A model for the mechanisms of sensitivity control in the submammalian vertebrate retina

A model is proposed for the mechanisms of sensitivity control at the outer and inner plexiform layers in the submammalian vertebrate retina on the basis of Werblin's results and other physiological results. The model is especially based on the following suggestions: The signal that acts to shift the bipolar curves is probably carried by horizontal cell processes extending from the surround to the center of the receptive field. Furthermore, amacrine cells carry a lateral antagonistic signal across the inner plexiform layer that affects the response properties of ganglion cells. The simulations of the model were made and the results of the ones considerably coincided with the experimental results of Werblin.     

Features and functions of nonlinear spatial integration by retinal ganglion cells

Ganglion cells in the vertebrate retina integrate visual information over their receptive fields. They do so by pooling presynaptic excitatory inputs from typically many bipolar cells, which themselves collect inputs from several photoreceptors. In addition, inhibitory interactions mediated by horizontal cells and amacrine cells modulate the structure of the receptive field. In many models, this spatial integration is assumed to occur in a linear fashion. Yet, it has long been known that spatial integration by retinal ganglion cells also incurs nonlinear phenomena. Moreover, several recent examples have shown that nonlinear spatial integration is tightly connected to specific visual functions performed by different types of retinal ganglion cells. This work discusses these advances in understanding the role of nonlinear spatial integration and reviews recent efforts to quantitatively study the nature and mechanisms underlying spatial nonlinearities. These new insights point towards a critical role of nonlinearities within ganglion cell receptive fields for capturing responses of the cells to natural and behaviorally relevant visual stimuli. In the long run, nonlinear phenomena of spatial integration may also prove important for implementing the actual neural code of retinal neurons when designing visual prostheses for the eye.     

Receptive field mechanisms of ganglion cells in the cat retina

On the basis of anatomical and physiological results of the vertebrate retina, a method is proposed for analysing the respective fields of ganglion cells in the cat retina. In the model, we assume the following: (a) Ganglion cells receive their input from bipolar and/or amacrine cells. (b) The nonlinearity of ganglion cell responses is due to the activities of transient type amacrine cells. The method has been proved to be effective. According to the results of this investigation, the receptive field properties of X type and Y type ganglion cells are heterogeneous. Thus, it may be considered that their receptive fields consist of center and surround mechanisms. The receptive field properties of X-cells are almost linear and the X-cells seem to receive most of their input from bipolar cells. On the other hand, the ones of Y-cells are highly nonlinear. Consequently, it is conceivable that the Y-cells receive their input mainly from transient type amacrine cells.     

Spatio-temporal cross-correlation analysis of catfish retinal neurons

1. The receptive field properties of visual neurons in the retina of the catfish are studied by a white noise spatio-temporal stimulus. The spatial and temporal inputs of the stimulus are independent and lead to complete linear characterizations and local nonlinear characterizations of the neural response. 2. Horizontal cells, bipolar cells, and sustained or Type N amacrine cells all yield spatially coherent linear correlations. The horizontal cells have the shortest latency by these methods and exhibit a late depolarizing component that is wider in spatial extent than the initial hyperpolarizing component. Depolarizing Type N neurons have center-hyperpolarizing local nonlinearity. 3. Transient or Type C amacrine cells do not correlate well with the intensity of the stimulus, even though the Fast variety responds vigorously to the stimulus. 4. Ganglion cells are classified into Excitatory, Inhibitory and Biphasic classes based upon their linear correlations. Some ganglions exhibit responses dependent upon the orientation of stimulus. Although linear correlation of the Excitatory class is similar to that of the depolarizing Type N cell, the locally nonlinear character of these cell types is distinct. The receptive field of the Inhibitory ganglion cells has strong locally excitatory nonlinearity.     

Spatial properties of goldfish ganglion cells

We systematically classified goldfish ganglion cells according to their spatial summation properties using the same techniques and criteria used in cat and monkey research. Results show that goldfish ganglion cells can be classified as X-, Y-, or W-like based on their responses to contrast-reversal gratings. Like cat X cells, goldfish X-like cells display linear spatial summation. Goldfish Y-like cells, like cat Y cells, respond with frequency doubling at all spatial positions when the contrast-reversal grating consists of high spatial frequencies. There is also a third class of neurons, which is neither X- nor Y-like; many of these cells' properties are similar to those of the "not-X" cells found in the eel retina. Spatial filtering characteristics were obtained for each cell by drifting sinusoidal gratings of various spatial frequencies and contrasts across the receptive field of the cell at a constant temporal rate. The spatial tuning curves of the cell depend on the temporal parameters of the stimulus; at high drift rates, the tuning curves lose their low spatial frequency attenuation. To explore this phenomenon, temporal contrast response functions were derived from the cells' responses to a spatially uniform field whose luminance varied sinusoidally in time. These functions were obtained for the center, the surround, and the entire receptive field. The results suggest that differences in the cells' spatial filtering across stimulus drift rate are due to changes in the interaction of the center and surround mechanisms; at low temporal frequencies, the center and surround responses are out-of-phase and mutually antagonistic, but at higher temporal rates their responses are in-phase and their interaction actually enhances the cell's responsiveness.     

Receptive field properties of rod-driven horizontal cells in the skate retina

The large receptive fields of retinal horizontal cells result primarily from extensive intercellular coupling via gap (electrical) junctions; thus, the extent of the receptive field provides an index of the degree to which the cells are electrically coupled. For rod-driven horizontal cells in the dark-adapted skate retina, a space constant of 1.18 +/- 0.15 mm (SD) was obtained from measurements with a moving slit stimulus, and a comparable value (1.43 +/- 0.55 mm) was obtained with variation in spot diameter. These values, and the extensive spread of a fluorescent dye (Lucifer Yellow) from the site of injection to neighboring cells, indicate that the horizontal cells of the all-rod retina of skate are well coupled electrically. Neither the receptive field properties nor the gap-junctional features of skate horizontal cells were influenced by the adaptive state of the retina: (a) the receptive field organization was unaffected by light adaptation, (b) similar dye coupling was seen in both dark- and light-adapted retinae, and (c) no significant differences were found in the gap-junctional particle densities measured in dark- and light-adapted retinas, i.e., 3,184 +/- 286/microns 2 (n = 8) and 3,073 +/- 494/microns 2 (n = 11), respectively. Moreover, the receptive fields of skate horizontal cells were not altered by either dopamine, glycine, GABA, or the GABAA receptor antagonists bicuculline and picrotoxin. We conclude that the rod-driven horizontal cells of the skate retina are tightly coupled to one another, and that the coupling is not affected by photic and pharmacological conditions that are known to modulate intercellular coupling between cone-driven horizontal cells in other species.     

An analogue model of the luminosity-channel in the vertebrate cone retina

A model of the vertebrate cone retina was tested with physiological stimuli. Results confirm previous findings that, except for photoreceptors, the spatial and temporal properties of simulated retinal elements conform to a linear system. The model is consistent with known physiological correlates. Tonic units detect intensity when the light spot is within the center field, while phasic units detect movement across borders of contrast. There is a dynamic balance between the tonic and phasic channels: the tonic channel is favored by a center field input voltage, while the phasic channel is favored by a surround field input voltage to bipolar cells. The ON discharge of the phasic ganglion cell is developed by the excitatory center field input to the depolarizing-center bipolar cell, which has the shortest delay, while the OFF discharge is the result of the excitatory surround field input voltage to the hyperpolarizing-center bipolar cell, which has the longest delay.     

A spatio-temporal model of ganglion cell receptive field in the cat retina

A spatio-temporal model of ganglion cell receptive fields is proposed on the basis of receptive field characteristics of cat retinal ganglion cells reported in our previous paper. The model consists of the linear and nonlinear mechanisms in the ganglion cell receptive field. The linear mechanism is assumed to be composed of antagonistic center and surround mechanisms. Then, by integrating these mechanisms we construct a spatio-temporal impulse response function of ganglion cell receptive field. Here we assume that spatio-temporal impulse response function may be factored into spatial and temporal terms. By Fouriertransforming the spatio-temporal impulse response function, we can obtain the spatio-temporal transfer function. Contrast sensitivity characteristics of X-and Y-cells in the cat retina may be explained by the transfer function.     

Modeling of the vertebrate visual system. II. Application to the turtle cone retina

The model of the vertebrate cone retina was adapted to the turtle retina with its red cone- and L-channel-dominances. The model consists of an ordering of four spatial organizations of unit hexagons, weighted inputs for all cones in the receptive fields, and linear polarization factors based on data from literature on turtle retina. Data generated by the model for spatial and chromatic patterns of receptive fields, intensity-response curves, dynamic ranges for cones, horizontal and bipolar cells proved remarkably consistent with literature. The model also generates observed phenomena such as near-field enhancement of cones due to stray light effects and electrical coupling of like-cones and far-field decrease in responses due to negative feedback from L-type horizontal cells to cones. Annular stimuli were shown to be more effective than spot stimuli for horizontal cells. The formal approach of the model demonstrates factors which play roles in various observed phenomena and all aspects of model can be displayed and tested both qualitatively and quantitatively.     

The spatial frequency sensitivity of bipolar cells

Retinal bipolar cells constitute the output stage of the outer layer of the retina. There are several constraints on the ability of the bipolar cell array to respond to the different spatial frequency components of the visual image, including (i) electrical coupling in the dendritic tree receiving receptor input; (iii) the "lateral inhibition" mediated by horizontal cells. Using simple mathematical models, we derive analytical expressions for the spatial frequency response of the bipolar cell array for the case in which horizontal cells are presynaptic to bipolar cells (feedforward model) and also for the case in which horizontal cells are presynaptic to receptors (feedback model). The results illustrate the importance of the three factors mentioned in determining the bipolar cells' properties. The optimal spatial frequency for stimulating the bipolar cell array, and the range of spatial frequencies transmitted onward to the inner plexiform layer, are thus related to the anatomical and electrical properties of the cells in the outer plexiform layer.     

A dynamic model of the receptive field of horizontal cells for monochromatic lights

Recently, the interactions between cones and horizontal cells in the turtle retina were studied and the schematic diagram of the neuronal connexions responsible for the colour coding of horizontal cells was proposed. We studied the dynamic characteristics of the receptive field of horizontal cells in the carp with a nonlinear analysis technique. In this paper we proposed a model of the receptive field of L 2- and R/G-cells in the carp for monochromatic lights on the basis of the proposed interactions and our experimental results. The spectral responses of the model were nearly coincided with the experimental ones for two monochromatic lights. The responses of the model were controlled by the recurrent action from L 2-cells to cones. Therefore, it is suggested that the recurrent action may control the spectral and spatial properties of horizontal cell responses.     

Synaptic organization and ionic basis of on and off channels in mudpuppy retina. III. A model of ganglion cell receptive field organization based on chloride-free experiments

A chloride-free environment produces selective changes in the retinal network which include a separation of on and off channels. The identification of chloride-sensitive and insensitivie neuronal activity permits identification of some of the connections and intervening polarities of synaptic interactions which are expressed in ganglion cell receptive field organization. These experiments support previous suggestions that surround antagonism is dependent on horizontal cell activity. In addition they suggest a model of the neuronal connections which subserve on-center, off-center, and on-off ganglion cells. Experimental tests of the on-off ganglion cell model favor the idea that this type of ganglion cell receives inhibitory input from amacrine cells and excitatory activation from depolarizing and hyperpolarizing bipolar cells.     

Electronic simulation of ganglion cells of generalized vertebrate cone retina

Electronic simulation of generalized vertebrate cone retina consists of 43x41 grid of red-, green-, and blue-sensitive cones. Each retinal element is simulated by a linear summator in series with a leaky integrator and spatial-temporal properties are developed by spatial organization of cone mosaic into unit hexagons and interplay of antagonistic inputs of differing time courses. Model has full compliments of horizontal and bipolar cells including color- and noncolor coding as well as single- and double-opponent receptive fields for bipolar cells. Electronic simulation also has negative feedback from L-horizontal cells to cones. Ganglion cells are formed by convergence of 7 bipolar cells, either all same and thus homogeneous, or else with a central-DPBC (or HPBC) and 6 surround-HPBCs (or DPBCs) and thus non-homogeneous. Responses of color- and non-color-coded ganglion cells as well as single- and double-opponents are investigated with stationary and moving light spots using white and colored lights. While responses to stationary light spots are predictable from digital models, responses to moving spots are complicated by differing time lags of components involved in total response. Therefore, responses to moving stimuli are more readily simulated by analogue models.     

The Gaussian derivative model for spatial-temporal vision: I. Cortical model

How do we see the motion of objects as well as their shapes? The Gaussian Derivative (GD) spatial model is extended to time to help answer this question. The GD spatio-temporal model requires only two numbers to describe the complete three-dimensional space-time shapes of individual receptive fields in primate visual cortex. These two numbers are the derivative numbers along the respective spatial and temporal principal axes of a given receptive field. Nine transformation parameters allow for a standard geometric association of these intrinsic axes with the extrinsic environment. The GD spatio-temporal model describes in one framework the following properties of primate simple cell fields: motion properties, number of lobes in space-time, spatial orientation. location, and size. A discrete difference-of-offset-Gaussians (DOOG) model provides a plausible physiological mechanism to form GD-like model fields in both space and time. The GD model hypothesizes that receptive fields at the first stage of processing in the visual cortex approximate 'derivative analyzers' that estimate local spatial and temporal derivatives of the intensity profile in the visual environment. The receptive fields as modeled provide operators that can allow later stages of processing in either a biological or machine vision system to estimate the motion as well as the shapes of objects in the environment.     

Influence of amacrine cells on receptive field organization of ganglion cells of the generalized vertebrate cone retina: Electronic simulation

Two classes of amacrine cells are simulated, small-field and large-field. Small-field amacrine cells are formed by input from a single bipolar cell, while large-field amacrine cell is formed by inputs from same 7 bipolar cells that form the ganglion cell. Only tonic amacrine cells are studied with both chromatic and luminosity types as well as double-and single-opponent receptive fields. Amacrine cells are used in both feedforward to ganglion cells and feedback to bipolar and horizontal cells. Feedback to bipolar cells or feedfoward to ganglion cells affected steady state levels in a predictable fashion. Negative feedback to bipolar cells and positive feedfoward to ganglion cells does not introduce transients to ganglion cells while negative feedback to horizontal cells and negative feedfoward does. Feedback to horizontal cells produces complex effects on bipolar, amacrine and ganglion cells dependent on such factors as center-surround field balance and negative feedback from luminosity type of horizontal cell to cones.     

Characteristics of bipolar-bipolar coupling in the carp retina

ON and OFF bipolar cells were identified in the light-adapted carp retina by means of intracellular recording and Lucifer yellow dye injection. The receptive field centers, determined by measuring the response amplitudes obtained by centered spots of different diameters, were 0.3-1.0 mm for ON bipolar cells and 0.3-0.4 mm for OFF bipolar cells. These central receptive field values were much larger than the dendritic field diameters measured by histological methods. Simultaneous intracellular recordings were made from pairs of neighboring bipolar cells. Current of either polarity injected into one member of a bipolar cell pair elicited a sign-conserving, sustained potential change in the other bipolar cell. The coupling efficiency was nearly identical for both depolarizing and hyperpolarizing currents. The maximum separation of coupled bipolar cells was approximately 130 microns. This electrical coupling was reciprocal and summative, and it was observed in cell types of similar function and morphology. Dye coupling was observed in 4 out of 34 stained cells. These results strongly suggest that there is a spatial summation of signals at the level of bipolar cells, which makes their central receptive fields much larger than their dendritic fields.     

Receptive field mechanisms of cat X and Y retinal ganglion cells

We investigated receptive field properties of cat retinal ganglion cells with visual stimuli which were sinusoidal spatial gratings amplitude modulated in time by a sum of sinusoids. Neural responses were analyzed into the Fourier components at the input frequencies and the components at sum and difference frequencies. The first-order frequency response of X cells had a marked spatial phase and spatial frequency dependence which could be explained in terms of linear interactions between center and surround mechanisms in the receptive field. The second-order frequency response of X cells was much smaller than the first-order frequency response at all spatial frequencies. The spatial phase and spatial frequency dependence of the first-order frequency response in Y cells in some ways resembled that of X cells. However, the Y first-order response declined to zero at a much lower spatial frequency than in X cells. Furthermore, the second-order frequency response was larger in Y cells; the second-order frequency components became the dominant part of the response for patterns of high spatial frequency. This implies that the receptive field center and surround mechanisms are physiologically quite different in Y cells from those in X cells, and that the Y cells also receive excitatory drive from an additional nonlinear receptive field mechanism.     

Spatial asymmetries in cat retinal ganglion cell responses

. Enroth-Cugell and Robson (1966) first proposed a classification of retinal ganglion cells into X cells, which exhibit approximate linear spatial summation and largely sustained responses, and Y cells, which exhibit nonlinearities and transient responses. Gaudiano (1992a, 1992b, 1994) has suggested that the dominant characteristics of both X and Y cells can be simulated with a single model simply by changing receptive field profiles to match those of the anatomical counterparts of X and Y cells. He also proposed that a significant component of the spatial nonlinearities observed in Y (and sometimes X) cells can result from photoreceptor nonlinearities coupled with push-pull bipolar connections. Specifically, an asymmetry was predicted in the ganglion cell response to rectangular gratings presented at different locations in the receptive field under two conditions: introduction/withdrawal (on-off) or contrast reversal. When measuring the response to these patterns as a function of spatial phase, the standard difference-of-Gaussians model predicts symmetrical responses about the receptive field center, while the push-pull model predicts slight but significant asymmetry in the on-off case only. To test this hypothesis, we have recorded ganglion cell responses from the optic tract fibers of anesthetized cat. The mean and standard deviations of responses to on-off and contrast-reversed patterns were compared. We found that all but one of the cells that yielded statistically significant data confirmed the hypothesis. These results largely support the theoretical prediction. Received: 21 March 1997 / Accepted in revised form: 6 May 1998     

Spatiotemporal testing and modeling of catfish retinal neurons.

The responses of retinal neurons depend on the interaction of both temporal and spatial aspects of a light stimulus. We developed a linear spatiotemporal model of receptor and horizontal cell layers in the catfish retina based on reciprocal interactions between both layers and coupling within each. Horizontal cell transfer properties were measured experimentally using white-noise intensity modulated light spots of different diameters and were compared with analytical predictions based on the model. Good agreement was obtained with a reasonable choice of model space-constants and feedback parameters. Furthermore, the same set of parameter values determined from spot experiments enabled accurate prediction of experimental horizontal cell responses to traveling gratings. The proposed feedback connections from horizontal cells to receptors quicken the time-course of responses in both layers and sharpen receptive fields.