where it says that the neurons firing increases as we put light on the center of the receptive (for the ON center type) and etc.

What I'm not sure about is the location of this circle, in other words, where is this circle that we put light on?

What I think is that the circle is the area of retina where we have the rod and cone shaped photoreceptors. Does this means that for every ganglion cell the photoreceptors connected to it are always shaped like a circle ?


A nice illustrative image of how the photoreceptors connect to the retinal ganglion cell (RGC), and thereby facilitate the center-surround structure is provided in figure 1 below. It shows a cross section through the retina.


Fig. 1. Photoreceptor organization and connections to the retinal ganglion cell. source: McGill University

The receptive fields (RFs) are determined by the number of photoreceptors connected to the RFs. RFs are smaller in the central high acuity area of the retina (the fovea) and increase in size more eccentrically. As a result, visual acuity is highest in the center visual field, and degrades more eccentrically in the field of view.


Receptive-field properties of Q retinal ganglion cells of the cat

The goal of this work was to provide a detailed quantitative description of the recepii ve-field properties of one of the types of rarely encountered retinal ganglion cells of cat the cell named the Q-cell by Enroth-Cugell et al. (1983). Quantitative comparisons are made between the discharge statistics and between the spatial receptive properties of Q-cells and the most common of cat retinal ganglion cells, the X-cells. The center-surround receptive field of the Q-cell is modeled here quantitatively and the typical Q-cell is described. The temporal properties of the Q-cell receptive field were also investigated and the dynamics of the center mechanism of the Q-cell modeled quantitatively. In addition, the response vs . contrast relationship for a Q-cell at optimal spatial and temporal frequencies is shown, and Q-cells are also demonstrated to have nonlinear spatial summation somewhat like that exhibited by Y-cells, although much higher contrasts are required to reveal this nonlinear behavior. Finally, the relationship between Q-cells and Barlow and Levick's (1969) luminance units was investigated and it was found that most Q-cells could not be luminance units.


Results

We used single-cell patch electrophysiology in an in vitro macaque retinal preparation in conjunction with computational modeling of the RGC RF to explore the impact of the surround on nonlinear RF structure and natural scene encoding. We started by testing the hypothesis outlined in Figure 1C,D. Consistent with this hypothesis, we found that the linearity of spatial integration in the RF center depends on surround activation. Next, we used natural and artificial stimuli to characterize nonlinear interactions between center and surround and to test circuit models for the origin of these interactions. Finally, we show that the intensity correlations characteristic of natural scenes promote nonlinear interactions and make spatial integration relatively insensitive to changes in local luminance across a visual scene.

The RF surround regulates nonlinear spatial integration in the RF center

To test the hypothesis of Figure 1C,D, we systematically manipulated surround signals while probing spatial integration in the RF center. We focused this test on Off parasol RGCs, because these cells show both stronger rectification of subunit output than On parasol cells (Chichilnisky and Kalmar, 2002) and nonlinear spatial integration in the context of naturalistic visual stimuli (Turner and Rieke, 2016). We began each experiment by centering the stimulus over the RF and measuring the linear RF (see Materials and methods and Figure 2—figure supplement 1). We then tailored visual stimuli for each cell such that the ‘center region’ stimulus did not extend into the pure surround RF subregion and the ‘surround region’ stimulus did not cover the center. These subregions are not exclusively associated with a center or surround mechanism since the antagonistic surround is spatially coextensive with the RF center (Figure 1A,B). Nonetheless, according to estimated RFs, the ‘center region’ stimulus activated the center mechanism ∼ 4 times more strongly than the surround mechanism and the ‘surround region’ stimulus activated the surround mechanism ∼ 5 times more strongly than the center mechanism. This degree of specificity allowed us to ask questions about interactions between these two RF subregions.

We previously found that nonlinear spatial integration endows Off parasol RGCs with sensitivity to spatial contrast in natural images (Turner and Rieke, 2016). To test whether surround activity modulates this spatial contrast sensitivity, we measured Off parasol RGC spike responses to natural image patches that contained high spatial contrast and were expected to activate the nonlinear component of the cell’s response (see Materials and methods for details on images and patch selection). For each image patch, we also presented a linear equivalent disc stimulus, which is a uniform disc with intensity equal to a weighted sum of the pixel intensities within the RF center. The weighting function was an estimate of each cell’s linear RF center from responses to expanding spots (see Materials and methods and Figure 2—figure supplement 1). A cell whose RF center behaves according to this linear RF model will respond equally to a natural image and its associated linear equivalent disc.

As shown previously, Off parasol cells responded much more strongly to natural images than to linear equivalent stimuli, especially when the natural image contains high spatial contrast (Figure 2A, left, Figure 2B see also [Turner and Rieke, 2016]). However, when a bright surround was presented with the center stimulus, the natural image and its linear equivalent disc produced near-equal responses (Figure 2A,B). Dark surrounds strongly suppressed both responses (Figure 2A, right). If responses to center and surround stimuli added linearly, the difference between responses to the natural image and linear equivalent disc should be maintained across surrounds and the points in Figure 2B should lie on a line offset from the diagonal. This was clearly not the case.

The RF surround regulates nonlinear spatial integration of natural images.

(A) We presented a natural image patch and its linear-equivalent disc stimulus to probe sensitivity to spatial contrast in natural scenes. Rows of each raster correspond to repeated presentations of the same stimulus for the example Off parasol RGC. (B) Spike count responses to an example image patch and its linear equivalent disc across a range of surround contrasts. The addition of a sufficiently bright surround (top three points) eliminates sensitivity to spatial contrast in this image patch. (C) Population summary showing the response difference between image and disc as a function of the difference in mean intensity between the RF center and surround. Negative values of this difference correspond to a surround that is brighter than the center, and positive values to a surround that is darker than the center (n = 21 image patch responses measured in five Off parasol RGCs).

Figure 2—source data 1

Included is a .mat file containing a data structure for the data in Figure 2.

Individual trial responses are included as binary vectors of spike times for natural image and associated linear equivalent disc stimuli, across a range of surround contrast conditions. Data are organized by cell and then by natural image. The natural image used in each set of responses is also included. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 ms and persist for 200 ms.

We used the difference in spike count between a natural image and its linear equivalent disc as a metric of spatial contrast sensitivity. This difference, as shown in Figure 2C, depended systematically on the difference in mean intensity in the center and surround regions. Specifically, spatial contrast sensitivity was maximal in response to stimuli for which center and surround intensities were similar and dropped as intensity in these regions diverged. Hence, nonlinear spatial integration is maximized when center and surround experience similar mean luminance. When the surround strongly hyperpolarizes presynaptic bipolar cells (for Off cells, a dark surround), the response is diminished as a result of the surround shifting the synapse into a quiescent state. When the surround depolarizes presynaptic bipolar cells (for Off cells, a bright surround), the nonlinear sensitivity of the center is reduced. Hence, as in the hypothesis of Figure 1, these experiments indicate that the activity of the RF surround, rather than only interacting with the fully formed RF center signal, can control spatial integration by the center.

Does the impact of the surround on spatial integration in the center depend on specific statistics of natural images or is it a more general phenomenon? To answer this question, we repeated these experiments using a flashed split-field grating rather than natural image patches (Figure 3). Because of the nonlinear subunit structure of the RF center, Off parasol cells respond strongly to such stimuli (Figure 3A). We presented the same grating together with a surround annulus and, in separate trials, the surround annulus alone (Figure 3A). When paired with a bright surround, the grating stimulus did not activate the cell much beyond its response to the surround alone. A dark surround suppressed responses with and without the grating, save for a small, brief response at the beginning of the presentation of the grating which is likely the result of the brief temporal delay of the surround relative to the center. A similar early response was present for natural images with dark surrounds (Figure 2A).

The RF surround regulates nonlinear spatial integration in the RF center.

(A) Left column: Example Off parasol RGC spike response to an isolated split-field grating stimulus in the RF center. Rows of each raster correspond to repeated presentations of the same stimulus for the example cell. There is no linear equivalent stimulus in this case since the grating has a mean of zero. Center column: when the center stimulus is paired with a bright surround, the grating and the surround alone produce very similar spike responses. Right column: a dark surround suppresses the response in both cases, and the grating is unable to elicit a strong response. (B) For the example cell in (A), we tested sensitivity to the center grating stimulus with a range of contrasts presented to the surround. Negative contrast surrounds (hyperpolarizing for Off bipolar cells) decrease the response. Positive contrast surrounds (depolarizing for Off bipolar cells) sum sub-linearly with the grating stimulus such that for the brightest surrounds, the addition of the grating only mildly enhances the cell’s response. Points show mean ( ± S.E.M.) spike count. (C) We measured the response difference between the grating stimulus and the surround-alone stimulus across a range of surround contrasts (horizontal axis) and for four different central grating contrasts (different lines). For each grating contrast, addition of either a bright or dark surround decreased sensitivity to the added grating. Points are population means ( ± S.E.M.) (n = 5 Off parasol RGCs). (D–F) same as (A–C) for excitatory synaptic current responses of an Off parasol RGC. Points represent mean ( ± S.E.M.) excitatory charge transfer for the example cell in (E) and population mean ( ± S.E.M.) (n = 7 Off parasol RGCs) in (F).

Figure 3—source data 1

Included is a .mat file containing a data structure for the data in Figure 3A–C.

Off parasol RGC spike responses are included as raw traces and binary vectors of spike times for a range of central grating contrasts and surround contrasts. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 ms and persist for 200 ms.

Figure 3—source data 2

Included is a .mat file containing a data structure for the data in Figure 3D–F.

Off parasol RGC excitatory current responses (in units of pA) have been baseline-subtracted. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 ms and persist for 200 ms.

Figure 3—source data 3

Included is a .mat file containing a data structure for the data in Figure 3—figure supplement 1.

On parasol RGC excitatory current responses (in units of pA) and have been baseline-subtracted. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 msec and persist for 200 ms.

We repeated this experiment for surround contrasts ranging from +0.9 to −0.9 (Figure 3B). While the surround-free grating (surround contrast = 0) stimulus showed strong nonlinear integration (indicated by its distance away from the unity line in Figure 3B), the presence of a surround stimulus diminished the response to the grating (indicated by the tendency of non-zero surround contrast points to lie closer to the line of unity). This was true for a range of central grating contrasts (Figure 3C), which indicates that this behavior is not the result of response saturation. Thus, just as for natural image patches, nonlinear spatial integration is maximal when the center and surround experience the same mean luminance (in this case a mean of zero) and decreases when the surround is brighter or dimmer than the center.

To test whether the effect of the surround on spatial integration was present in the bipolar synaptic output, we repeated these experiments while measuring a ganglion cell’s excitatory synaptic inputs (Figure 3D see Materials and methods for isolation of excitatory inputs). Modulation of spatial integration by surround activity was similar in excitatory inputs and spike responses (Figure 3E,F), which indicates that it is already present in the bipolar synaptic output and is not substantially shaped by post-synaptic integration or spike generation mechanisms. A similar effect can be seen in the excitatory inputs to On parasol RGCs (Figure 3—figure supplement 1). This shows that this effect of the surround is not unique to the Off parasol excitatory pathway, but may be a more general feature of center-surround RF organization in the retina. Compared to Off parasol RGCs, On parasol RGCs are more easily shifted into a regime of linear spatial integration, presumably because of the shallower rectification of nonlinear subunits in the receptive field of On parasol cells (Chichilnisky and Kalmar, 2002 Turner and Rieke, 2016).

The experiments described in Figures 2 and 3 show that inputs to the RF surround can influence how the RF center integrates signals across space, consistent with the hypothesis outlined in Figure 1. For both the spike output and excitatory synaptic input to an Off parasol RGC, the peak spatial nonlinearity was observed when center and surround experienced similar mean luminance (Figure 2C and Figure 3C,F).

Nonlinear center-surround interactions are dominated by a single, shared nonlinearity

The hypothesis in Figure 1 relies on a specific form of nonlinear center-surround interaction, whereby center and surround signals combine upstream of a shared, rectifying nonlinearity. To characterize center-surround interactions in a more complete and unbiased manner, we used Gaussian-distributed noise stimulation and a linear-nonlinear cascade modeling approach. We presented Gaussian-distributed random noise to the center region alone, surround region alone or both regions together while measuring excitatory synaptic inputs to On and Off parasol cells (Figure 4A). While thus far we have focused exclusively on Off parasol RGCs, the hypothesis in Figure 1 should also apply to excitatory input to On parasol RGCs, and hence we performed these experiments on both parasol types. For this analysis, we estimated the excitatory conductance by dividing the measured excitatory currents by the driving force. We computed linear filters for each RF region using reverse correlation based on trials in which the center or surround was stimulated in isolation (Figure 4A, left and middle columns).

Linear-nonlinear cascade modeling supports an architecture where center and surround combine linearly before passing through a shared nonlinearity.

(A) We presented Gaussian noise to either the center region (left), surround region (middle) or center and surround regions simultaneously (right) while measuring excitatory synaptic current responses. Measured excitatory currents (in pA) have been converted to excitatory conductance (in nS). Example traces are from a representative Off parasol RGC. (B) The independent model treats the filtered center and surround inputs with private nonlinear functions, and the outputs of these two nonlinearities are then summed to produce the excitatory conductance response. (C) The shared model integrates filtered center and surround inputs linearly, and this summed input is then passed through a single, shared nonlinearity. (D) The stacked model combines the independent and shared models by treating center and surround with private nonlinearities before summation and treatment with a third, shared nonlinearity. (E) We tested the ability of each of these models to predict held-out responses to center-surround stimulation. The shared model outperforms the independent model in both On and Off parasol RGCs (n = 7 On cells, p = 0.03 n = 8 Off cells, p = 0.008 ). (F) The fraction of explained variance was the same for the shared compared to the stacked model ( p > 0.90 for both On and Off cells). Dashed lines show estimates of the response reliability, which sets an upper bound for model performance (see Materials and methods for details).

Figure 4—source data 1

Included is a .mat file containing a data structure for the data in Figure 4 and 5.

Stimuli and corresponding responses of On and Off parasol RGCs to center-surround white noise stimulation have been concatenated into vector arrays. Note that the data were collected in interleaved trials. This data includes excitatory conductance responses (in nS) that were estimated using measured excitatory current responses and an estimate of the excitatory driving force for each cell. Data are sampled at 10 Khz.

We constructed three models of how center and surround inputs combine to determine the cell’s excitatory conductance response when both RF regions are stimulated (see Materials and methods for details). (1) In the ‘independent’ model (Figure 4B), inputs to the center and surround are filtered using their respective linear filters and then passed through separate nonlinear functions. The outputs of the two nonlinearities are then summed to give the response of the cell. (2) In the ‘shared’ model (Figure 4C), filtered center and surround inputs are summed linearly before passing through a single, shared nonlinear function. The output of this nonlinearity is the cell’s response. (3) The ‘stacked’ model (Figure 4D) combines models (1) and (2) by treating center and surround with private nonlinearities before summation and treatment with a third, shared nonlinearity. Representative predictions and measured responses are shown in Figure 4—figure supplement 1. The shared model is a special case of the stacked model, where the upstream independent functions are linear. Similarly, the independent model is a special case of the stacked model, where the output function after summation is linear.

We fit the nonlinear functions in each model using a subset of simultaneous center-surround trials and used the remaining simultaneous trials to test how well each model could predict the cell’s response. These models generally captured ∼ 60% of the total response variance, and ∼ 80% of the explainable variance (see Materials and methods). While the models appear to perform better for On compared to Off parasol RGCs (see Figure 4E,F), this difference is not statistically significant (p=0.19). The shared model outperformed the independent model (Figure 4E). The shared model performed as well as the more complicated stacked model (Figure 4F), despite the latter having many more free parameters (10 free parameters) than the shared model (five free parameters). In addition, the private nonlinearities fit in the stacked model tended to be quite shallow and much nearer to linear than the sharply rectified shared nonlinearity (Figure 4D). Hence the stacked model in practice effectively behaved like the shared model. The modeling result in Figure 4F supports the hypothesis that the dominant nonlinear interaction between center and surround is characterized by a shared nonlinearity, and that upstream of this nonlinearity center and surround interact approximately linearly.

The hypothesis in Figure 1 suggests that the effective rectification experienced by each subunit will depend on surround activation. The experiments used for the modeling above allowed us to directly examine whether this is the case. To do this, we estimated center and surround activation by convolving center and surround filters with the appropriate stimuli. We then plotted the measured excitatory conductance against these estimates of center and surround activation Figure 5A shows an example for the same Off parasol RGC as Figure 4A–D.

The RF surround changes the apparent rectification of inputs from the center.

(A) Response surface showing the mean excitatory conductance response from an Off parasol RGC as a function of filtered inputs to both the center and surround (center or surround ‘activation’, that is their generator signals). (B) Sections through this surface at various levels of surround activation reveal that the shape of the nonlinear dependence of excitatory conductance on center activation changes as the surround is modulated. (C) To quantify this change in center rectification, we used a rectification index (see Materials and methods), where values near 0 indicate a linear relationship between center activation and conductance response, and values near one indicate a sharply rectified relationship. Points are mean ( ± S.E.M.) (n = 7 On parasol cells and n = 8 Off parasol cells). Inset shows the expected relationship between rectification index and surround activation for a shared nonlinearity model (black curve) and an independent nonlinearity model (gray curve).

These joint response distributions show that the relationship between center activation and excitatory conductance depends on surround activation. When the surround is only weakly activated (near zero on ‘surround’ axis in Figure 5A), this nonlinear relationship is rectified (Figure 5B). Rectification persists when the surround hyperpolarizes presynaptic bipolar cells (negative on ‘surround’ axis in Figure 5A, blue trace in Figure 5A,B). But when the surround depolarizes bipolar cells (positive on ‘surround’ axis in Figure 5A), the relationship between center activation and excitatory conductance becomes more linear (i.e. less rectified Figure 5A,B, red trace). We quantified this change in center rectification with surround activation using a rectification index (RI, see Materials and methods for calculation of this metric). A RI value of zero indicates a linear relationship between center activation and conductance response, whereas RI values near one indicate strong rectification (i.e. there is a large increase in response with positive center activation, but very little or no decrease in response with negative center activation). For both On and Off cells, rectification decreased as surround activation increased (Figure 5C). In agreement with previous observations (Chichilnisky and Kalmar, 2002 Turner and Rieke, 2016), Off cells were more rectified than On cells. The inset to Figure 5C shows the relationship between surround activation and RI for independent and shared nonlinearity models. When center and surround nonlinearities are independent, the rectification of the center does not depend on the activity of the surround because the surround enters only after the center is fully formed (horizontal gray line in inset). The shared nonlinearity model, on the other hand, predicts a decrease in rectification as the surround becomes more depolarizing, in agreement with the behavior of parasol RGCs.

The experiments described provide additional quantitative support for the circuit architecture of Figure 1B in which center and surround signals add linearly prior to a shared nonlinearity.

RF center and surround interact nonlinearly during naturalistic visual stimulation

To test whether inputs to the RF center and surround interact nonlinearly under naturalistic stimulus conditions, we used a visual stimulus designed to approximate natural primate viewing conditions based on the Database Of Visual Eye movementS (DOVES, (Van Der Linde et al., 2009 van Hateren and van der Schaaf, 1998). An example image and a corresponding eye movement trajectory is shown in Figure 6A. We masked the stimulus to the RF center region, surround region or both. Figure 6B shows spike responses of an example Off parasol RGC to three movie stimuli: stimulation of the center region alone (Figure 6B, green), stimulation of the surround region alone (Figure 6B, purple), or simultaneous stimulation of both the center and surround regions (Figure 6B, black). Responses to isolated center or surround stimuli are shown in Figure 6C for average spike responses (Figure 6C, top) and excitatory synaptic inputs (Figure 6C, bottom).

Natural movie stimuli elicit nonlinear interactions between the RF center and surround.

(A) Natural image and associated eye movement trajectory from (Van Der Linde et al., 2009). Right: example movie frames showing isolated center (top), surround (middle), and center-surround stimuli (bottom). (B) Rasters show example Off parasol RGC spike responses to these three movie stimuli. Top shows eye movement position. (C) Spike output (top) and excitatory synaptic input (bottom) in response to isolated center and surround stimuli. (D) Spike and excitatory synaptic input responses to the center-surround stimulus. Gray trace shows the linear sum of isolated responses to center- and surround-region stimuli. (E) Spike count in response to the center-surround stimulus compared to the linear sum of isolated center and surround responses. Each point is a different natural movie. Center and surround sum sub-linearly (On parasol RGCs: n = 20 natural movies across 8 cells, p < 9 × 10 − 5 Off parasol RGCs: n = 18 natural movies across 7 cells, p < 2 × 10 − 4 ). (F) Same as (E) but for excitatory charge transfer responses (On parasol RGCs: p < 2 × 10 − 4 Off parasol RGCs: p < 3 × 10 − 4 ). (G) For the example in (A–D), the difference between measured and linearly-summed spike responses was correlated with differences in excitatory synaptic inputs (r = 0.91). (H) Population data for the analysis in (G).

To determine whether center and surround signals interact nonlinearly, we compared the linear sum of center and surround responses (Figure 6D, gray traces) to the measured response to simultaneous stimulation of both the center and surround regions (Figure 6D, black traces). For both spike and excitatory current responses, the measured center-surround response was smaller than the linear sum of the two responses measured independently. Thus, RF center and surround interact nonlinearly. This interaction, like that in Figure 4 and 5, is present in the excitatory synaptic input, and hence reflects properties of bipolar synaptic output rather than nonlinearities in synaptic integration or spike generation in the ganglion cell.

Sublinear interactions between center and surround inputs held across cells and fixations for both spike output (Figure 6E) and excitatory synaptic input (Figure 6F). For each cell, the difference between the linear sum of responses to center and surround inputs and the measured simultaneous response for spike outputs was correlated with the same difference for excitatory inputs (Figure 6G,H). This is consistent with the interpretation that the nonlinear interaction seen at the level of spike output is largely inherited from the excitatory synaptic inputs. Sublinear interactions in spike output and excitatory synaptic input were more strongly correlated for Off than On parasol RGCs (Figure 6H). This may be because inhibitory input impacts On parasol responses to natural stimuli more than Off parasol responses (Turner and Rieke, 2016). Taken together, these observations demonstrate that the nonlinear center-surround interactions characterized in Figures 2–5 are prominent for naturalistic visual inputs.

Natural spatial correlations promote nonlinear center-surround interactions

How do nonlinear center-surround interactions depend on stimulus statistics, especially those that characterize natural scenes? Naturalistic center and surround stimuli tended to elicit responses at different times (Figure 6). This is consistent with the spatial correlations in intensity that characterize natural images (Simoncelli and Olshausen, 2001) and the antagonistic nature of the surround—for example an Off parasol RGC would be depolarized by negative contrast in the RF center and hyperpolarized by negative contrast in the surround. We tested the effect of spatial correlations on nonlinear center-surround interactions using a synthetic visual stimulus inspired by our natural movie stimuli.

This stimulus consisted of a uniform disc in the center and a uniform annulus in the surround. The intensity of each region was sampled from a natural image (Figure 7A,B) and presented to either the center region alone, surround region alone, or both regions simultaneously. We updated the intensity of each region every 200 ms, which is consistent with typical human fixation periods (Van Der Linde et al., 2009). Center and surround intensities were determined from the mean intensity within the disc and annulus for randomly chosen image locations. The intensity correlations characteristic of natural scenes were evident when we plotted the center intensity against the corresponding surround intensity (Figure 7C, left, ‘Control’). Shuffling the surround intensities relative to those of the center eliminated spatial correlations, while maintaining the same marginal distributions (Figure 7C, right, ‘Shuffled’). When spatial correlations were intact, inputs to the center and surround combined sub-linearly in the excitatory synaptic input to the cell (Figure 7D), as they did in the full natural movie responses (Figure 6). When we shuffled the surround intensities relative to the center, nonlinear center-surround interactions were much weaker (Figure 7E,F). This was true for excitatory synaptic inputs to both On and Off parasol RGCs (Figure 7G).

Spatial correlations in natural scenes promote nonlinear center-surround interactions.

(A) Example image (van Hateren and van der Schaaf, 1998) used to construct natural intensity stimuli. (B) Intensity histogram from the image in (A). Dashed vertical line indicates the mean intensity, which was used as the mean gray level in experiments that follow. (C) Center and surround intensity values for 40 image patches from the image in (A). (D) Example stimuli (top) and Off parasol RGC excitatory current responses to isolated center and surround (middle) and center-surround (bottom) stimulation. Gray trace in bottom shows linear sum of isolated center and surround responses. (E) Same as (D) for shuffled surround intensities. (F) The response magnitude (charge transfer) of each fixation is plotted for measured center-surround and linearly summed center and surround responses. Circles show mean responses for each fixation, squares show mean ( ± S.E.M.) across all fixations in this example cell. (G) Population data showing the mean difference between responses to the center-surround stimulus and the linearly summed response. Circles show average differences for each cell tested, and squares show population mean ( ± S.E.M) (n = 7 On parasol RGCs, p < 0.02 n = 8 Off parasol RGCs, p < 8 × 10 − 3 ). (H) White noise center-surround stimuli had variable center-surround correlations but constant marginal distributions. Shown are example excitatory current responses in an Off parasol RGC. Black traces show the measured center-surround stimulus response and gray traces show the linear sum of center and surround responses. (I) Population data from the experiments in (H) showing that nonlinear center-surround interactions depend on the correlation between center and surround inputs (n = 8 On parasol RGCs n = 8 Off parasol RGCs).

Figure 7—source data 1

Included is a .mat file containing a data structure for the data in Figure 7A–G.

The structure contains excitatory current responses (baseline subtracted, in pA) of On and Off parasol RGCs to center-surround naturalistic luminance stimuli. Data are sampled at 10 Khz.

To further probe the impact of intensity correlations on center-surround interactions, we generated Gaussian random noise stimuli that updated with a 200-ms period. For this stimulus, a single random intensity fills the entire center disc and a different, random intensity fills the entire surround annulus. This noise stimulus had a tunable degree of correlation between center and surround intensity, ranging from −1 (perfectly anti-correlated) to 0 (uncorrelated) to +1 (perfectly correlated, that is modulated in unison). When noise stimuli in the center and surround were negatively correlated, inputs to the center and surround summed linearly or very nearly so (Figure 7H, left). As the center-surround intensity correlations increased, sublinear interactions became more obvious (Figure 7H, middle and right). Strongly positively correlated noise stimuli induced center-surround interactions that resembled those seen using naturally correlated luminance stimuli (Figure 7H, right). This dependence of nonlinear center-surround interactions on center-surround intensity correlations was present in both On and Off parasol RGCs (Figure 7I).

These results indicate that nonlinear center-surround interactions depend strongly on center-surround intensity correlations, and hence that the importance of these interactions could be underestimated from stimuli such as spatial noise that lack intensity correlations.

A luminance-matched surround promotes spatial contrast sensitivity in the center

The experiments described above show that surround signals, rather than only interacting with the fully formed center signal, can alter how the center integrates over space. Two aspects of these results deserve emphasis: (1) nonlinear spatial integration is maximized when center and surround experience similar mean luminances (Figures 2 and 3) and (2) natural stimuli elicit strong nonlinear center-surround interactions due to positive correlations between center and surround intensities (Figures 6 and 7). These observations lead to the hypothesis, tested below, that surround activation can make spatial integration in the RF center relatively insensitive to changes in mean luminance.

Natural visual stimuli, such as the change in input encountered after a saccade, typically include changes in mean luminance and spatial contrast. Such stimuli will activate both linear and nonlinear response components, and these may not interact in a straightforward manner. To make this more concrete, consider a population of Off bipolar cells acting as subunits in the center of the RGC RF. At rest, the synapse of each bipolar cell is in a sharply rectified state. A decrease in mean luminance over the RF center will depolarize the synapse associated with each RF subunit, shifting each into a locally linear state (Figure 8A, top), and decreasing spatial contrast sensitivity. When such a stimulus is paired with a luminance-matched surround stimulus, the antagonistic surround may at least partially cancel this depolarization this could keep each subunit in a locally rectified state (Figure 8A, bottom, blue arrow) and preserve spatial contrast sensitivity.

Intensity correlations across space promote nonlinear spatial integration in the RF center.

(A) Schematic showing the hypothesized interaction between center and surround inputs on local subunit rectification. A depolarizing input to the center may push the synapse into a locally linear state. A simultaneous surround input that is matched in luminance (blue arrow) can hyperpolarize the synaptic terminal and bring the synapse back into a rectified state, whereas a poorly matched surround will not (orange arrow). (B) During Off parasol spike recordings, we presented split-field grating stimuli to the RF center under three surround conditions. For each stimulus condition, rows of the raster correspond to repeated presentations of the same stimulus for the example cell. (C) Summary data showing the population mean ± S.E.M. NLI (see text) as a function of the mean intensity (relative to the background) of the center grating (n = 8 Off parasol RGCs). (D–F) We presented natural image patches and their linear equivalent disc stimuli to measure the NLI under three surround conditions: no surround, a matched surround image, and a shuffled surround image. (G) Schematic of a nonlinear subunit RF model. Each subunit has a difference-of-Gaussians spatial receptive field. The output of each subunit is passed through a private, rectifying output nonlinearity. Subunit outputs are then summed over visual space to yield the modeled RGC response. (H,I) We changed the strength of the subunit surround to model RGCs with three different surround strengths: a weak surround (light gray trace), an intermediate-strength surround (gray trace), and a strong surround (black trace). We presented this RF model with the natural image/disc stimuli shown in (E) and, following that analysis, measured the NLI as a function of the mean intensity of the image in the RF center.

We tested this prediction in Off parasol RGCs, using modified grating stimuli with nonzero mean luminance. For each grating stimulus, we also presented a corresponding linear equivalent disc stimulus, which has the same mean luminance as the grating, but lacks any spatial contrast. The degree to which a cell’s response to these two stimuli differs is a measure of the sensitivity of the cell to spatial contrast, or, equivalently, the strength of nonlinear spatial integration.

We presented these stimuli to Off parasol RGCs while measuring spike responses. A grating with a dark mean luminance signal produced a similar response as a linear equivalent stimulus (Figure 8B, left), indicating that the cell is insensitive to the spatial contrast present in the grating. Compare this to these cells’ highly nonlinear responses to zero-mean grating stimuli (e.g. Figure 3). When a dark mean grating is paired with a luminance-matched surround, however, the grating again produces a much stronger response than its linear equivalent stimulus (Figure 8B, middle), which is consistent with the restoration of spatial contrast sensitivity via the mechanism in Figure 8A. Pairing the grating stimulus with poorly matched surrounds does not restore spatial contrast sensitivity (Figure 8B, right), indicating that this is not a general consequence of surround activation.

To quantify the spatial contrast sensitivity in these experiments, we used a nonlinearity index (NLI, See Equation 1 and [Turner and Rieke, 2016]):

This measure normalizes responses within each surround condition. A positive NLI indicates that the cell responds more strongly to a grating stimulus than to its linear equivalent disc stimulus, and is thus sensitive to spatial contrast. A NLI near zero indicates that the cell’s response is mostly determined by the mean luminance component of the stimulus, and not the spatial contrast. The NLI was maximal for all surround conditions for zero-mean gratings. As the center intensity decreased (moving towards the left in Figure 8C), the NLI decreased along with it, but this drop was less pronounced under the matched surround condition. Hence matched surround activation decreased the sensitivity of nonlinear spatial integration to changes in mean luminance.

Intensity correlations in natural images promote nonlinear spatial integration

The results presented thus far show that systematically varying the input to the surround relative to the center can alter sensitivity to spatial contrast in both artificial and natural stimuli (Figures 2, 3 and 8A–C). However, it is not clear from these experiments how much this effect is present during the course of more naturalistic activation of the RF surround. The intensity correlations present in natural images (e.g. Figure 7C) should ensure that the mean intensity difference between the RF center and surround is often near zero. Because spatial contrast sensitivity was maximized by small differences between mean center and surround intensity (Figure 2), we hypothesized that full natural image stimulation of the RF surround would increase spatial contrast sensitivity in the RF center compared to stimulation of the RF center alone.

To test this hypothesis, we presented natural image patches (and their corresponding linear equivalent disc stimuli) to the RF center while pairing each with three distinct surround conditions: no surround stimulation (Figure 8E) the naturally occurring surround present in the rest of the natural image patch (‘Matched surround’), and, a randomly selected surround from the same full natural scene (‘Shuffled surround’). We recorded Off parasol spike responses to these six stimuli for each of 20–40 randomly selected image patches from a single natural scene. For each image patch, we computed the NLI (Equation 1) for responses measured in each of the three surround conditions. We compared the NLIs to the mean intensity of the image in the RF center (I) relative to the background intensity (B), that is Relative center intensity = ( I − B ) / B . As in the modified gratings experiments (Figure 8C), a darker mean luminance signal was associated with a decrease in spatial contrast sensitivity (Figure 8F, black curve). This drop-off in spatial contrast sensitivity was less pronounced with the naturally occurring surround, (Figure 8F, blue curve). Specifically, sensitivity to fine spatial structure was two to three times greater in the presence of a matched surround than without a surround. Randomly selected surrounds did not enhance spatial contrast sensitivity in this way but instead altered the NLI in a manner predicted by the experiments in Figure 2 (see Figure 8—figure supplement 1).

These observations are consistent with the idea that natural images provide inputs to the surround that can preserve the spatial contrast sensitivity of the RF center compared to center inputs alone. Key to this relative invariance of contrast sensitivity is the ability of the surround to control the degree of rectification of the bipolar subunits that comprise the RF center and the strong positive correlations between center and surround inputs created by natural images.

The appropriate surround activation can preserve spatial contrast sensitivity in the context of both natural image and grating stimuli. Note, however, that the NLI is, on average, lower for randomly selected images than for grating stimuli (compare Figure 8F and C). This is expected because the spatial structure of grating stimuli is designed to highlight nonlinear spatial integration by differentially activating subunits in the RF center (i.e. depolarizing some while hyperpolarizing others). Randomly-selected image patches, however, often do not contain much spatial structure that will differentially activate subunits in the RF center.

To explore the relationship between naturalistic surround activation and spatial contrast sensitivity in a manner not possible in our experiments, we constructed a simple spatial RF model composed of nonlinear, center-surround subunits (Figure 8G see (Enroth-Cugell and Freeman, 1987) and Materials and methods). Following the analysis used for the data in Figure 8F, we computed the mean NLI for the model as a function of the relative center intensity for a surround-free stimulus (Figure 8I, ‘no surround’) and for the naturally occurring surround stimulus (Figure 8I, ‘moderate surround’). As in the Off parasol spike data, the inclusion of the naturally occurring surround extended spatial contrast sensitivity in the face of stronger local luminance signals. We repeated the same analysis for versions of the RF model with both a weaker and a stronger surround. A stronger RF surround is associated with greater spatial contrast sensitivity, especially for images that contain a strong local luminance signal. Similar results were seen for a spatiotemporal RF model that includes temporal filters measured in the experiments shown in Figure 4 (Figure 8—figure supplement 2).


What is the location of the center-surround receptive fields of retinal ganglion cells? - Psychology

A very standard way to start any discussion of a new and difficult term is to give the definition. Levine and Shefner (1991) define a receptive field as an "area in which stimulation leads to response of a particular sensory neuron" (p. 671). This definition uses very standard terms but taken out of context as definitions usually are, it does not seem very helpful. So, to give the term receptive field some context it is important to know that this rather odd term was developed as a way of understanding some experimental finding.

  1. A stimulus - it can be in any sensory system. For these examples, let us use the visual system so the stimulus will be a form of light probably projected on a screen.
  2. An animal. The animal is anesthetized but altert. It is important that the animal does not move during the experiment so that stimuli can be located precisely relative to the animal.
  3. A microelectrode that penetrates the cell body of a single-cell. If this cell is in the visual system it could be located in the retina or lateral geniculate nucleus or even the visual cortex.
  4. A means of recording the acivity of the cell. Action potential show of as spikes on the record.

This is an oversimplication of the technical challenges that must be faced in making an adequate recrode of the activity from a single-cell but these elements are sufficient for understanding what a receptive field is.

The Determination of a Receptive Field

Below is an animation that will illustrate an early experiment in the determination of a receptive field.

This animation illustrates the initial step of a typical experiment mapping the receptive field of a single cell in the visual system. This cell could be at any of many different locations in the brain that process visual information. For the purposes of this illustration let us say that the cell is a retinal ganglion cell which were first mapped by Kuffler (1953). Basically, the light is shined of various locations of the screen and the activity of the cell is recorded in response to that stimulus location.

Continuing this procedure, will develop of map of all the regions of the sensory surface that causes a change in the firing rate of the cell. What was obvious from these first studies was that there was not a one-to-one correspondence between the region stimulated and the cell that fired. A relatively large area of the sensory surface could affect that firing rate of any one cell. In addition, stimulation of any one region would affect the firing rate of several cells. This animation follows procedures similar to those actually used by Kuffler (1953) to determine the receptive fields of retinal ganglion cells. What is not indicated in this animation is the microelectrode actually penetrating a retinal ganglion cell.

Where is the Receptive Field?

After studying Figure 1, either click on the area of the diagram where you think you think will find the receptive field.


What is the location of the center-surround receptive fields of retinal ganglion cells? - Psychology

Along with the concept of a receptive field comes the idea of what the receptive field is "seeing". By this I mean, what information is being processed by receiving information from a relatively large region of the sensory surface (retina, skin, etc) and what information is sent on the cells that receive input from that cell. One way to understand the function of a receptive field is to try to figure out what the "best stimulus" is, i.e., that stimulus that leads to the greatest stimulation of the cell.

For example, in the present cell let us suppose that the firing rate is four times a second (thus, the above line shows one second of recording).

A very simple way to think about receptive fields is that light that falls in excitatory regions, those regions that increase the cells firing rate, are positive and add to the total stimulation.
Light that falls in the inhibitory regions, those regions that decrease the cell&aposs firing rate, are negative and subtract from the total stimulation.

Figure 2. Firing of a cell in the absence of sensory stimulation.

Question 1: Which of the following stimuli will lead to the greatest firing rate (Click on that stimulus):

For the following questions we will use a center-surround receptive field such as one found in the retinal ganglion cells. The center is excitatory and the surround inhibitory. A white colored area represents the stimulus and the grey colored area (or the background color) represents the absence of a stimulus.

Figure 3. Examples of four different stimuli on a receptive field. Which is the best stimulus for this receptive field.


Contents

There are about 0.7 to 1.5 million retinal ganglion cells in the human retina. [2] With about 4.6 million cone cells and 92 million rod cells, or 96.6 million photoreceptors per retina, [3] on average each retinal ganglion cell receives inputs from about 100 rods and cones. However, these numbers vary greatly among individuals and as a function of retinal location. In the fovea (center of the retina), a single ganglion cell will communicate with as few as five photoreceptors. In the extreme periphery (edge of the retina), a single ganglion cell will receive information from many thousands of photoreceptors. [ citation needed ]

Retinal ganglion cells spontaneously fire action potentials at a base rate while at rest. Excitation of retinal ganglion cells results in an increased firing rate while inhibition results in a depressed rate of firing.

There is wide variability in ganglion cell types across species. In primates, including humans, there are generally three classes of RGCs:

  • W-ganglion: small, 40% of total, broad fields in retina, excitation from rods. Detection of direction movement anywhere in the field.
  • X-ganglion: medium diameter, 55% of total, small field, color vision. Sustained response.
  • Y- ganglion: largest, 5%, very broad dendritic field, respond to rapid eye movement or rapid change in light intensity. Transient response.

Based on their projections and functions, there are at least five main classes of retinal ganglion cells:

    (parvocellular, or P pathway P cells) (magnocellular, or M pathway M cells) (koniocellular, or K pathway)
  • Other ganglion cells projecting to the superior colliculus for eye movements (saccades) [4]

P-type Edit

P-type retinal ganglion cells project to the parvocellular layers of the lateral geniculate nucleus. These cells are known as midget retinal ganglion cells, based on the small sizes of their dendritic trees and cell bodies. About 80% of all retinal ganglion cells are midget cells in the parvocellular pathway. They receive inputs from relatively few rods and cones. They have slow conduction velocity, and respond to changes in color but respond only weakly to changes in contrast unless the change is great. They have simple center-surround receptive fields, where the center may be either ON or OFF while the surround is the opposite.

M-type Edit

M-type retinal ganglion cells project to the magnocellular layers of the lateral geniculate nucleus. These cells are known as parasol retinal ganglion cells, based on the large sizes of their dendritic trees and cell bodies. About 10% of all retinal ganglion cells are parasol cells, and these cells are part of the magnocellular pathway. They receive inputs from relatively many rods and cones. They have fast conduction velocity, and can respond to low-contrast stimuli, but are not very sensitive to changes in color. They have much larger receptive fields which are nonetheless also center-surround.

K-type Edit

BiK-type retinal ganglion cells project to the koniocellular layers of the lateral geniculate nucleus. K-type retinal ganglion cells have been identified only relatively recently. Koniocellular means "cells as small as dust" their small size made them hard to find. About 10% of all retinal ganglion cells are bistratified cells, and these cells go through the koniocellular pathway. They receive inputs from intermediate numbers of rods and cones. They may be involved in color vision. They have very large receptive fields that only have centers (no surrounds) and are always ON to the blue cone and OFF to both the red and green cone.

Photosensitive ganglion cell Edit

Photosensitive ganglion cells, including but not limited to the giant retinal ganglion cells, contain their own photopigment, melanopsin, which makes them respond directly to light even in the absence of rods and cones. They project to, among other areas, the suprachiasmatic nucleus (SCN) via the retinohypothalamic tract for setting and maintaining circadian rhythms. Other retinal ganglion cells projecting to the lateral geniculate nucleus (LGN) include cells making connections with the Edinger-Westphal nucleus (EW), for control of the pupillary light reflex, and giant retinal ganglion cells.

Most mature ganglion cells are able to fire action potentials at a high frequency because of their expression of Kv3 potassium channels. [5] [6] [7]

Degeneration of axons of the retinal ganglion cells (the optic nerve) is a hallmark of glaucoma. [8]

Retinal growth: the beginning Edit

Retinal ganglion cells (RGCs) are born between embryonic day 11 and post-natal day zero in the mouse and between week 5 and week 18 in utero in human development. [9] [10] [11] In mammals, RGCs are typically added at the beginning in the dorsal central aspect of the optic cup, or eye primordium. Then RC growth sweeps out ventrally and peripherally from there in a wave-like pattern. [12] This process depends on a host of factors, ranging from signaling factors like FGF3 and FGF8 to proper inhibition of the Notch signaling pathway. Most importantly, the bHLH (basic helix-loop-helix)-domain containing transcription factor Atoh7 and its downstream effectors, such as Brn3b and Isl-1, work to promote RGC survival and differentiation. [9] The "differentiation wave" that drives RGC development across the retina is also regulated in particular of the bHLH factors Neurog2 and Ascl1 and FGF/Shh signaling, deriving from the periphery. [9] [12] [13]

Growth within the retinal ganglion cell (optic fiber) layer Edit

Early progenitor RGCs will typically extend processes connecting to the inner and outer limiting membranes of the retina with the outer layer adjacent to the retinal pigment epithelium and inner adjacent to the future vitreous humor. The cell soma will pull towards the pigment epithelium, undergo a terminal cell division and differentiation, and then migrate backwards towards the inner limiting membrane in a process called somal translocation. The kinetics of RGC somal translocation and underlying mechanisms are best understood in the zebrafish. [14] The RGC will then extend an axon in the retinal ganglion cell layer, which is directed by laminin contact. [15] The retraction of the apical process of the RGC is likely mediated by Slit–Robo signaling. [9]

RGCs will grow along glial end feet positioned on the inner surface (side closest to the future vitreous humor). Neural cell adhesion molecule (N-CAM) will mediate this attachment via homophilic interactions between molecules of like isoforms (A or B). Slit signaling also plays a role, preventing RGCs from growing into layers beyond the optic fiber layer. [16]

Axons from the RGCs will grow and extend towards the optic disc, where they exit the eye. Once differentiated, they are bordered by an inhibitory peripheral region and a central attractive region, thus promoting extension of the axon towards the optic disc. CSPGs exist along the retinal neuroepithelium (surface over which the RGCs lie) in a peripheral high–central low gradient. [9] Slit is also expressed in a similar pattern, secreted from the cells in the lens. [16] Adhesion molecules, like N-CAM and L1, will promote growth centrally and will also help to properly fasciculate (bundle) the RGC axons together. Shh is expressed in a high central, low peripheral gradient, promoting central-projecting RGC axons extension via Patched-1, the principal receptor for Shh, mediated signaling. [17]

Growth into and through the optic nerve Edit

RGCs exit the retinal ganglion cell layer through the optic disc, which requires a 45° turn. [9] This requires complex interactions with optic disc glial cells which will express local gradients of Netrin-1, a morphogen that will interact with the Deleted in Colorectal Cancer (DCC) receptor on growth cones of the RGC axon. This morphogen initially attracts RGC axons, but then, through an internal change in the growth cone of the RGC, netrin-1 becomes repulsive, pushing the axon away from the optic disc. [18] This is mediated through a cAMP-dependent mechanism. Additionally, CSPGs and Eph–ephrin signaling may also be involved.

RGCs will grow along glial cell end feet in the optic nerve. These glia will secrete repulsive semaphorin 5a and Slit in a surround fashion, covering the optic nerve which ensures that they remain in the optic nerve. Vax1, a transcription factor, is expressed by the ventral diencephalon and glial cells in the region where the chiasm is formed, and it may also be secreted to control chiasm formation. [19]

Growth at the optic chiasm Edit

When RGCs approach the optic chiasm, the point at which the two optic nerves meet, at the ventral diencephalon around embryonic days 10–11 in the mouse, they have to make the decision to cross to the contralateral optic tract or remain in the ipsilateral optic tract. In the mouse, about 5% of RGCs, mostly those coming from the ventral-temporal crescent (VTc) region of the retina, will remain ipsilateral, while the remaining 95% of RGCs will cross. [9] This is largely controlled by the degree of binocular overlap between the two fields of sight in both eyes. Mice do not have a significant overlap, whereas, humans, who do, will have about 50% of RGCs cross and 50% will remain ipsilateral.

Building the repulsive outline of the chiasm Edit

Once RGCs reach the chiasm, the glial cells supporting them will change from an intrafascicular to radial morphology. A group of diencephalic cells that express the cell surface antigen stage-specific embryonic antigen (SSEA)-1 and CD44 will form an inverted V-shape. [20] They will establish the posterior aspect of the optic chiasm border. Additionally, Slit signaling is important here: Heparin sulfate proteoglycans, proteins in the ECM, will anchor the Slit morphogen at specific points in the posterior chiasm border. [21] RGCs will begin to express Robo, the receptor for Slit, at this point, thus facilitating the repulsion.

Contralateral projecting RGCs Edit

RGC axons traveling to the contralateral optic tract need to cross. Shh, expressed along the midline in the ventral diencephalon, provides a repulsive cue to prevent RGCs from crossing the midline ectopically. However, a hole is generated in this gradient, thus allowing RGCs to cross.

Molecules mediating attraction include NrCAM, which is expressed by growing RGCs and the midline glia and acts along with Sema6D, mediated via the plexin-A1 receptor. [9] VEGF-A is released from the midline directs RGCs to take a contralateral path, mediated by the neuropilin-1 (NRP1) receptor. [22] cAMP seems to be very important in regulating the production of NRP1 protein, thus regulating the growth cones response to the VEGF-A gradient in the chiasm. [23]

Ipsilateral projecting RGCs Edit

The only component in mice projecting ipsilaterally are RGCs from the ventral-temporal crescent in the retina, and only because they express the Zic2 transcription factor. Zic2 will promote the expression of the tyrosine kinase receptor EphB1, which, through forward signaling (see review by Xu et al. [24] ) will bind to ligand ephrin B2 expressed by midline glia and be repelled to turn away from the chiasm. Some VTc RGCs will project contralaterally because they express the transcription factor Islet-2, which is a negative regulator of Zic2 production. [25]

Shh plays a key role in keeping RGC axons ipsilateral as well. Shh is expressed by the contralaterally projecting RGCs and midline glial cells. Boc, or Brother of CDO (CAM-related/downregulated by oncogenes), a co-receptor for Shh that influences Shh signaling through Ptch1, [26] seems to mediate this repulsion, as it is only on growth cones coming from the ipsilaterally projecting RGCs. [17]

Other factors influencing ipsilateral RGC growth include the Teneurin family, which are transmembrane adhesion proteins that use homophilic interactions to control guidance, and Nogo, which is expressed by midline radial glia. [27] [28] The Nogo receptor is only expressed by VTc RGCs. [9]

Finally, other transcription factors seem to play a significant role in altering. For example, Foxg1, also called Brain-Factor 1, and Foxd1, also called Brain Factor 2, are winged-helix transcription factors that are expressed in the nasal and temporal optic cups and the optic vesicles begin to evaginate from the neural tube. These factors are also expressed in the ventral diencephalon, with Foxd1 expressed near the chiasm, while Foxg1 is expressed more rostrally. They appear to play a role in defining the ipsilateral projection by altering expression of Zic2 and EphB1 receptor production. [9] [29]

Growth in the optic tract Edit

Once out of the optic chiasm, RGCs will extend dorsocaudally along the ventral diencephalic surface making the optic tract, which will guide them to the superior colliculus and lateral geniculate nucleus in the mammals, or the tectum in lower vertebrates. [9] Sema3d seems to be promote growth, at least in the proximal optic tract, and cytoskeletal re-arrangements at the level of the growth cone appear to be significant. [30]

In most mammals, the axons of retinal ganglion cells are not myelinated where they pass through the retina. However, the parts of axons that are beyond the retina, are myelinated. This myelination pattern is functionally explained by the relatively high opacity of myelin—myelinated axons passing over the retina would absorb some of the light before it reaches the photoreceptor layer, reducing the quality of vision. There are human eye diseases where this does, in fact, happen. In some vertebrates, such as the chicken, the ganglion cell axons are myelinated inside the retina. [31]


Receptor Density

In addition to having different visual functions, the rods and cones are also distributed across the retina in different densities. The cones are primarily found in the fovea, the region of the retina with the highest visual acuity. The remainder of the retina is predominantly rods. The region of the optic disc has no photoreceptors because the axons of the ganglion cells are leaving the retina and forming the optic nerve.

Figure 19.5. Rods and cones are distributed across the retina in different densities. Cones are located at the fovea. Rods are located everywhere else. The optic disc lacks all photoreceptors since the optic nerve fibers are exiting the eye at this location. ‘Retinal Receptor Density’ by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License.


What is the location of the center-surround receptive fields of retinal ganglion cells? - Psychology

A very standard way to start any discussion of a new and difficult term is to give the definition. Levine and Shefner (1991) define a receptive field as an "area in which stimulation leads to response of a particular sensory neuron" (p. 671). This definition uses very standard terms but taken out of context as definitions usually are, it does not seem very helpful. So, to give the term receptive field some context it is important to know that this rather odd term was developed as a way of understanding some experimental finding.

  1. A stimulus - it can be in any sensory system. For these examples, let us use the visual system so the stimulus will be a form of light probably projected on a screen.
  2. An animal. The animal is anesthetized but altert. It is important that the animal does not move during the experiment so that stimuli can be located precisely relative to the animal.
  3. A microelectrode that penetrates the cell body of a single-cell. If this cell is in the visual system it could be located in the retina or lateral geniculate nucleus or even the visual cortex.
  4. A means of recording the acivity of the cell. Action potential show of as spikes on the record.

This is an oversimplication of the technical challenges that must be faced in making an adequate recrode of the activity from a single-cell but these elements are sufficient for understanding what a receptive field is.

The Determination of a Receptive Field

Below is an animation that will illustrate an early experiment in the determination of a receptive field.

This animation illustrates the initial step of a typical experiment mapping the receptive field of a single cell in the visual system. This cell could be at any of many different locations in the brain that process visual information. For the purposes of this illustration let us say that the cell is a retinal ganglion cell which were first mapped by Kuffler (1953). Basically, the light is shined of various locations of the screen and the activity of the cell is recorded in response to that stimulus location.

Continuing this procedure, will develop of map of all the regions of the sensory surface that causes a change in the firing rate of the cell. What was obvious from these first studies was that there was not a one-to-one correspondence between the region stimulated and the cell that fired. A relatively large area of the sensory surface could affect that firing rate of any one cell. In addition, stimulation of any one region would affect the firing rate of several cells. This animation follows procedures similar to those actually used by Kuffler (1953) to determine the receptive fields of retinal ganglion cells. What is not indicated in this animation is the microelectrode actually penetrating a retinal ganglion cell.

Where is the Receptive Field?

After studying Figure 1, either click on the area of the diagram where you think you think will find the receptive field.


What is the location of the center-surround receptive fields of retinal ganglion cells? - Psychology

Along with the concept of a receptive field comes the idea of what the receptive field is "seeing". By this I mean, what information is being processed by receiving information from a relatively large region of the sensory surface (retina, skin, etc) and what information is sent on the cells that receive input from that cell. One way to understand the function of a receptive field is to try to figure out what the "best stimulus" is, i.e., that stimulus that leads to the greatest stimulation of the cell.

For example, in the present cell let us suppose that the firing rate is four times a second (thus, the above line shows one second of recording).

A very simple way to think about receptive fields is that light that falls in excitatory regions, those regions that increase the cells firing rate, are positive and add to the total stimulation.
Light that falls in the inhibitory regions, those regions that decrease the cell&aposs firing rate, are negative and subtract from the total stimulation.

Figure 2. Firing of a cell in the absence of sensory stimulation.

Question 1: Which of the following stimuli will lead to the greatest firing rate (Click on that stimulus):

For the following questions we will use a center-surround receptive field such as one found in the retinal ganglion cells. The center is excitatory and the surround inhibitory. A white colored area represents the stimulus and the grey colored area (or the background color) represents the absence of a stimulus.

Figure 3. Examples of four different stimuli on a receptive field. Which is the best stimulus for this receptive field.


Receptor Density

In addition to having different visual functions, the rods and cones are also distributed across the retina in different densities. The cones are primarily found in the fovea, the region of the retina with the highest visual acuity. The remainder of the retina is predominantly rods. The region of the optic disc has no photoreceptors because the axons of the ganglion cells are leaving the retina and forming the optic nerve.

Figure 19.5. Rods and cones are distributed across the retina in different densities. Cones are located at the fovea. Rods are located everywhere else. The optic disc lacks all photoreceptors since the optic nerve fibers are exiting the eye at this location. ‘Retinal Receptor Density’ by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License.


Contents

There are about 0.7 to 1.5 million retinal ganglion cells in the human retina. [2] With about 4.6 million cone cells and 92 million rod cells, or 96.6 million photoreceptors per retina, [3] on average each retinal ganglion cell receives inputs from about 100 rods and cones. However, these numbers vary greatly among individuals and as a function of retinal location. In the fovea (center of the retina), a single ganglion cell will communicate with as few as five photoreceptors. In the extreme periphery (edge of the retina), a single ganglion cell will receive information from many thousands of photoreceptors. [ citation needed ]

Retinal ganglion cells spontaneously fire action potentials at a base rate while at rest. Excitation of retinal ganglion cells results in an increased firing rate while inhibition results in a depressed rate of firing.

There is wide variability in ganglion cell types across species. In primates, including humans, there are generally three classes of RGCs:

  • W-ganglion: small, 40% of total, broad fields in retina, excitation from rods. Detection of direction movement anywhere in the field.
  • X-ganglion: medium diameter, 55% of total, small field, color vision. Sustained response.
  • Y- ganglion: largest, 5%, very broad dendritic field, respond to rapid eye movement or rapid change in light intensity. Transient response.

Based on their projections and functions, there are at least five main classes of retinal ganglion cells:

    (parvocellular, or P pathway P cells) (magnocellular, or M pathway M cells) (koniocellular, or K pathway)
  • Other ganglion cells projecting to the superior colliculus for eye movements (saccades) [4]

P-type Edit

P-type retinal ganglion cells project to the parvocellular layers of the lateral geniculate nucleus. These cells are known as midget retinal ganglion cells, based on the small sizes of their dendritic trees and cell bodies. About 80% of all retinal ganglion cells are midget cells in the parvocellular pathway. They receive inputs from relatively few rods and cones. They have slow conduction velocity, and respond to changes in color but respond only weakly to changes in contrast unless the change is great. They have simple center-surround receptive fields, where the center may be either ON or OFF while the surround is the opposite.

M-type Edit

M-type retinal ganglion cells project to the magnocellular layers of the lateral geniculate nucleus. These cells are known as parasol retinal ganglion cells, based on the large sizes of their dendritic trees and cell bodies. About 10% of all retinal ganglion cells are parasol cells, and these cells are part of the magnocellular pathway. They receive inputs from relatively many rods and cones. They have fast conduction velocity, and can respond to low-contrast stimuli, but are not very sensitive to changes in color. They have much larger receptive fields which are nonetheless also center-surround.

K-type Edit

BiK-type retinal ganglion cells project to the koniocellular layers of the lateral geniculate nucleus. K-type retinal ganglion cells have been identified only relatively recently. Koniocellular means "cells as small as dust" their small size made them hard to find. About 10% of all retinal ganglion cells are bistratified cells, and these cells go through the koniocellular pathway. They receive inputs from intermediate numbers of rods and cones. They may be involved in color vision. They have very large receptive fields that only have centers (no surrounds) and are always ON to the blue cone and OFF to both the red and green cone.

Photosensitive ganglion cell Edit

Photosensitive ganglion cells, including but not limited to the giant retinal ganglion cells, contain their own photopigment, melanopsin, which makes them respond directly to light even in the absence of rods and cones. They project to, among other areas, the suprachiasmatic nucleus (SCN) via the retinohypothalamic tract for setting and maintaining circadian rhythms. Other retinal ganglion cells projecting to the lateral geniculate nucleus (LGN) include cells making connections with the Edinger-Westphal nucleus (EW), for control of the pupillary light reflex, and giant retinal ganglion cells.

Most mature ganglion cells are able to fire action potentials at a high frequency because of their expression of Kv3 potassium channels. [5] [6] [7]

Degeneration of axons of the retinal ganglion cells (the optic nerve) is a hallmark of glaucoma. [8]

Retinal growth: the beginning Edit

Retinal ganglion cells (RGCs) are born between embryonic day 11 and post-natal day zero in the mouse and between week 5 and week 18 in utero in human development. [9] [10] [11] In mammals, RGCs are typically added at the beginning in the dorsal central aspect of the optic cup, or eye primordium. Then RC growth sweeps out ventrally and peripherally from there in a wave-like pattern. [12] This process depends on a host of factors, ranging from signaling factors like FGF3 and FGF8 to proper inhibition of the Notch signaling pathway. Most importantly, the bHLH (basic helix-loop-helix)-domain containing transcription factor Atoh7 and its downstream effectors, such as Brn3b and Isl-1, work to promote RGC survival and differentiation. [9] The "differentiation wave" that drives RGC development across the retina is also regulated in particular of the bHLH factors Neurog2 and Ascl1 and FGF/Shh signaling, deriving from the periphery. [9] [12] [13]

Growth within the retinal ganglion cell (optic fiber) layer Edit

Early progenitor RGCs will typically extend processes connecting to the inner and outer limiting membranes of the retina with the outer layer adjacent to the retinal pigment epithelium and inner adjacent to the future vitreous humor. The cell soma will pull towards the pigment epithelium, undergo a terminal cell division and differentiation, and then migrate backwards towards the inner limiting membrane in a process called somal translocation. The kinetics of RGC somal translocation and underlying mechanisms are best understood in the zebrafish. [14] The RGC will then extend an axon in the retinal ganglion cell layer, which is directed by laminin contact. [15] The retraction of the apical process of the RGC is likely mediated by Slit–Robo signaling. [9]

RGCs will grow along glial end feet positioned on the inner surface (side closest to the future vitreous humor). Neural cell adhesion molecule (N-CAM) will mediate this attachment via homophilic interactions between molecules of like isoforms (A or B). Slit signaling also plays a role, preventing RGCs from growing into layers beyond the optic fiber layer. [16]

Axons from the RGCs will grow and extend towards the optic disc, where they exit the eye. Once differentiated, they are bordered by an inhibitory peripheral region and a central attractive region, thus promoting extension of the axon towards the optic disc. CSPGs exist along the retinal neuroepithelium (surface over which the RGCs lie) in a peripheral high–central low gradient. [9] Slit is also expressed in a similar pattern, secreted from the cells in the lens. [16] Adhesion molecules, like N-CAM and L1, will promote growth centrally and will also help to properly fasciculate (bundle) the RGC axons together. Shh is expressed in a high central, low peripheral gradient, promoting central-projecting RGC axons extension via Patched-1, the principal receptor for Shh, mediated signaling. [17]

Growth into and through the optic nerve Edit

RGCs exit the retinal ganglion cell layer through the optic disc, which requires a 45° turn. [9] This requires complex interactions with optic disc glial cells which will express local gradients of Netrin-1, a morphogen that will interact with the Deleted in Colorectal Cancer (DCC) receptor on growth cones of the RGC axon. This morphogen initially attracts RGC axons, but then, through an internal change in the growth cone of the RGC, netrin-1 becomes repulsive, pushing the axon away from the optic disc. [18] This is mediated through a cAMP-dependent mechanism. Additionally, CSPGs and Eph–ephrin signaling may also be involved.

RGCs will grow along glial cell end feet in the optic nerve. These glia will secrete repulsive semaphorin 5a and Slit in a surround fashion, covering the optic nerve which ensures that they remain in the optic nerve. Vax1, a transcription factor, is expressed by the ventral diencephalon and glial cells in the region where the chiasm is formed, and it may also be secreted to control chiasm formation. [19]

Growth at the optic chiasm Edit

When RGCs approach the optic chiasm, the point at which the two optic nerves meet, at the ventral diencephalon around embryonic days 10–11 in the mouse, they have to make the decision to cross to the contralateral optic tract or remain in the ipsilateral optic tract. In the mouse, about 5% of RGCs, mostly those coming from the ventral-temporal crescent (VTc) region of the retina, will remain ipsilateral, while the remaining 95% of RGCs will cross. [9] This is largely controlled by the degree of binocular overlap between the two fields of sight in both eyes. Mice do not have a significant overlap, whereas, humans, who do, will have about 50% of RGCs cross and 50% will remain ipsilateral.

Building the repulsive outline of the chiasm Edit

Once RGCs reach the chiasm, the glial cells supporting them will change from an intrafascicular to radial morphology. A group of diencephalic cells that express the cell surface antigen stage-specific embryonic antigen (SSEA)-1 and CD44 will form an inverted V-shape. [20] They will establish the posterior aspect of the optic chiasm border. Additionally, Slit signaling is important here: Heparin sulfate proteoglycans, proteins in the ECM, will anchor the Slit morphogen at specific points in the posterior chiasm border. [21] RGCs will begin to express Robo, the receptor for Slit, at this point, thus facilitating the repulsion.

Contralateral projecting RGCs Edit

RGC axons traveling to the contralateral optic tract need to cross. Shh, expressed along the midline in the ventral diencephalon, provides a repulsive cue to prevent RGCs from crossing the midline ectopically. However, a hole is generated in this gradient, thus allowing RGCs to cross.

Molecules mediating attraction include NrCAM, which is expressed by growing RGCs and the midline glia and acts along with Sema6D, mediated via the plexin-A1 receptor. [9] VEGF-A is released from the midline directs RGCs to take a contralateral path, mediated by the neuropilin-1 (NRP1) receptor. [22] cAMP seems to be very important in regulating the production of NRP1 protein, thus regulating the growth cones response to the VEGF-A gradient in the chiasm. [23]

Ipsilateral projecting RGCs Edit

The only component in mice projecting ipsilaterally are RGCs from the ventral-temporal crescent in the retina, and only because they express the Zic2 transcription factor. Zic2 will promote the expression of the tyrosine kinase receptor EphB1, which, through forward signaling (see review by Xu et al. [24] ) will bind to ligand ephrin B2 expressed by midline glia and be repelled to turn away from the chiasm. Some VTc RGCs will project contralaterally because they express the transcription factor Islet-2, which is a negative regulator of Zic2 production. [25]

Shh plays a key role in keeping RGC axons ipsilateral as well. Shh is expressed by the contralaterally projecting RGCs and midline glial cells. Boc, or Brother of CDO (CAM-related/downregulated by oncogenes), a co-receptor for Shh that influences Shh signaling through Ptch1, [26] seems to mediate this repulsion, as it is only on growth cones coming from the ipsilaterally projecting RGCs. [17]

Other factors influencing ipsilateral RGC growth include the Teneurin family, which are transmembrane adhesion proteins that use homophilic interactions to control guidance, and Nogo, which is expressed by midline radial glia. [27] [28] The Nogo receptor is only expressed by VTc RGCs. [9]

Finally, other transcription factors seem to play a significant role in altering. For example, Foxg1, also called Brain-Factor 1, and Foxd1, also called Brain Factor 2, are winged-helix transcription factors that are expressed in the nasal and temporal optic cups and the optic vesicles begin to evaginate from the neural tube. These factors are also expressed in the ventral diencephalon, with Foxd1 expressed near the chiasm, while Foxg1 is expressed more rostrally. They appear to play a role in defining the ipsilateral projection by altering expression of Zic2 and EphB1 receptor production. [9] [29]

Growth in the optic tract Edit

Once out of the optic chiasm, RGCs will extend dorsocaudally along the ventral diencephalic surface making the optic tract, which will guide them to the superior colliculus and lateral geniculate nucleus in the mammals, or the tectum in lower vertebrates. [9] Sema3d seems to be promote growth, at least in the proximal optic tract, and cytoskeletal re-arrangements at the level of the growth cone appear to be significant. [30]

In most mammals, the axons of retinal ganglion cells are not myelinated where they pass through the retina. However, the parts of axons that are beyond the retina, are myelinated. This myelination pattern is functionally explained by the relatively high opacity of myelin—myelinated axons passing over the retina would absorb some of the light before it reaches the photoreceptor layer, reducing the quality of vision. There are human eye diseases where this does, in fact, happen. In some vertebrates, such as the chicken, the ganglion cell axons are myelinated inside the retina. [31]


Receptive field

Complexity of the receptive field ranges from the unidimensional chemical structure of odorants to the multidimensional spacetime of human visual field, through the bidimensional skin surface, being a receptive field for touch perception. Receptive fields can positively or negatively alter the membrane potential with or without affecting the rate of action potentials. [1]

A sensory space can be dependent of an animal's location. For a particular sound wave traveling in an appropriate transmission medium, by means of sound localization, an auditory space would amount to a reference system that continuously shifts as the animal moves (taking into consideration the space inside the ears as well). Conversely, receptive fields can be largely independent of the animal's location, as in the case of place cells. A sensory space can also map into a particular region on an animal's body. For example, it could be a hair in the cochlea or a piece of skin, retina, or tongue or other part of an animal's body. Receptive fields have been identified for neurons of the auditory system, the somatosensory system, and the visual system.

The term receptive field was first used by Sherrington in 1906 to describe the area of skin from which a scratch reflex could be elicited in a dog. [2] In 1938, Hartline started to apply the term to single neurons, this time from the frog retina. [1]

This concept of receptive fields can be extended further up the nervous system. If many sensory receptors all form synapses with a single cell further up, they collectively form the receptive field of that cell. For example, the receptive field of a ganglion cell in the retina of the eye is composed of input from all of the photoreceptors which synapse with it, and a group of ganglion cells in turn forms the receptive field for a cell in the brain. This process is called convergence.

Receptive fields have been used in modern artificial deep neural networks that work with local operations.


83 Center-Surround Antagonism in Receptive Fields

Being able to describe the differences between an ON-center and OFF-center receptive field.

Know what types of retinal cells have the center-surround receptive fields.

The definition of a visual receptive field is the region of visual space in which a change in lightness or color will cause a change in the neuron’s firing rate. Almost all receptive fields have structure — different changes in different parts of the receptive field will have different effects on the neuron’s response. A key function of this receptive field structure: neurons only respond to edges. When center and surround are balanced, the RGC (retinal ganglion cell) will not change its firing rate in response to uniform illumination.

Fig.8.10.1. Caption. In this figure we can see that retinal ganglion cells have the center-surround receptive fields and that they respond to light differently on the center only, surround only, both center and surround, or on neither center nor surround. (Provided by: Wikimedia Commons, License: CC-BY-4.0 )

Most neurons in the retina and thalamus have small receptive fields that have a very basic organization, which resembles two concentric circles. This concentric receptive field structure is usually known as center-surround organization. On-center retinal ganglion cells respond to light spots surrounded by dark backgrounds like a star in a dark sky. Off-center retinal ganglion cells respond to dark spots surrounded by light backgrounds like a fly in a bright sky.


Contents

Retinal ganglion cells [ edit | edit source ]

On center and off center retinal ganglion cells respond oppositely to light in the center and surround of their receptive fields. A strong response means high frequency firing, a weak response is firing at a low frequency, and no response means no action potential is fired.

The organization of ganglion cells' receptive fields, composed of inputs from many rods and cones, provides a way of detecting contrast, and is used for detecting objects' edges. Each receptive field is arranged into a central disk, the "centre", and a concentric ring, the "surround", each region responding oppositely to light. For example, light in the centre might increase the firing of a particular ganglion cell, whereas light in the surround would decrease the firing of that cell.

There are two types of ganglion cells: "on-center" and "off-center". An on-center cell is stimulated when the center of its receptive field is exposed to light, and is inhibited when the surround is exposed to light. Off-center cells have just the opposite reaction. Stimulation of the center of an on-center cell's receptive field produces depolarization and an increase in the firing of the ganglion cell, stimulation of the surround produces a hyperpolarization and a decrease in the firing of the cell, and stimulation of both the center and surround produces only a mild response (due to mutual inhibition of center and surround). An off-center cell is stimulated by activation of the surround and inhibited by stimulation of the center (see figure).

Photoreceptors that are part of the receptive fields of more than one ganglion cell are able to excite or inhibit postsynaptic neurons because they release the neurotransmitter glutamate at their synapses, which can act to depolarize or to hyperpolarize a cell, depending on the ion channels it opens.

When photoreceptors in the center of an on-center ganglion cell's receptive field are stimulated, they stop releasing glutamate (because photoreceptors are depolarized in the absence of light and respond to light by hyperpolarizing). At their synapses with the on-center cell, glutamate acts as an inhibitory neurotransmitter, opening channels that hyperpolarize the cell. Stopping the release of glutamate inhibits an inhibitory effect, leading to an increase in the firing of the on-centre cell.

Conversely, when photoreceptors in the surround of an on-center ganglion cell's receptive field are stimulated, although they respond by stopping the release of glutamate, at their synapses with the ganglion cell, glutamate acts as an excitatory neurotransmitter, opening channels that depolarize the cell. Stopping the release of glutamate inhibits an excitatory effect, leading to a decrease in the firing of the on-centre cell. A photoreceptor can make synapses with both on-center and off-center cells and thus has synapses in which glutamate is excitatory as well as those in which it is inhibitory.

The center-surround receptive field organization allows ganglion cells to transmit information not merely about whether photoreceptor cells are firing, but also about the differences in firing rates of cells in the center and surround. This allows them to transmit information about contrast. The size of the receptive field governs the spatial frequency of the information: small receptive fields are stimulated by high spatial frequencies, fine detail large receptive fields are stimulated by low spatial frequencies, coarse detail. Retinal ganglion cell receptive fields convey information about discontinuities in the distribution of light falling on the retina these often specify the edges of objects.

Lateral geniculate nucleus [ edit | edit source ]

Further along in the visual system, groups of ganglion cells form the receptive fields of cells in the lateral geniculate nucleus. Receptive fields are similar to those of ganglion cells, with an antagonistic center-surround system and cells that are either on- or off center.

Visual cortex [ edit | edit source ]

Receptive fields of cells in the visual cortex are larger and have more-complex stimulus requirements than retinal ganglion cells or lateral geniculate nucleus cells. Hubel and Wiesel (e.g., Hubel, 1963) classified receptive fields of cells in the visual cortex into simple cells, complex cells, and hypercomplex cells. Simple cell receptive fields are elongated, for example with an excitatory central oval, and an inhibitory surrounding region, or approximately rectangular, with one long side being excitatory and the other being inhibitory. Images for these receptive fields need to have a particular orientation in order to excite the cell. For complex-cell receptive fields, a correctly oriented bar of light might need to move in a particular direction in order to excite the cell. For hypercomplex receptive fields, the bar might also need to be of a particular length.

Extrastriate visual areas [ edit | edit source ]

In extrastriate visual areas, cells can have very large receptive fields requiring very complex images to excite the cell. For example in the inferotemporal cortex, receptive fields cross the midline of visual space and require images such as radial gratings or hands. It is also believed that in the fusiform face area, images of faces excite the cortex more than other images. This property was one of the earliest major results obtained through fMRI (Kanwisher, McDermott and Chun, 1997) the finding was confirmed later at the neuronal level (Tsao, Freiwald, Tootell and Livingstone, 2006). In a similar vein, people have looked for other category-specific areas some recent research for example suggests the parahippocampal place area might be somewhat specialised for buildings. However, more recent research has suggested that the fusiform face area is specialised not just for faces, but also for any discrete, within-category discrimination.


Receptive-field properties of Q retinal ganglion cells of the cat

The goal of this work was to provide a detailed quantitative description of the recepii ve-field properties of one of the types of rarely encountered retinal ganglion cells of cat the cell named the Q-cell by Enroth-Cugell et al. (1983). Quantitative comparisons are made between the discharge statistics and between the spatial receptive properties of Q-cells and the most common of cat retinal ganglion cells, the X-cells. The center-surround receptive field of the Q-cell is modeled here quantitatively and the typical Q-cell is described. The temporal properties of the Q-cell receptive field were also investigated and the dynamics of the center mechanism of the Q-cell modeled quantitatively. In addition, the response vs . contrast relationship for a Q-cell at optimal spatial and temporal frequencies is shown, and Q-cells are also demonstrated to have nonlinear spatial summation somewhat like that exhibited by Y-cells, although much higher contrasts are required to reveal this nonlinear behavior. Finally, the relationship between Q-cells and Barlow and Levick's (1969) luminance units was investigated and it was found that most Q-cells could not be luminance units.


Results

We used single-cell patch electrophysiology in an in vitro macaque retinal preparation in conjunction with computational modeling of the RGC RF to explore the impact of the surround on nonlinear RF structure and natural scene encoding. We started by testing the hypothesis outlined in Figure 1C,D. Consistent with this hypothesis, we found that the linearity of spatial integration in the RF center depends on surround activation. Next, we used natural and artificial stimuli to characterize nonlinear interactions between center and surround and to test circuit models for the origin of these interactions. Finally, we show that the intensity correlations characteristic of natural scenes promote nonlinear interactions and make spatial integration relatively insensitive to changes in local luminance across a visual scene.

The RF surround regulates nonlinear spatial integration in the RF center

To test the hypothesis of Figure 1C,D, we systematically manipulated surround signals while probing spatial integration in the RF center. We focused this test on Off parasol RGCs, because these cells show both stronger rectification of subunit output than On parasol cells (Chichilnisky and Kalmar, 2002) and nonlinear spatial integration in the context of naturalistic visual stimuli (Turner and Rieke, 2016). We began each experiment by centering the stimulus over the RF and measuring the linear RF (see Materials and methods and Figure 2—figure supplement 1). We then tailored visual stimuli for each cell such that the ‘center region’ stimulus did not extend into the pure surround RF subregion and the ‘surround region’ stimulus did not cover the center. These subregions are not exclusively associated with a center or surround mechanism since the antagonistic surround is spatially coextensive with the RF center (Figure 1A,B). Nonetheless, according to estimated RFs, the ‘center region’ stimulus activated the center mechanism ∼ 4 times more strongly than the surround mechanism and the ‘surround region’ stimulus activated the surround mechanism ∼ 5 times more strongly than the center mechanism. This degree of specificity allowed us to ask questions about interactions between these two RF subregions.

We previously found that nonlinear spatial integration endows Off parasol RGCs with sensitivity to spatial contrast in natural images (Turner and Rieke, 2016). To test whether surround activity modulates this spatial contrast sensitivity, we measured Off parasol RGC spike responses to natural image patches that contained high spatial contrast and were expected to activate the nonlinear component of the cell’s response (see Materials and methods for details on images and patch selection). For each image patch, we also presented a linear equivalent disc stimulus, which is a uniform disc with intensity equal to a weighted sum of the pixel intensities within the RF center. The weighting function was an estimate of each cell’s linear RF center from responses to expanding spots (see Materials and methods and Figure 2—figure supplement 1). A cell whose RF center behaves according to this linear RF model will respond equally to a natural image and its associated linear equivalent disc.

As shown previously, Off parasol cells responded much more strongly to natural images than to linear equivalent stimuli, especially when the natural image contains high spatial contrast (Figure 2A, left, Figure 2B see also [Turner and Rieke, 2016]). However, when a bright surround was presented with the center stimulus, the natural image and its linear equivalent disc produced near-equal responses (Figure 2A,B). Dark surrounds strongly suppressed both responses (Figure 2A, right). If responses to center and surround stimuli added linearly, the difference between responses to the natural image and linear equivalent disc should be maintained across surrounds and the points in Figure 2B should lie on a line offset from the diagonal. This was clearly not the case.

The RF surround regulates nonlinear spatial integration of natural images.

(A) We presented a natural image patch and its linear-equivalent disc stimulus to probe sensitivity to spatial contrast in natural scenes. Rows of each raster correspond to repeated presentations of the same stimulus for the example Off parasol RGC. (B) Spike count responses to an example image patch and its linear equivalent disc across a range of surround contrasts. The addition of a sufficiently bright surround (top three points) eliminates sensitivity to spatial contrast in this image patch. (C) Population summary showing the response difference between image and disc as a function of the difference in mean intensity between the RF center and surround. Negative values of this difference correspond to a surround that is brighter than the center, and positive values to a surround that is darker than the center (n = 21 image patch responses measured in five Off parasol RGCs).

Figure 2—source data 1

Included is a .mat file containing a data structure for the data in Figure 2.

Individual trial responses are included as binary vectors of spike times for natural image and associated linear equivalent disc stimuli, across a range of surround contrast conditions. Data are organized by cell and then by natural image. The natural image used in each set of responses is also included. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 ms and persist for 200 ms.

We used the difference in spike count between a natural image and its linear equivalent disc as a metric of spatial contrast sensitivity. This difference, as shown in Figure 2C, depended systematically on the difference in mean intensity in the center and surround regions. Specifically, spatial contrast sensitivity was maximal in response to stimuli for which center and surround intensities were similar and dropped as intensity in these regions diverged. Hence, nonlinear spatial integration is maximized when center and surround experience similar mean luminance. When the surround strongly hyperpolarizes presynaptic bipolar cells (for Off cells, a dark surround), the response is diminished as a result of the surround shifting the synapse into a quiescent state. When the surround depolarizes presynaptic bipolar cells (for Off cells, a bright surround), the nonlinear sensitivity of the center is reduced. Hence, as in the hypothesis of Figure 1, these experiments indicate that the activity of the RF surround, rather than only interacting with the fully formed RF center signal, can control spatial integration by the center.

Does the impact of the surround on spatial integration in the center depend on specific statistics of natural images or is it a more general phenomenon? To answer this question, we repeated these experiments using a flashed split-field grating rather than natural image patches (Figure 3). Because of the nonlinear subunit structure of the RF center, Off parasol cells respond strongly to such stimuli (Figure 3A). We presented the same grating together with a surround annulus and, in separate trials, the surround annulus alone (Figure 3A). When paired with a bright surround, the grating stimulus did not activate the cell much beyond its response to the surround alone. A dark surround suppressed responses with and without the grating, save for a small, brief response at the beginning of the presentation of the grating which is likely the result of the brief temporal delay of the surround relative to the center. A similar early response was present for natural images with dark surrounds (Figure 2A).

The RF surround regulates nonlinear spatial integration in the RF center.

(A) Left column: Example Off parasol RGC spike response to an isolated split-field grating stimulus in the RF center. Rows of each raster correspond to repeated presentations of the same stimulus for the example cell. There is no linear equivalent stimulus in this case since the grating has a mean of zero. Center column: when the center stimulus is paired with a bright surround, the grating and the surround alone produce very similar spike responses. Right column: a dark surround suppresses the response in both cases, and the grating is unable to elicit a strong response. (B) For the example cell in (A), we tested sensitivity to the center grating stimulus with a range of contrasts presented to the surround. Negative contrast surrounds (hyperpolarizing for Off bipolar cells) decrease the response. Positive contrast surrounds (depolarizing for Off bipolar cells) sum sub-linearly with the grating stimulus such that for the brightest surrounds, the addition of the grating only mildly enhances the cell’s response. Points show mean ( ± S.E.M.) spike count. (C) We measured the response difference between the grating stimulus and the surround-alone stimulus across a range of surround contrasts (horizontal axis) and for four different central grating contrasts (different lines). For each grating contrast, addition of either a bright or dark surround decreased sensitivity to the added grating. Points are population means ( ± S.E.M.) (n = 5 Off parasol RGCs). (D–F) same as (A–C) for excitatory synaptic current responses of an Off parasol RGC. Points represent mean ( ± S.E.M.) excitatory charge transfer for the example cell in (E) and population mean ( ± S.E.M.) (n = 7 Off parasol RGCs) in (F).

Figure 3—source data 1

Included is a .mat file containing a data structure for the data in Figure 3A–C.

Off parasol RGC spike responses are included as raw traces and binary vectors of spike times for a range of central grating contrasts and surround contrasts. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 ms and persist for 200 ms.

Figure 3—source data 2

Included is a .mat file containing a data structure for the data in Figure 3D–F.

Off parasol RGC excitatory current responses (in units of pA) have been baseline-subtracted. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 ms and persist for 200 ms.

Figure 3—source data 3

Included is a .mat file containing a data structure for the data in Figure 3—figure supplement 1.

On parasol RGC excitatory current responses (in units of pA) and have been baseline-subtracted. For all responses, data are sampled at 10 Khz, and both center and surround stimuli appear after 200 msec and persist for 200 ms.

We repeated this experiment for surround contrasts ranging from +0.9 to −0.9 (Figure 3B). While the surround-free grating (surround contrast = 0) stimulus showed strong nonlinear integration (indicated by its distance away from the unity line in Figure 3B), the presence of a surround stimulus diminished the response to the grating (indicated by the tendency of non-zero surround contrast points to lie closer to the line of unity). This was true for a range of central grating contrasts (Figure 3C), which indicates that this behavior is not the result of response saturation. Thus, just as for natural image patches, nonlinear spatial integration is maximal when the center and surround experience the same mean luminance (in this case a mean of zero) and decreases when the surround is brighter or dimmer than the center.

To test whether the effect of the surround on spatial integration was present in the bipolar synaptic output, we repeated these experiments while measuring a ganglion cell’s excitatory synaptic inputs (Figure 3D see Materials and methods for isolation of excitatory inputs). Modulation of spatial integration by surround activity was similar in excitatory inputs and spike responses (Figure 3E,F), which indicates that it is already present in the bipolar synaptic output and is not substantially shaped by post-synaptic integration or spike generation mechanisms. A similar effect can be seen in the excitatory inputs to On parasol RGCs (Figure 3—figure supplement 1). This shows that this effect of the surround is not unique to the Off parasol excitatory pathway, but may be a more general feature of center-surround RF organization in the retina. Compared to Off parasol RGCs, On parasol RGCs are more easily shifted into a regime of linear spatial integration, presumably because of the shallower rectification of nonlinear subunits in the receptive field of On parasol cells (Chichilnisky and Kalmar, 2002 Turner and Rieke, 2016).

The experiments described in Figures 2 and 3 show that inputs to the RF surround can influence how the RF center integrates signals across space, consistent with the hypothesis outlined in Figure 1. For both the spike output and excitatory synaptic input to an Off parasol RGC, the peak spatial nonlinearity was observed when center and surround experienced similar mean luminance (Figure 2C and Figure 3C,F).

Nonlinear center-surround interactions are dominated by a single, shared nonlinearity

The hypothesis in Figure 1 relies on a specific form of nonlinear center-surround interaction, whereby center and surround signals combine upstream of a shared, rectifying nonlinearity. To characterize center-surround interactions in a more complete and unbiased manner, we used Gaussian-distributed noise stimulation and a linear-nonlinear cascade modeling approach. We presented Gaussian-distributed random noise to the center region alone, surround region alone or both regions together while measuring excitatory synaptic inputs to On and Off parasol cells (Figure 4A). While thus far we have focused exclusively on Off parasol RGCs, the hypothesis in Figure 1 should also apply to excitatory input to On parasol RGCs, and hence we performed these experiments on both parasol types. For this analysis, we estimated the excitatory conductance by dividing the measured excitatory currents by the driving force. We computed linear filters for each RF region using reverse correlation based on trials in which the center or surround was stimulated in isolation (Figure 4A, left and middle columns).

Linear-nonlinear cascade modeling supports an architecture where center and surround combine linearly before passing through a shared nonlinearity.

(A) We presented Gaussian noise to either the center region (left), surround region (middle) or center and surround regions simultaneously (right) while measuring excitatory synaptic current responses. Measured excitatory currents (in pA) have been converted to excitatory conductance (in nS). Example traces are from a representative Off parasol RGC. (B) The independent model treats the filtered center and surround inputs with private nonlinear functions, and the outputs of these two nonlinearities are then summed to produce the excitatory conductance response. (C) The shared model integrates filtered center and surround inputs linearly, and this summed input is then passed through a single, shared nonlinearity. (D) The stacked model combines the independent and shared models by treating center and surround with private nonlinearities before summation and treatment with a third, shared nonlinearity. (E) We tested the ability of each of these models to predict held-out responses to center-surround stimulation. The shared model outperforms the independent model in both On and Off parasol RGCs (n = 7 On cells, p = 0.03 n = 8 Off cells, p = 0.008 ). (F) The fraction of explained variance was the same for the shared compared to the stacked model ( p > 0.90 for both On and Off cells). Dashed lines show estimates of the response reliability, which sets an upper bound for model performance (see Materials and methods for details).

Figure 4—source data 1

Included is a .mat file containing a data structure for the data in Figure 4 and 5.

Stimuli and corresponding responses of On and Off parasol RGCs to center-surround white noise stimulation have been concatenated into vector arrays. Note that the data were collected in interleaved trials. This data includes excitatory conductance responses (in nS) that were estimated using measured excitatory current responses and an estimate of the excitatory driving force for each cell. Data are sampled at 10 Khz.

We constructed three models of how center and surround inputs combine to determine the cell’s excitatory conductance response when both RF regions are stimulated (see Materials and methods for details). (1) In the ‘independent’ model (Figure 4B), inputs to the center and surround are filtered using their respective linear filters and then passed through separate nonlinear functions. The outputs of the two nonlinearities are then summed to give the response of the cell. (2) In the ‘shared’ model (Figure 4C), filtered center and surround inputs are summed linearly before passing through a single, shared nonlinear function. The output of this nonlinearity is the cell’s response. (3) The ‘stacked’ model (Figure 4D) combines models (1) and (2) by treating center and surround with private nonlinearities before summation and treatment with a third, shared nonlinearity. Representative predictions and measured responses are shown in Figure 4—figure supplement 1. The shared model is a special case of the stacked model, where the upstream independent functions are linear. Similarly, the independent model is a special case of the stacked model, where the output function after summation is linear.

We fit the nonlinear functions in each model using a subset of simultaneous center-surround trials and used the remaining simultaneous trials to test how well each model could predict the cell’s response. These models generally captured ∼ 60% of the total response variance, and ∼ 80% of the explainable variance (see Materials and methods). While the models appear to perform better for On compared to Off parasol RGCs (see Figure 4E,F), this difference is not statistically significant (p=0.19). The shared model outperformed the independent model (Figure 4E). The shared model performed as well as the more complicated stacked model (Figure 4F), despite the latter having many more free parameters (10 free parameters) than the shared model (five free parameters). In addition, the private nonlinearities fit in the stacked model tended to be quite shallow and much nearer to linear than the sharply rectified shared nonlinearity (Figure 4D). Hence the stacked model in practice effectively behaved like the shared model. The modeling result in Figure 4F supports the hypothesis that the dominant nonlinear interaction between center and surround is characterized by a shared nonlinearity, and that upstream of this nonlinearity center and surround interact approximately linearly.

The hypothesis in Figure 1 suggests that the effective rectification experienced by each subunit will depend on surround activation. The experiments used for the modeling above allowed us to directly examine whether this is the case. To do this, we estimated center and surround activation by convolving center and surround filters with the appropriate stimuli. We then plotted the measured excitatory conductance against these estimates of center and surround activation Figure 5A shows an example for the same Off parasol RGC as Figure 4A–D.

The RF surround changes the apparent rectification of inputs from the center.

(A) Response surface showing the mean excitatory conductance response from an Off parasol RGC as a function of filtered inputs to both the center and surround (center or surround ‘activation’, that is their generator signals). (B) Sections through this surface at various levels of surround activation reveal that the shape of the nonlinear dependence of excitatory conductance on center activation changes as the surround is modulated. (C) To quantify this change in center rectification, we used a rectification index (see Materials and methods), where values near 0 indicate a linear relationship between center activation and conductance response, and values near one indicate a sharply rectified relationship. Points are mean ( ± S.E.M.) (n = 7 On parasol cells and n = 8 Off parasol cells). Inset shows the expected relationship between rectification index and surround activation for a shared nonlinearity model (black curve) and an independent nonlinearity model (gray curve).

These joint response distributions show that the relationship between center activation and excitatory conductance depends on surround activation. When the surround is only weakly activated (near zero on ‘surround’ axis in Figure 5A), this nonlinear relationship is rectified (Figure 5B). Rectification persists when the surround hyperpolarizes presynaptic bipolar cells (negative on ‘surround’ axis in Figure 5A, blue trace in Figure 5A,B). But when the surround depolarizes bipolar cells (positive on ‘surround’ axis in Figure 5A), the relationship between center activation and excitatory conductance becomes more linear (i.e. less rectified Figure 5A,B, red trace). We quantified this change in center rectification with surround activation using a rectification index (RI, see Materials and methods for calculation of this metric). A RI value of zero indicates a linear relationship between center activation and conductance response, whereas RI values near one indicate strong rectification (i.e. there is a large increase in response with positive center activation, but very little or no decrease in response with negative center activation). For both On and Off cells, rectification decreased as surround activation increased (Figure 5C). In agreement with previous observations (Chichilnisky and Kalmar, 2002 Turner and Rieke, 2016), Off cells were more rectified than On cells. The inset to Figure 5C shows the relationship between surround activation and RI for independent and shared nonlinearity models. When center and surround nonlinearities are independent, the rectification of the center does not depend on the activity of the surround because the surround enters only after the center is fully formed (horizontal gray line in inset). The shared nonlinearity model, on the other hand, predicts a decrease in rectification as the surround becomes more depolarizing, in agreement with the behavior of parasol RGCs.

The experiments described provide additional quantitative support for the circuit architecture of Figure 1B in which center and surround signals add linearly prior to a shared nonlinearity.

RF center and surround interact nonlinearly during naturalistic visual stimulation

To test whether inputs to the RF center and surround interact nonlinearly under naturalistic stimulus conditions, we used a visual stimulus designed to approximate natural primate viewing conditions based on the Database Of Visual Eye movementS (DOVES, (Van Der Linde et al., 2009 van Hateren and van der Schaaf, 1998). An example image and a corresponding eye movement trajectory is shown in Figure 6A. We masked the stimulus to the RF center region, surround region or both. Figure 6B shows spike responses of an example Off parasol RGC to three movie stimuli: stimulation of the center region alone (Figure 6B, green), stimulation of the surround region alone (Figure 6B, purple), or simultaneous stimulation of both the center and surround regions (Figure 6B, black). Responses to isolated center or surround stimuli are shown in Figure 6C for average spike responses (Figure 6C, top) and excitatory synaptic inputs (Figure 6C, bottom).

Natural movie stimuli elicit nonlinear interactions between the RF center and surround.

(A) Natural image and associated eye movement trajectory from (Van Der Linde et al., 2009). Right: example movie frames showing isolated center (top), surround (middle), and center-surround stimuli (bottom). (B) Rasters show example Off parasol RGC spike responses to these three movie stimuli. Top shows eye movement position. (C) Spike output (top) and excitatory synaptic input (bottom) in response to isolated center and surround stimuli. (D) Spike and excitatory synaptic input responses to the center-surround stimulus. Gray trace shows the linear sum of isolated responses to center- and surround-region stimuli. (E) Spike count in response to the center-surround stimulus compared to the linear sum of isolated center and surround responses. Each point is a different natural movie. Center and surround sum sub-linearly (On parasol RGCs: n = 20 natural movies across 8 cells, p < 9 × 10 − 5 Off parasol RGCs: n = 18 natural movies across 7 cells, p < 2 × 10 − 4 ). (F) Same as (E) but for excitatory charge transfer responses (On parasol RGCs: p < 2 × 10 − 4 Off parasol RGCs: p < 3 × 10 − 4 ). (G) For the example in (A–D), the difference between measured and linearly-summed spike responses was correlated with differences in excitatory synaptic inputs (r = 0.91). (H) Population data for the analysis in (G).

To determine whether center and surround signals interact nonlinearly, we compared the linear sum of center and surround responses (Figure 6D, gray traces) to the measured response to simultaneous stimulation of both the center and surround regions (Figure 6D, black traces). For both spike and excitatory current responses, the measured center-surround response was smaller than the linear sum of the two responses measured independently. Thus, RF center and surround interact nonlinearly. This interaction, like that in Figure 4 and 5, is present in the excitatory synaptic input, and hence reflects properties of bipolar synaptic output rather than nonlinearities in synaptic integration or spike generation in the ganglion cell.

Sublinear interactions between center and surround inputs held across cells and fixations for both spike output (Figure 6E) and excitatory synaptic input (Figure 6F). For each cell, the difference between the linear sum of responses to center and surround inputs and the measured simultaneous response for spike outputs was correlated with the same difference for excitatory inputs (Figure 6G,H). This is consistent with the interpretation that the nonlinear interaction seen at the level of spike output is largely inherited from the excitatory synaptic inputs. Sublinear interactions in spike output and excitatory synaptic input were more strongly correlated for Off than On parasol RGCs (Figure 6H). This may be because inhibitory input impacts On parasol responses to natural stimuli more than Off parasol responses (Turner and Rieke, 2016). Taken together, these observations demonstrate that the nonlinear center-surround interactions characterized in Figures 2–5 are prominent for naturalistic visual inputs.

Natural spatial correlations promote nonlinear center-surround interactions

How do nonlinear center-surround interactions depend on stimulus statistics, especially those that characterize natural scenes? Naturalistic center and surround stimuli tended to elicit responses at different times (Figure 6). This is consistent with the spatial correlations in intensity that characterize natural images (Simoncelli and Olshausen, 2001) and the antagonistic nature of the surround—for example an Off parasol RGC would be depolarized by negative contrast in the RF center and hyperpolarized by negative contrast in the surround. We tested the effect of spatial correlations on nonlinear center-surround interactions using a synthetic visual stimulus inspired by our natural movie stimuli.

This stimulus consisted of a uniform disc in the center and a uniform annulus in the surround. The intensity of each region was sampled from a natural image (Figure 7A,B) and presented to either the center region alone, surround region alone, or both regions simultaneously. We updated the intensity of each region every 200 ms, which is consistent with typical human fixation periods (Van Der Linde et al., 2009). Center and surround intensities were determined from the mean intensity within the disc and annulus for randomly chosen image locations. The intensity correlations characteristic of natural scenes were evident when we plotted the center intensity against the corresponding surround intensity (Figure 7C, left, ‘Control’). Shuffling the surround intensities relative to those of the center eliminated spatial correlations, while maintaining the same marginal distributions (Figure 7C, right, ‘Shuffled’). When spatial correlations were intact, inputs to the center and surround combined sub-linearly in the excitatory synaptic input to the cell (Figure 7D), as they did in the full natural movie responses (Figure 6). When we shuffled the surround intensities relative to the center, nonlinear center-surround interactions were much weaker (Figure 7E,F). This was true for excitatory synaptic inputs to both On and Off parasol RGCs (Figure 7G).

Spatial correlations in natural scenes promote nonlinear center-surround interactions.

(A) Example image (van Hateren and van der Schaaf, 1998) used to construct natural intensity stimuli. (B) Intensity histogram from the image in (A). Dashed vertical line indicates the mean intensity, which was used as the mean gray level in experiments that follow. (C) Center and surround intensity values for 40 image patches from the image in (A). (D) Example stimuli (top) and Off parasol RGC excitatory current responses to isolated center and surround (middle) and center-surround (bottom) stimulation. Gray trace in bottom shows linear sum of isolated center and surround responses. (E) Same as (D) for shuffled surround intensities. (F) The response magnitude (charge transfer) of each fixation is plotted for measured center-surround and linearly summed center and surround responses. Circles show mean responses for each fixation, squares show mean ( ± S.E.M.) across all fixations in this example cell. (G) Population data showing the mean difference between responses to the center-surround stimulus and the linearly summed response. Circles show average differences for each cell tested, and squares show population mean ( ± S.E.M) (n = 7 On parasol RGCs, p < 0.02 n = 8 Off parasol RGCs, p < 8 × 10 − 3 ). (H) White noise center-surround stimuli had variable center-surround correlations but constant marginal distributions. Shown are example excitatory current responses in an Off parasol RGC. Black traces show the measured center-surround stimulus response and gray traces show the linear sum of center and surround responses. (I) Population data from the experiments in (H) showing that nonlinear center-surround interactions depend on the correlation between center and surround inputs (n = 8 On parasol RGCs n = 8 Off parasol RGCs).

Figure 7—source data 1

Included is a .mat file containing a data structure for the data in Figure 7A–G.

The structure contains excitatory current responses (baseline subtracted, in pA) of On and Off parasol RGCs to center-surround naturalistic luminance stimuli. Data are sampled at 10 Khz.

To further probe the impact of intensity correlations on center-surround interactions, we generated Gaussian random noise stimuli that updated with a 200-ms period. For this stimulus, a single random intensity fills the entire center disc and a different, random intensity fills the entire surround annulus. This noise stimulus had a tunable degree of correlation between center and surround intensity, ranging from −1 (perfectly anti-correlated) to 0 (uncorrelated) to +1 (perfectly correlated, that is modulated in unison). When noise stimuli in the center and surround were negatively correlated, inputs to the center and surround summed linearly or very nearly so (Figure 7H, left). As the center-surround intensity correlations increased, sublinear interactions became more obvious (Figure 7H, middle and right). Strongly positively correlated noise stimuli induced center-surround interactions that resembled those seen using naturally correlated luminance stimuli (Figure 7H, right). This dependence of nonlinear center-surround interactions on center-surround intensity correlations was present in both On and Off parasol RGCs (Figure 7I).

These results indicate that nonlinear center-surround interactions depend strongly on center-surround intensity correlations, and hence that the importance of these interactions could be underestimated from stimuli such as spatial noise that lack intensity correlations.

A luminance-matched surround promotes spatial contrast sensitivity in the center

The experiments described above show that surround signals, rather than only interacting with the fully formed center signal, can alter how the center integrates over space. Two aspects of these results deserve emphasis: (1) nonlinear spatial integration is maximized when center and surround experience similar mean luminances (Figures 2 and 3) and (2) natural stimuli elicit strong nonlinear center-surround interactions due to positive correlations between center and surround intensities (Figures 6 and 7). These observations lead to the hypothesis, tested below, that surround activation can make spatial integration in the RF center relatively insensitive to changes in mean luminance.

Natural visual stimuli, such as the change in input encountered after a saccade, typically include changes in mean luminance and spatial contrast. Such stimuli will activate both linear and nonlinear response components, and these may not interact in a straightforward manner. To make this more concrete, consider a population of Off bipolar cells acting as subunits in the center of the RGC RF. At rest, the synapse of each bipolar cell is in a sharply rectified state. A decrease in mean luminance over the RF center will depolarize the synapse associated with each RF subunit, shifting each into a locally linear state (Figure 8A, top), and decreasing spatial contrast sensitivity. When such a stimulus is paired with a luminance-matched surround stimulus, the antagonistic surround may at least partially cancel this depolarization this could keep each subunit in a locally rectified state (Figure 8A, bottom, blue arrow) and preserve spatial contrast sensitivity.

Intensity correlations across space promote nonlinear spatial integration in the RF center.

(A) Schematic showing the hypothesized interaction between center and surround inputs on local subunit rectification. A depolarizing input to the center may push the synapse into a locally linear state. A simultaneous surround input that is matched in luminance (blue arrow) can hyperpolarize the synaptic terminal and bring the synapse back into a rectified state, whereas a poorly matched surround will not (orange arrow). (B) During Off parasol spike recordings, we presented split-field grating stimuli to the RF center under three surround conditions. For each stimulus condition, rows of the raster correspond to repeated presentations of the same stimulus for the example cell. (C) Summary data showing the population mean ± S.E.M. NLI (see text) as a function of the mean intensity (relative to the background) of the center grating (n = 8 Off parasol RGCs). (D–F) We presented natural image patches and their linear equivalent disc stimuli to measure the NLI under three surround conditions: no surround, a matched surround image, and a shuffled surround image. (G) Schematic of a nonlinear subunit RF model. Each subunit has a difference-of-Gaussians spatial receptive field. The output of each subunit is passed through a private, rectifying output nonlinearity. Subunit outputs are then summed over visual space to yield the modeled RGC response. (H,I) We changed the strength of the subunit surround to model RGCs with three different surround strengths: a weak surround (light gray trace), an intermediate-strength surround (gray trace), and a strong surround (black trace). We presented this RF model with the natural image/disc stimuli shown in (E) and, following that analysis, measured the NLI as a function of the mean intensity of the image in the RF center.

We tested this prediction in Off parasol RGCs, using modified grating stimuli with nonzero mean luminance. For each grating stimulus, we also presented a corresponding linear equivalent disc stimulus, which has the same mean luminance as the grating, but lacks any spatial contrast. The degree to which a cell’s response to these two stimuli differs is a measure of the sensitivity of the cell to spatial contrast, or, equivalently, the strength of nonlinear spatial integration.

We presented these stimuli to Off parasol RGCs while measuring spike responses. A grating with a dark mean luminance signal produced a similar response as a linear equivalent stimulus (Figure 8B, left), indicating that the cell is insensitive to the spatial contrast present in the grating. Compare this to these cells’ highly nonlinear responses to zero-mean grating stimuli (e.g. Figure 3). When a dark mean grating is paired with a luminance-matched surround, however, the grating again produces a much stronger response than its linear equivalent stimulus (Figure 8B, middle), which is consistent with the restoration of spatial contrast sensitivity via the mechanism in Figure 8A. Pairing the grating stimulus with poorly matched surrounds does not restore spatial contrast sensitivity (Figure 8B, right), indicating that this is not a general consequence of surround activation.

To quantify the spatial contrast sensitivity in these experiments, we used a nonlinearity index (NLI, See Equation 1 and [Turner and Rieke, 2016]):

This measure normalizes responses within each surround condition. A positive NLI indicates that the cell responds more strongly to a grating stimulus than to its linear equivalent disc stimulus, and is thus sensitive to spatial contrast. A NLI near zero indicates that the cell’s response is mostly determined by the mean luminance component of the stimulus, and not the spatial contrast. The NLI was maximal for all surround conditions for zero-mean gratings. As the center intensity decreased (moving towards the left in Figure 8C), the NLI decreased along with it, but this drop was less pronounced under the matched surround condition. Hence matched surround activation decreased the sensitivity of nonlinear spatial integration to changes in mean luminance.

Intensity correlations in natural images promote nonlinear spatial integration

The results presented thus far show that systematically varying the input to the surround relative to the center can alter sensitivity to spatial contrast in both artificial and natural stimuli (Figures 2, 3 and 8A–C). However, it is not clear from these experiments how much this effect is present during the course of more naturalistic activation of the RF surround. The intensity correlations present in natural images (e.g. Figure 7C) should ensure that the mean intensity difference between the RF center and surround is often near zero. Because spatial contrast sensitivity was maximized by small differences between mean center and surround intensity (Figure 2), we hypothesized that full natural image stimulation of the RF surround would increase spatial contrast sensitivity in the RF center compared to stimulation of the RF center alone.

To test this hypothesis, we presented natural image patches (and their corresponding linear equivalent disc stimuli) to the RF center while pairing each with three distinct surround conditions: no surround stimulation (Figure 8E) the naturally occurring surround present in the rest of the natural image patch (‘Matched surround’), and, a randomly selected surround from the same full natural scene (‘Shuffled surround’). We recorded Off parasol spike responses to these six stimuli for each of 20–40 randomly selected image patches from a single natural scene. For each image patch, we computed the NLI (Equation 1) for responses measured in each of the three surround conditions. We compared the NLIs to the mean intensity of the image in the RF center (I) relative to the background intensity (B), that is Relative center intensity = ( I − B ) / B . As in the modified gratings experiments (Figure 8C), a darker mean luminance signal was associated with a decrease in spatial contrast sensitivity (Figure 8F, black curve). This drop-off in spatial contrast sensitivity was less pronounced with the naturally occurring surround, (Figure 8F, blue curve). Specifically, sensitivity to fine spatial structure was two to three times greater in the presence of a matched surround than without a surround. Randomly selected surrounds did not enhance spatial contrast sensitivity in this way but instead altered the NLI in a manner predicted by the experiments in Figure 2 (see Figure 8—figure supplement 1).

These observations are consistent with the idea that natural images provide inputs to the surround that can preserve the spatial contrast sensitivity of the RF center compared to center inputs alone. Key to this relative invariance of contrast sensitivity is the ability of the surround to control the degree of rectification of the bipolar subunits that comprise the RF center and the strong positive correlations between center and surround inputs created by natural images.

The appropriate surround activation can preserve spatial contrast sensitivity in the context of both natural image and grating stimuli. Note, however, that the NLI is, on average, lower for randomly selected images than for grating stimuli (compare Figure 8F and C). This is expected because the spatial structure of grating stimuli is designed to highlight nonlinear spatial integration by differentially activating subunits in the RF center (i.e. depolarizing some while hyperpolarizing others). Randomly-selected image patches, however, often do not contain much spatial structure that will differentially activate subunits in the RF center.

To explore the relationship between naturalistic surround activation and spatial contrast sensitivity in a manner not possible in our experiments, we constructed a simple spatial RF model composed of nonlinear, center-surround subunits (Figure 8G see (Enroth-Cugell and Freeman, 1987) and Materials and methods). Following the analysis used for the data in Figure 8F, we computed the mean NLI for the model as a function of the relative center intensity for a surround-free stimulus (Figure 8I, ‘no surround’) and for the naturally occurring surround stimulus (Figure 8I, ‘moderate surround’). As in the Off parasol spike data, the inclusion of the naturally occurring surround extended spatial contrast sensitivity in the face of stronger local luminance signals. We repeated the same analysis for versions of the RF model with both a weaker and a stronger surround. A stronger RF surround is associated with greater spatial contrast sensitivity, especially for images that contain a strong local luminance signal. Similar results were seen for a spatiotemporal RF model that includes temporal filters measured in the experiments shown in Figure 4 (Figure 8—figure supplement 2).


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