In this paper we give necessary and sufficient optimality conditions for a vectoroptimization problem over cones involving support functions in objective as well asconstraints, using cone-convex and other related functions. We also associate a unifieddual to the primal problem and establish weak, strong and converse duality results. Anumber of previously studied problems appear as special cases.

At certain temporal frequencies, the human cone flicker electroretinogram (ERG) contains multiple additional responses following the termination of a flicker train. The purpose of this study was to determine whether these poststimulus responses are a continuing response to the terminated flicker train or represent the oscillation of a resonant system. ERGs were recorded from 10 visually normal adults in response to full-field sinusoidally modulated flicker trains presented against a short-wavelength rod-saturating adapting field. The amplitude and timing properties of the poststimulus responses were evaluated within the context of a model of a second-order resonant system. At stimulus frequencies between 41.7 and 71.4 Hz, the majority of subjects showed at least three additional ERG responses following the termination of the flicker train. The interval between the poststimulus responses was approximately constant across stimulus frequency, with a mean of 14.4 ms, corresponding to a frequency of 69.4 Hz. The amplitude and timing characteristics of the poststimulus ERG responses were well described by an underdamped second-order system with a resonance frequency of 70.3 Hz. The observed poststimulus ERG responses may represent resonant oscillations of retinal ON bipolar cells, as has been proposed for electrophysiological recordings of poststimulus responses from retinal ganglion cells. However, further investigation is required to determine the types of retinal neurons involved in the generation of the poststimulus responses of the human flicker ERG.

Acetylcholine is present in and released from starburst amacrine cells in the inner plexiform layer (IPL), but its role in retinal function except, perhaps, in early development, is unclear. Nicotinic acetylcholine receptors are thought to be present on ganglion, amacrine, and bipolar cell processes in the IPL, and it is known that acetylcholine increases the spontaneous and light-evoked responses of retinal ganglion cells. The effects of acetylcholine on bipolar cells are not known, and here we report the effects of nicotine on the b-wave of the electroretinogram in larval zebrafish. The b-wave originates mainly from ON-bipolar cells, and the larval zebrafish retina is cone-dominated. Only small rod responses can be elicited with dim lights in wild-type larval zebrafish retinas, but rod responses can be recorded over a range of intensities in a mutant (no optokinetic response f) fish that has no cone function. We find that nicotine strongly enhances cone-driven b-wave response amplitudes but depresses rod driven b-wave response amplitudes without, however, affecting rod- or cone-driven b-wave light sensitivity.

Much of what is currently known about the visual response of retinal bipolar cells is based on studies of rod-dominant responses to flashes in the dark in the isolated retina. This minireview summarizes quantitative findings on contrast processing in the intact light-adapted retina based on intracellular recording from more than 400 cone-driven bipolar cells in the tiger salamander: 1) In the main, the contrast responses of ON and OFF cells are surprisingly similar, suggesting a need to refine the view that ON and OFF cells provide the selective substrates for processing of positive and negative contrasts, respectively. 2) Overall, the response is quite nonlinear, showing very high gain for small contrasts, some 10–15 times greater than that of cones, but then quickly approaches saturation for higher contrasts. 3) Under optimal conditions of light adaptation, both classes of bipolar cells show evidence for efficient coding with respect to the contrasts in natural images. 4) There is a marked diversity within both the ON and OFF bipolar cell populations and an absence of discrete subtypes. The dynamic ranges bracket the range of contrasts in nature. 5) For both ON and OFF cells, the receptive field organization shows a striking symmetry between center and surround for responses of the same polarity and thus opposite contrast polarities. 6) The latency difference between ON and OFF cells is about 30 ms, which seems qualitatively consistent with a delay due to the G-protein cascade in ON bipolar cells. 7) In sum, we report quantitative evidence for at least 11 transformations in signal processing that occur between the voltage response of cones and the voltage response of bipolar cells.

Dopaminergic interplexiform cells in the retina of the blue acara were investigated using an antiserum against tyrosine hydroxylase and PAP visualization. In whole-mount preparations, we observed a homogeneous distribution of cell bodies throughout the retina without any indication of regional specialization. At the fine and ultrastructural level, we studied the morphology of labeled telodendria within the outer plexiform layer. Apart from contacts with horizontal cell perikarya and bipolar cell dendrites, we observed direct contacts, mostly in the form of close appositions, with cone pedicles and rod spherules. Quantitative evaluation and reconstruction of serial sections showed that all cone pedicles and most rod terminals were approached in this way. The dopaminergic pathway terminating on horizontal cells and photoreceptors is discussed with respect to the localization of dopamine receptors in the outer retina, and the control of adaptive changes such as retinomotor movements, spinule formation, and horizontal cell coupling.

This study examines the spatiotemporal relationships between retinal pigment epithelium (RPE) and photoreceptors (PR) during development of Macaca nemestrina retina. Our aim was to learn more about the developmental dynamics of these two important cell populations, particularly whether developmental changes in RPE cell densities mimic those of PR at selected retinal points. Twelve eyes ranging in age from 100 fetal days (Fd) to adulthood were flatmounted; the retinal perimeters were traced; and then sample punches were taken of the RPE and neural retina at the fovea, optic disc, mid- and far-nasal periphery, and far temporal, inferior and superior periphery. The two tissues were gently separated and the RPE cells and photoreceptors from the same region of the punch were counted using Nomarski contrast interference optics. We found that the total number of cones remains stable around 4 million between Fd100 and adulthood, but RPE number increases from 1.6 million at Fd100 to 2.56 million in adulthood. At the fovea, the core:RPE ratio increases from 5.4:1 at Fd100 to 28:1 by adulthood. In the temporal periphery by contrast, the cone:RPE ratio declines from 2.2:1 at Fd100–110 to less than 1:1 in the adult. In the vicinity of the optic disc, the ratio of (cones + rods): RPE remains around 35:1 throughout development, but in the retinal periphery it decreases to the adult value of 22:1. These changing ratios indicate that photoreceptors and RPE cells are redistributed independently during development, and that these two cellular sheets slide over one another to achieve their final distribution. This situation suggests that the forces or factors causing foveation are intrinsic to the neural retina.

The short wavelength-sensitive (blue) cone bipolar cells was found to have a nonrandom distribution by analyzing the nearest neighbors and by calculating the density recovery profile (DRP). Blue cones had been shown previously to have a nonrandom distribution (Curcio et al., 1991). The relationship between the two arrays was then analyzed by calculating the cross-correlational density recovery profile (cDRP), which indicates the local density of blue cones around each blue cone bipolar cell. Although both cell types appeared to be distributed uniformly at the macroscopic level, the cDRP was 1.7 times higher within 15 μm of each bipolar cell perikaryon than in the surrounding area. The area of higher density was approximately the same as that in which the blue cone bipolar cells made synaptic contacts with blue cones. The finding that the blue cones and the blue cone bipolar cells were closer together than expected suggests that the positions of the perikarya of these neurons were influenced by their synaptic connections or other developmental interactions.

Retinal bipolar cells exhibit a center-surround antagonistic receptive field to a light stimulus (Werblin & Dowling, 1969; Kaneko, 1970), and thus constitute an early stage of spatial information processing. We injected Lucifer Yellow and a small biotinylated tracer, biocytin, into bipolar cells of the teleost retina to examine electrical coupling in these cells. Lucifer-Yellow coupling was observed in one of 55 stained bipolar cells; the coupling pattern was one injected bipolar cell and three surrounding cells. Biocytin coupling was observed in 16 of 55 stained bipolar cells, six of which were ON center and ten OFF center. Although biocytin usually coupled to three to six bipolar cells, some OFF-center bipolar cells showed strong coupling to more than 20 cells. The biocytin-coupled bipolar cells were morphologically homologous. Membrane appositions resembling gap junctions were found between dendrites and between axon terminals of neighboring bipolar cells.

In the strongest biocytin-coupled bipolar cells, the contacts between bipolar cells and cone photoreceptor cells were examined after reconstruction of the dendritic trees of five well-stained, serially sectioned OFF-center bipolar cells. Each of these bipolar cells was in contact with different numbers of cones: 11 to 20 for twin cones and two to four for single cones. This implies that, although these bipolar cells belong to the same category, the signal inputs differ among bipolar cells. Numerical simulation conducted on a hexagonal array network model demonstrated that the electrical coupling of bipolar cells can decrease the difference in input (≈80%) without causing significant loss of spatial resolution. Our results suggest that electrical coupling of bipolar cells has the advantage of decreasing the dispersion of input signals from cones, and permits bipolar cells of the same class to respond to light with similar properties.

We have examined the morphology and distribution of neurones that contain nicotinamide adenine dinucleotide phosphate (NADPH) diaphorase in human retinae. NADPH-diaphorase reactivity was observed in three different classes of amacrine cells (ND1, ND2, ND3 cells) and in the cone photoreceptors. ND1 cells had relatively large somata (mean, 12.3 ¼m) located in the inner nuclear layer (INL) and in the ganglion cell layer (GCL). Their dendrites were often strongly labeled and spread into either the middle or outer strata of the inner plexiform layer (IPL). The somata of ND2 cells were medium-sized (mean, 8.2 ¼m) and located in the INL and in the GCL; their dendrites were usually beaded and often spread in either the middle or outer strata of the IPL. ND3 cells had small, round somata (mean, 5.2 ¼m) located in either the INL or GCL, and were without labeled processes. The total number of NADPH-diaphorase cells (all classes) was estimated at 118,000, with a mean density of about 100/mm2. The most striking fea ture of NADPH-diaphorase cells in humans was that their distribution was relatively uniform across the retina, with no evidence of a peak in density at the foveal rim.

The response to spatially focal flicker is enhanced by dim, spatially diffuse, rod-stimulating backgrounds. This effect is called suppressive rod-cone interaction (SRCI) as it reflects a tonic, suppressive influence of dark-adapted rods upon cone pathways which is removed by selective rod-light adaptation. SRCI is observed in amphibian retina with intracellular recordings from most cone-driven cells including the cones themselves, and is most obvious using stimuli flickering at frequencies too rapid for rods to follow. SRCI is blocked by glutamate analogs which selectively block the photic response of horizontal cells (HCs). In the presence of these agents, flicker responses from bipolar cells and cones are enhanced to levels normally seen only with selective rod-light adaptation. In the HCs themselves, SRCI is similarly blocked by lead chloride which blocks rod-, but not cone-related activity.

In amphibian and cat HCs and in human observers, SRCI is limited by a space constant of very similar value (between 100 and 150 μm). We suggest that SRCI in all three species is mediated by HCs: in amphibians, SRCI must at least partially reflect rod-modulation of HC feedback onto cones.

Polyclonal (7493 and 7317) and monoclonal (mAb3) antibodies, generated to the α subunit of the voltage-gated sodium channel (αNaCh), were employed to assess the cell types containing αNaCh-like immunoreactivity in the mature cat and monkey retina. Immunoblot analyses of retinal proteins in the cat revealed that the polyclonal and monoclonal antibodies we employed labeled a band in the 260–kDa region which corresponds to the molecular mass of the α subunit of the NaCh. In both the cat and monkey, these antibodies immunolabeled several distinct types of retinal cells. With the polyclonal antibodies immunoreactivity was observed in ganglion cells and their intraretinal axons, in horizontal cells, and unexpectedly, in cones. In addition, in both species, a limited number of heavily labeled profiles, presumed to be bipolar cells, were seen in the inner nuclear layer. In cat and monkey the monoclonal antibody labeled axons in the fiber layer, ganglion cell somata, and a continuous band of immunoreactive cell bodies (presumed bipolar cells) situated in the outer half of the inner nuclear layer. By immunolabeling isolated cells dissociated from the cat retina, it was possible to demonstrate unequivocally that a population of bipolar cells was labeled by the monoclonal and the polyclonal antibodies we employed. The differences in the labeling observed with the monoclonal antibody as compared to the polyclonal antibodies were interpreted as reflecting the presence of different α-subunit subtypes in the mammalian retina. Collectively, our findings suggest that αNaCh-like proteins are expressed by a more diverse population of retinal cells than expected on the basis of previous physiological and immunohistochemical studies.

Foveal dark adaptation in 58 subjects and photopigment regeneration in 60 subjects from 10–78 years of age exhibit parallel slowing of recovery rate with increasing age, with significant correlation of the two functions among individuals. The data are suggestive of an initial slight decline in rate before age 50, followed by a greater decline occuring at different ages in different ages in different individuals. Longitudinal data for one subject from age 40–65 show an increase in pigment regeneration time constant consistent with this idea. Foveal sensitivity and photopigment density both decrease with increasing age and are significantly correlated among individuals, although sensitivity declines more with age than does photopigment density. In contrast to earlier proposals based upon the Rushton-Dowling equation, we found no universal constant of proportionality to relate log relative threshold to photopigment within our population.

The habitat occupied by larval winter flounder (Pseudopleuronectes americanus) differs considerably in light regime from that of the adult. To understand how the visual system has adapted to such changes, photoreceptor spectral absorbance was measured microspectrophotometrically in premetamorphic and postmetamorphic specimens of winter flounder. Before metamorphosis, larval flounder retinas contain only one kind of photoreceptor which is morphologically cone-like with peak absorbance at 519 nm. After metamorphosis, the adult retina has three types of photoreceptors: single cones, double cones, and rods. The visual pigment in single cones has a peak absorbance at λmax = 457 nm, the double cones at λmax = 531 and 547 nm, and the rod photoreceptors at λmax = 506 nm. Double cones were morphologically identical, but the two members contained either different (531/547 nm) or identical pigments (531/531 nm). The latter type were found only in the dorsal retina. The measured spectral half-bandwidths (HBW) were typical of visual pigments with chromophores derived from vitamin A1 with the possible exception of the long-wavelength absorbing pigment in double cones which appeared slightly broader. Because the premetamorphic pigment absorbance has a different λmax than those of the postmetamorphic pigments, different opsin genes must be expressed before and after metamorphosis.

The spectral sensitivities of rods and cones in macaque and human retinas were determined by recording the membrane current from single outer segments. In the macaque retina, the wavelengths of maximum sensitivity were at about 430, 530, and 561 nm for the blue, green, and red cones, respectively, and at 491 nm for the rods. The shapes of the spectra of the three cones were similar when plotted on a log wavenumber scale; the rod spectrum was slightly broader. Spectral sensitivities of the red and green cones from a human retina were virtually identical to those of macaque cones. For comparison with human psychophysical measurements, the rod and cone spectra were adjusted to give the sensitivities expected for light incident on the cornea of the human eye. These functions satisfactorily predicted the scotopic and photopic luminosity functions as well as results from human color-matching experiments. The adjusted spectra of the red and green cones also agreed well with the π-mechanisms of Stiles (1953, 1959).

Winter flounder (Pseudopleuronectes americanus) are hatched as bilaterally symmetric larvae which live near the ocean surface. At metamorphosis, they become laterally compressed, one eye migrates to the opposite side of the head, and they live the remainder of their lives lying on their blind side on the ocean floor. The present study characterizes and quantifies retinal cell distribution throughout the larval period and contrasts it with the adult retina. Based on light- and electron-microscopic analyses, retinas of larval flounder contain only a single cone-like photoreceptor type, arranged in a hexagonal array. In contrast, after metamorphosis, the adult retina has three types of photoreceptors: rods, single cones, and double cones. Rod photoreceptors are numerous in the ventral retina and decrease in density dorsad. The cone photoreceptor density, in contrast to rods, is higher in the dorsal retina decreasing ventrad. Adult cone photoreceptors are arranged in a square mosaic with four double cones surrounding one single cone. The differences in larval and adult retinal morphology reflect the distinctly different habitat each occupies.

Photoreceptors periodically shed light-sensitive membranes; rods at light onset, cones at night. The spectral characteristics of light required to initiate shedding by 502-rods were studied in the frog retina. After 24 h of white light, animals were dark primed for 1 h then presented with 1 h of nearly monochromatic light to induce the shedding response. The light delivered a total photon flux of 2.5 or 0.5 μE/m2s. Following conventional fixation and plastic embedding, 1 μm sections were examined with light microscopy. The number of photoreceptor tips (phagosomes) shed by 100 consecutive rods were counted and plotted as a function of wavelength. Bright light induced at least 15 phagosomes per 100 rods at all wavelengths tested, 420−640 nm, and this shedding was more than doubled with light from 540−600 nm. When the light was dimmed, there was no shedding response except for this 540−600 nm window. This shedding peak closely corresponds to the absorbance curve of the frog's 575-cone photopigment and implies that the 575-cone can drive rod shedding. The broad background effect further indicates that all photoreceptors have an input and suggests that a luminosity cell, such as the internal horizontal cell, may be involved.

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 anisotropics were investigated using correlograms. We find that (1) median distance between Voronoi neighbors increases with eccentricity, but the minimum distance is constant (6–8 μm) 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 Pu m 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.

The major neurons and neural circuits that are involved in the transmission of color signals through the human retina to produce the color and spatially opponent P cell or midget ganglion cell responses are described. The older findings of single cone to midget bipolar connectivity is reviewed, and the single midget bipolar cell to midget ganglion cell connectivity as revealed by a recent serial section electron microscope study is described in detail. Our present knowledge concerning the discrimination of the blue-cone subtype from the other longer wavelength cones in the human at the outer plexiform layer is summarized, and our most recent findings concerning horizontal cell connectivity to the different spectral types of cones are discussed. Finally, a hypothetical pathway is proposed for color-opponent surrounds of midget ganglion cells using both horizontal cells at the outer plexiform layer and amacrine cell pathways at the inner plexiform layer.