Cone receptive field in cat retina computed from microcircuitry

A dynamical adaptation model of visual spatiotemporal processing in cones and horizontal cells

In this work, we introduce a phenomenological model for the cone-horizontal cell assembly, including spatial integration and formation of receptive field-like structures. The model extends our previous dynamical adaptation description with gain control accounting for processes in single cones, valid in severe nonlinear regimes. Here, a spatially extended feedback mechanism is introduced from horizontal cells to cones to account for experimental evidence, contributing thus to the development of a center-surround receptive field in cones and downstream bipolar cells. Feedback gain is defined on different spatial scales by weighting spatial filters: a short scale accounting for cone input to the feedback mechanism and a large scale driven by the syncytium characteristics of horizontal cells. A third spatial scale improves the description, mimicking neighboring cone-cone coupling. This overall spatial integration couples to temporal signal processing, thus obtaining a spatiotemporal model of outer retina responses capable of reproducing nonlinear features in both dimensions (space and time). The model was tested and validated using measurements on horizontal cells from different studies, with excellent performance. By its phenomenological nature, signal processing properties are inferred from model parameters. The model can be used in arrays of processing units with more complex incoming patterns of visual stimuli.

Influence of Aging on the Retina and Visual Motion Processing for Optokinetic Responses in Mice

The decline in visual function due to normal aging impacts various aspects of our daily lives. Previous reports suggest that the aging retina exhibits mislocalization of photoreceptor terminals and reduced amplitudes of scotopic and photopic electroretinogram (ERG) responses in mice. These abnormalities are thought to contribute to age-related visual impairment; however, the extent to which visual function is impaired by aging at the organismal level is unclear. In the present study, we focus on the age-related changes of the optokinetic responses (OKRs) in visual processing. Moreover, we investigated the initial and late phases of the OKRs in young adult (2-3 months old) and aging mice (21-24 months old). The initial phase was evaluated by measuring the open-loop eye velocity of OKRs using sinusoidal grating patterns of various spatial frequencies (SFs) and moving at various temporal frequencies (TFs) for 0.5 s. The aging mice exhibited initial OKRs with a spatiotemporal frequency tuning that was slightly different from those in young adult mice. The late-phase OKRs were investigated by measuring the slow-phase velocity of the optokinetic nystagmus evoked by sinusoidal gratings of various spatiotemporal frequencies moving for 30 s. We found that optimal SF and TF in the normal aging mice are both reduced compared with those in young adult mice. In addition, we measured the OKRs of 4.1G-null (4.1G ^-/-) mice, in which mislocalization of photoreceptor terminals is observed even at the young adult stage. We found that the late phase OKR was significantly impaired in 4.1G ^{- / -} mice, which exhibit significantly reduced SF and TF compared with control mice. These OKR abnormalities observed in 4.1G ^{- / -} mice resemble the abnormalities found in normal aging mice. This finding suggests that these mice can be useful mouse models for studying the aging of the retinal tissue and declining visual function. Taken together, the current study demonstrates that normal aging deteriorates to visual motion processing for both the initial and late phases of OKRs. Moreover, it implies that the abnormalities of the visual function in the normal aging mice are at least partly due to mislocalization of photoreceptor synapses.

Role of the mouse retinal photoreceptor ribbon synapse in visual motion processing for optokinetic responses

The ribbon synapse is a specialized synaptic structure in the retinal outer plexiform layer where visual signals are transmitted from photoreceptors to the bipolar and horizontal cells. This structure is considered important in high-efficiency signal transmission; however, its role in visual signal processing is unclear. In order to understand its role in visual processing, the present study utilized Pikachurin-null mutant mice that show improper formation of the photoreceptor ribbon synapse. We examined the initial and late phases of the optokinetic responses (OKRs). The initial phase was examined by measuring the open-loop eye velocity of the OKRs to sinusoidal grating patterns of various spatial frequencies moving at various temporal frequencies for 0.5 s. The mutant mice showed significant initial OKRs with a spatiotemporal frequency tuning (spatial frequency, 0.09 ± 0.01 cycles/°; temporal frequency, 1.87 ± 0.12 Hz) that was slightly different from the wild-type mice (spatial frequency, 0.11 ± 0.01 cycles/°; temporal frequency, 1.66 ± 0.12 Hz). The late phase of the OKRs was examined by measuring the slow phase eye velocity of the optokinetic nystagmus induced by the sinusoidal gratings of various spatiotemporal frequencies moving for 30 s. We found that the optimal spatial and temporal frequencies of the mutant mice (spatial frequency, 0.11 ± 0.02 cycles/°; temporal frequency, 0.81 ± 0.24 Hz) were both lower than those in the wild-type mice (spatial frequency, 0.15 ± 0.02 cycles/°; temporal frequency, 1.93 ± 0.62 Hz). These results suggest that the ribbon synapse modulates the spatiotemporal frequency tuning of visual processing along the ON pathway by which the late phase of OKRs is mediated.

Ideal observer analysis of signal quality in retinal circuits

The function of the retina is crucial, for it must encode visual signals so the brain can detect objects in the visual world. However, the biological mechanisms of the retina add noise to the visual signal and therefore reduce its quality and capacity to inform about the world. Because an organism's survival depends on its ability to unambiguously detect visual stimuli in the presence of noise, its retinal circuits must have evolved to maximize signal quality, suggesting that each retinal circuit has a specific functional role. Here we explain how an ideal observer can measure signal quality to determine the functional roles of retinal circuits. In a visual discrimination task the ideal observer can measure from a neural response the increment threshold, the number of distinguishable response levels, and the neural code, which are fundamental measures of signal quality relevant to behavior. It can compare the signal quality in stimulus and response to determine the optimal stimulus, and can measure the specific loss of signal quality by a neuron's receptive field for non-optimal stimuli. Taking into account noise correlations, the ideal observer can track the signal-to-noise ratio available from one stage to the next, allowing one to determine each stage's role in preserving signal quality. A comparison between the ideal performance of the photon flux absorbed from the stimulus and actual performance of a retinal ganglion cell shows that in daylight a ganglion cell and its presynaptic circuit loses a factor of approximately 10-fold in contrast sensitivity, suggesting specific signal-processing roles for synaptic connections and other neural circuit elements. The ideal observer is a powerful tool for characterizing signal processing in single neurons and arrays along a neural pathway.

A two pathway model for tonic suppressed-by-contrast cells in the cat retina

A two pathway spatiotemporal model is proposed to describe the function of tonic suppressed-by-contrast cells of the cat retina. The model is able to describe the experimentally determined responses of such neurons to drifting sinusoidal gratings. It is also able to predict their responses to alternating sinusoidal gratings and flashing or moving spots of light, and these predictions resemble experimental observations, at least qualitatively. The model is physiologically plausible, it can be used to summarize the dynamic responses of the tonic suppressed-by-contrast cells of the cat and potentially to account for the responses of the suppressed-by-contrast cells of other species.

How robust is a neural circuit?

Design in engineering begins with the problem of robustness-by what factor should intrinsic capacity exceed normal demand? Here we consider robustness for a neural circuit that crosses the retina from cones to ganglion cells. The circuit's task is to represent the visual scene at many successive stages, each time by modulating a stream of stochastic events: photoisomerizations, then transmitter quanta, then spikes. At early stages, the event rates are high to achieve some critical signal-to-noise ratio and temporal bandwidth, which together set the information rate. Then neural circuits concentrate the information and repackage it, so that nearly the same total information can be represented by modulating far lower event rates. This is important for spiking because of its high metabolic cost. Considering various measurements at the outer and inner retina, we conclude that the "safety factors" are about 2-10, similar to other tissues.

Retinal bipolar cell input mechanisms in giant danio. I. Electroretinographic analysis

Electroretinograms (ERGs) were recorded from the giant danio (Danio aequipinnatus) to study glutamatergic input mechanisms onto bipolar cells. Glutamate analogs were applied to determine which receptor types mediate synaptic transmission from rods and cones to on and off bipolar cells. Picrotoxin, strychnine, and tetrodotoxin were used to isolate the effects of the glutamate analogs to the photoreceptor-bipolar cell synapse. Under photopic conditions, the group III metabotropic glutamate receptor (mGluR) antagonist (RS)-alpha-cyclopropyl-4-phosphonophenylglycine (CPPG) only slightly reduced the b-wave, whereas the excitatory amino acid transporter (EAAT) blocker dl-threo-beta-benzyl-oxyaspartate (TBOA) removed most of it. Complete elimination of the b-wave required both antagonists. The alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA)/kainate receptor antagonist 2,3-dioxo-6-nitro-1,2,3,4-tetrahydrobenzo[f]quinoxaline-7-sulfonamide (NBQX) blocked the d-wave. Under scotopic conditions, rod and cone inputs onto on bipolar cells were studied by comparing the sensitivities of the b-wave to photopically matched green and red stimuli. The b-wave was >1 log unit more sensitive to the green than to the red stimulus under control conditions. In CPPG or l-AP4 (l-(+)-2-amino-4-phosphonobutyric acid, a group III mGluR agonist), the sensitivity of the b-wave to the green stimulus was dramatically reduced and the b-waves elicited by the 2 stimuli became nearly matched. The d-wave elicited by dim green stimuli, which presumably could be detected only by the rods, was eliminated by NBQX.

IN CONCLUSION

1) cone signals onto on bipolar cells involve mainly EAATs but also mGluRs (presumably mGluR6) to a lesser extent; 2) rods signal onto on bipolars by mainly mGluR6; 3) off bipolar cells receive signals from both photoreceptor types by AMPA/kainate receptors.

The influence of different retinal subcircuits on the nonlinearity of ganglion cell behavior

Y-type retinal ganglion cells show a pronounced, nonlinear, frequency-doubling behavior in response to modulated sinewave gratings. This is not observed in X-type cells. The source of this spatial nonlinear summation is still under debate. We have designed a realistic biophysical model of the cat retina to test the influence of different retinal cell classes and subcircuits on the linearity of ganglion cell responses. The intraretinal connectivity consists of the fundamental feedforward pathway via bipolar cells, lateral horizontal cell connectivity, and two amacrine circuits. The wiring diagram of X- and Y-cells is identical apart from two aspects: (1) Y-cells have a wider receptive field and (2) they receive input from a nested amacrine circuit consisting of narrow- and wide-field amacrine cells. The model was tested with contrast-reversed gratings. First and second harmonic response components were determined to estimate the degree of nonlinearity. By means of circuit dissection, we found that a high degree of the Y-cell nonlinear behavior arises from the spatial integration of temporal photoreceptor nonlinearities. Furthermore, we found a weaker and less uniform influence of the nested amacrine circuit. Different sources of nonlinearities interact in a multiplicative manner, and the influence of the amacrine circuit is approximately 25% weaker than that of the photoreceptor. The model predicts that significant nonlinearities occur already at the level of horizontal cell responses. Pharmacological inactivation of the amacrine circuit is expected to exert a milder effect in reducing ganglion cell nonlinearity.

Parallel Circuits from Cones to the On-Beta Ganglion Cell

Neural integration depends critically upon circuit architecture; yet the architecture has never been established quantitatively (numbers of cells and synapses) for any vertebrate local circuit. Here we describe circuits in the cat retina that connect cones to the on-beta ganglion cell. This cell type is important because on- and off-beta cells contribute about 50% of the optic nerve fibres and the major retinal input to the striate cortex. Three adjacent on-beta cells in the area centralis and their bipolar connections to cones were reconstructed from electron micrographs of 279 serial sections. The beta dendritic field is 34+/-2 microm in diameter and encompasses 35 cones. All of these cones connect to the beta cell via 14 - 17 bipolar cells. These bipolar cells were shown previously by cluster analysis to be of four types (b1 - b4); three of these types (b1, b2 and b3) provided 97% of the bipolar contacts to the beta cell, in the ratio 4:2:1. On average, bipolar cells nearest the centre of the beta dendritic field contribute more synapses than those towards the edge, but the peaked distribution of bipolar synapses across the dendritic field is only slightly broader than the optical pointspread function of the cat's eye, and is narrower by half than the centre of the ganglion cell receptive field. This implies that the distribution of bipolar synapses across the beta cell dendritic field contributes little to the extent or shape of the receptive field. Since all three bipolar circuits connect to the same set of cones, they must carry the same spatial and chromatic information; they might convey different temporal frequencies. The numbers of bipolar synapses (mean +/- SD=154+/-8) and amacrine synapses (59 +/- 5) converging on three adjacent beta cellsare remarkably constant (SD approximately +/-5% of the mean). Thus, as the circuits repeat locally, the fundamental design is accurately reproduced.

The receptive fields of cat retinal ganglion cells in physiological and pathological states: where we are after half a century of research

Studies on the receptive field properties of cat retinal ganglion cells over the past half-century are reviewed within the context of the role played by the receptive field in visual information processing. Emphasis is placed on the work conducted within the past 20 years, but a summary of key contributions from the 1950s to 1970s is provided. We have sought to review aspects of the ganglion cell receptive field that have not been featured prominently in previous review articles. Our review of the receptive field properties of X- and Y-cells focuses on quantitative studies and includes consideration of the function of the receptive field in visual signal processing. We discuss the non-classical as well as the classical receptive field. Attention is also given to the receptive field properties of the less well-studied cat ganglion cells-the W-cells-and the effect of pathology on cat ganglion cell properties. Although work from our laboratories is highlighted, we hope that we have given a reasonably balanced view of the current state of the field.

Center surround receptive field structure of cone bipolar cells in primate retina

In non-mammalian vertebrates, retinal bipolar cells show center-surround receptive field organization. In mammals, recordings from bipolar cells are rare and have not revealed a clear surround. Here we report center-surround receptive fields of identified cone bipolar cells in the macaque monkey retina. In the peripheral retina, cone bipolar cell nuclei were labeled in vitro with diamidino-phenylindole (DAPI), targeted for recording under microscopic control, and anatomically identified by intracellular staining. Identified cells included 'diffuse' bipolar cells, which contact multiple cones, and 'midget' bipolar cells, which contact a single cone. Responses to flickering spots and annuli revealed a clear surround: both hyperpolarizing (OFF) and depolarizing (ON) cells responded with reversed polarity to annular stimuli. Center and surround dimensions were calculated for 12 bipolar cells from the spatial frequency response to drifting, sinusoidal luminance modulated gratings. The frequency response was bandpass and well fit by a difference of Gaussians receptive field model. Center diameters were all two to three times larger than known dendritic tree diameters for both diffuse and midget bipolar cells in the retinal periphery. In one instance intracellular staining revealed tracer spread between a recorded cell and its nearest neighbors, suggesting that homotypic electrical coupling may contribute to receptive field center size. Surrounds were around ten times larger in diameter than centers and in most cases the ratio of center to surround strength was approximately 1. We suggest that the center-surround receptive fields of the major primate ganglion cell types are established at the bipolar cell, probably by the circuitry of the outer retina.

The AII amacrine network: coupling can increase correlated activity

Retinal ganglion cells in the cat respond to single rhodopsin isomerizations with one to three spikes. This quantal signal is transmitted in the retina by the rod bipolar pathway: rod-->rod bipolar-->AII-->cone bipolar-->ganglion cell. The two-dimensional circuit underlying this pathway includes extensive convergence from rods to an AII amacrine cell, divergence from a rod to several AII and ganglion cells, and coupling between the AII amacrine cells. In this study we explored the function of coupling by reconstructing several AII amacrine cells and the gap junctions between them from electron micrographs; and simulating the AII network with and without coupling. The simulation showed that coupling in the AII network can: (1) improve the signal/noise ratio in the AII network; (2) improve the signal/noise ratio for a single rhodopsin isomerization striking in the periphery of the ganglion cell receptive field center, and therefore in most ganglion cells responding to a single isomerization; (3) expand the AII and ganglion cells' receptive field center; and (4) expand the "correlation field". All of these effects have one major outcome: an increase in correlation between ganglion cell activity. Well correlated activity between the ganglion cells could improve the brain's ability to discriminate few absorbed external photons from the high background of spontaneous thermal isomerizations. Based on the possible benefits of coupling in the AII network, we suggest that coupling occurs at low scotopic luminances.

Parallel cone bipolar to on-beta ganglion cell pathways in the cat retina: spatial responses, spatial aliasing, and spatial variance

An important issue in understanding the retina is finding candidate functional roles for different cell pathways and the details of their anatomy and physiology. We consider various spatial properties of the three main cone ==> cone bipolar cell ==> on-beta ganglion cell pathways in the cat retina and possible roles for the particulars of their anatomy. The cone bipolar cells in these pathways have distinct morphologies and modest differences in their convergence, divergence, densities, and synaptic weighting; and it is unclear whether the pathways differ in their spatial properties or in some other manner. Since differences in spatial processing of cells are best studied on a systemwide level, we developed the multirate filter-based method of retinal modeling, a technique for relating the anatomy of multiple cell layers to its systemic effects. We demonstrate that (1) despite the anatomic distinctions among the three main cone bipolar cell pathways, their spatial responses are essentially identical; (2) despite the spatial averaging in the pathways, there is essentially no filtering of the nonaliasing signal components after the cone layer; (3) instead, this averaging combined with prefiltering by the eye's optics and cone gap junctions prevents spatial aliasing; and (4) the averaging and prefiltering combined allow cell responses to be similar despite significant cell-to-cell anatomic differences.

Simulation of an anatomically defined local circuit: the cone-horizontal cell network in cat retina

The outer plexiform layer of the retina contains a neural circuit in which cone synaptic terminals are electrically coupled and release glutamate onto wide-field and narrow-field horizontal cells. These are also electrically coupled and feed back through a GABAergic synapse to cones. In cat this circuit's structure is known in some detail, and much of the chemical architecture and neural responses are also known, yet there has been no attempt to synthesize this knowledge. We constructed a large-scale compartmental model (up to 50,000 compartments) to incorporate the known anatomical and biophysical facts. The goal was to discover how the various circuit components interact to form the cone receptive field, and thereby what possible function is implied. The simulation reproduced many features known from intracellular recordings: (1) linear response of cone and horizontal cell to intensity, (2) some aspects of temporal responses of cone and horizontal cell, (3) broad receptive field of the wide-field horizontal cell, and (4) center-surround cone receptive field (derived from a "deconvolution model"). With the network calibrated in this manner, we determined which of its features are necessary to give the cone receptive field a Gaussian center-surround shape. A Gaussian-like center that matches the center derived from the ganglion cell requires both optical blur and cone coupling: blur alone is too narrow, coupling alone gives an exponential shape without a central dome-shaped peak. A Gaussian-like surround requires both types of horizontal cell: the narrow-field type for the deep, proximal region and the wide-field type for the shallow, distal region. These results suggest that the function of the cone-horizontal cell circuit is to reduce the influence of noise by spatio-temporally filtering the cone signal before it passes through the first chemical synapse on the pathway to the brain.

Directional hyperacuity in ganglion cells of the rabbit retina

Biological visual systems can detect positional changes that are finer than these systems' acuity to sine-wave gratings, a property known as hyperacuity. Some systems can even detect changes finer that the photoreceptor spacing. We report here that rabbit's directionally selective ganglion cells not only detect positional changes in the hyperacuity range, but also discriminate the direction of their motion. Our experiments show that directional selectivity occurs for edges of light moving as little as 1.1 microns (26" of visual angle) across the retina. This distance corresponds to a hyperacuity, since the acuity to sine-wave gratings of rabbit's On-Off DS ganglion cells is about 125 microns (50'). In addition, this distance is smaller than the minimal spacing between rabbit photoreceptors (1.9 microns or 46"), as estimated from cell-density studies (Young & Vaney, 1991). Such a hyperacuity suggests low-noise high-gain signal transmission from photoreceptors to ganglion cells and that directional selectivity can arise in small portions of retinal dendritic processes.

Subcellular localization of GABAA receptor on bipolar cells in macaque and human retina

The subcellular distribution of GABAA receptor in the macaque and human retina was studied by immunocytochemistry with monoclonal antibodies for the alpha and beta subunits with a particular focus on bipolar cells. Immunoreactivity to GABAA receptor was present on dendritic tips of all bipolar cells. The stain was strongest on bipolar membranes in apposition to horizontal cell processes. Stain was concentrated on the tips of flat and invaginating cone bipolar cells at the base of the cone pedicle and on the invaginating tips of rod bipolar cells. Stain on the cone pedicle membrane was restricted to sites of apposition to stained bipolar dendrites; pedicle membrane in apposition to horizontal cell processes was unstained. Stain was also present on bipolar axon terminals in both on and off strata of the inner plexiform layer. All bipolar cell somas stained faintly; horizontal and Müller cell somas were unstained. The alpha and beta subunits distributed similarly in monkey and human retina. Presence of GABAA receptor on the bipolar dendritic tips suggests that horizontal cells directly affect bipolar cells. Thus, GABAA receptor might mediate the receptive field surround of both off and on bipolar cells. Presence of GABAA receptor on bipolar axon terminals suggests that much of the inhibition feeding back from GABAergic amacrine to bipolar cells is GABAA-mediated.

Conductances evoked by light in the ON-beta ganglion cell of cat retina

When a bar of light (215 x 5000 microns) illuminates the receptive field of an ON-beta ganglion cell of cat retina, the cell depolarizes. Intracellular recording from the cat eyecup preparation shows that this depolarization is due to an increase in conductance (2.4 +/- 0.6 nS). Different phases of this depolarization have different reversal potentials, but all of these reversal potentials are more positive than the cell's resting potential in the dark. When the light is turned on, there is an initial transient depolarization; the reversal potential measured for this transient is positive (23 +/- 11 mV). As the light is left on, the cell partially repolarizes to a sustained depolarization; the reversal potential measured for this sustained depolarization is close to zero (-1 +/- 5 mV). When the light is turned off, the cell repolarizes further; the reversal potential measured for this repolarization is negative (-18 +/- 7 mV), but still above the resting potential in the dark (-50 mV). To explain this variety of reversal potentials, at least two different synaptic conductances are required: one to ions which have a positive reversal potential and another to ions which have a negative reversal potential. Comparing the responses to broad and narrow bars suggests that these two conductances are associated with the center and surround, respectively. Finally, since an ON-beta cell in the area centralis receives about 200 synapses, these results indicate that a single synapse produces an average conductance increase of about 15 pS during a near-maximal depolarization.

Synaptic feedback, depolarization, and color opponency in cone photoreceptors

For some 20 years, synaptic feedback from horizontal cells to cones has often been invoked, more or less convincingly, in discussions of retinal action and vision. However, feedback in cones has proved to be rather complex and difficult to study experimentally. The mechanisms and consequences of feedback are therefore still only partly understood. This review attempts to assess the knowns and unknowns. The limitations of the evidence for feedback are reviewed to support the position that unequivocal evidence still largely rests on intracellular recording from cones. Of the three distinct types of depolarization observed in cones, the graded depolarization is taken as the fundamental manifestation of feedback. The evidence for the hypothesis that GABA is the neurotransmitter for feedback appears reasonably strong but several complications will have to be resolved to make the hypothesis more secure. There is evidence that feedback contributes to aspects of light adaptation and spatiotemporal processing of visual information. The contributions seem modest in magnitude. The role of feedback in shaping the color-opponent responses of retinal neurons is evaluated with particular emphasis on pharmacological studies, spatial and temporal aspects of the response of chromatic horizontal cells, and the enigmatic nature of depolarizations in blue- and green-sensitive cones. On this and other evidence, it is suggested that feedback may impress some detectable wavelength dependency in some cones but the dominant mechanisms for color opponency probably reside beyond the photoreceptors.

Signal sampling and propagation through multiple cell layers in the retina: modeling and analysis with multirate filtering

The retina is a multilayered structure. Each layer consists of one or more classes of cell, each at its own density and with its own anatomic and physiologic properties. Signals converge from many cells in one layer onto single cells in another layer, and a signal from a single cell diverges to many cells in the next layer. In this methods paper we develop a general approach to retinal analysis and modeling that incorporates multiple cell classes, their densities, and related anatomic properties. The method is based on multirate filtering, a branch of signal processing in which signals of different sampling rates are manipulated. By drawing a correspondence between cell density and signal sampling rate, we define multirate models that incorporate different cell densities, convergence, divergence, variation in dendritic field shape, cell-to-cell variation in synaptic weights, and other anatomic features. We develop the multirate approach and apply it to the cat cone-->cone bipolar CBb1-->on-beta ganglion cell pathway as an example. We calculate the spatial frequency responses of the CBb1 and on-beta cells based on the cone spatial frequency response and find that the attenuation of high frequencies in the cones prevents aliasing that would otherwise occur in CBb1 and on-beta cells. We compare the calculations with cat psychophysics. We show that the optics of the cat eye are insufficient in themselves for the prevention of aliasing in these cells; additional attenuation by the cone-cone gap junctions and the cone aperture is necessary. By including this postreceptoral filtering, we demonstrate that the highest spatial frequency that can be passed by the retina without aliasing is determined not always only by the densities of cones, bipolar cells, and ganglion cells but also by the synaptic and the dendritic weighting between these cells.

Packing geometry of human cone photoreceptors: variation with eccentricity and evidence for local anisotropy

Disorder in the packing geometry of the human cone mosaic is believed to help alleviate spatial aliasing effects. To characterize cone packing geometry, we gathered positions of cone inner segments at seven locations along four primary and two oblique meridians in an adult human retina. We generated statistical descriptors based on the distribution of distances and angles to Voronoi neighbors. Parameters of a compressed-jittered model were fit to the actual mosaic. Local anisotropies were investigated using correlograms. We find that (1) median distance between Voronoi neighbors increases with eccentricity, but the minimum distance is constant (6-8 microns) across peripheral retina; (2) the cone mosaic is least compressed and jittered at the edge of the foveal rod-free zone; (3) disorder in the foveal center resembles that described by Pum et al. (1990); (4) cone spacing is 10-15% less in one direction than in the orthogonal direction; and (5) cone spacing is greater in the radial direction (along meridians) than in the tangential direction (along lines of isoeccentricity). The nearly constant minimum distance implies that high spatial frequencies may be sampled even in peripheral retina. Local anisotropy of the cone mosaic is discussed in relation to the growth of the primate retina during development and to the orientation biases of retinal ganglion cells.

NeuronC: a computational language for investigating functional architecture of neural circuits

A computational language was developed to simulate neural circuits. A model of a neural circuit with up to 50,000 compartments is constructed from predefined parts of neurons, called "neural elements". A 2-dimensional (2-D) light stimulus and a photoreceptor model allow simulating a visual physiology experiment. Circuit function is computed by integrating difference equations according to standard methods. Large-scale structure in the neural circuit, such as whole neurons, their synaptic connections, and arrays of neurons, are constructed with procedural rules. The language was evaluated with a simulation of the receptive field of a single cone in cat retina, which required a model of cone-horizontal cell network on the order of 1000 neurons. The model was calibrated by adjusting biophysical parameters to match known physiological data. Eliminating specific synaptic connections from the circuit suggested the influence of individual neuron types on the receptive field of a single cone. An advantage of using neural elements in such a model is to simplify the description of a neuron's structure. An advantage of using procedural rules to define connections between neurons is to simplify the network definition.

Computational model of the on-alpha ganglion cell receptive field based on bipolar cell circuitry

The on-alpha ganglion cell in the area centralis of the cat retina receives approximately 450 synapses from type b1 cone bipolar cells. This bipolar type forms a closely spaced array (9 microns), which contributes from 1 to 7 synapses per b1 cell throughout the on-alpha dendritic field. Here we use a compartmental model of an on-alpha cell, based on a reconstruction from electron micrographs of serial sections, to compute the contribution of the b1 array to the on-alpha receptive field. The computation shows that, for a physiologic range of specific membrane resistance (9500-68,000 omega.cm2) and a linear synapse, inputs are equally effective at all points on the on-alpha dendritic tree. This implies that the electrotonic properties of the dendritic tree contribute very little to the domed shapes of the receptive field center and surround. Rather, these shapes arise from the domed distribution of synapses across the on-alpha dendritic field. Various sources of "jitter" in the anatomical circuit, such as variation in bipolar cell spacing and fluctuations in the number of synapses per bipolar cell, are smoothed by the overall circuit design. However, the computed center retains some minor asymmetries and lumps, due to anatomical jitter, as found in actual alpha-cell receptive fields.

Convergence and divergence of cones onto bipolar cells in the central area of cat retina

In the central area of cat retina the cone bipolar cells that innervate sublamina b of the inner plexiform layer comprise five types, four with narrow dendritic fields and one with a wide dendritic field. This was shown in the preceding paper (Cohen & Sterling 1990 a) by reconstruction from electron micrographs of serial sections. Here we show by further analysis of the same material that the coverage factor (dendritic spread x cell density) is about one for each of the narrow-field types (b1, b2, and b4). The same is probably true for the other narrow-field type (b3), but this could not be proved because its dendrites were too fine to trace. The dendrites of types b1, b2, and b4 collect from all the cone pedicles within their reach and do not bypass local pedicles in favour of more distant ones. The dendrites of type b5, the wide-field cell, bypass many pedicles. On average 5.1 +/- 1.0 pedicles coverage on a b1 bipolar cell; 6.0 +/- 1.2 converge on a b2 cell and 5.7 +/- 1.5 converge on a b4 cell. Divergence within a type is minimal: one pedicle contacts only 1.2 b1 cells, 1.0 b2 cells, and 1.0 b4 cells. Divergence across types is broad: each pedicle apparently contacts all four types of the narrow-field bipolar cells that innervate sublamina b. Each pedicle probably also contacts an additional 4-5 types of narrow-field bipolar cell that innervate sublamina a. There are several possible advantages to encoding the cone signal into multiple, parallel, narrow-field pathways.(ABSTRACT TRUNCATED AT 250 WORDS)