Retinal light adaptation--evidence for a feedback mechanism

Clinical vision and molecular loss: Integrating visual psychophysics with molecular genetics reveals key details of normal and abnormal visual processing

Over the past two decades we have developed techniques and models to investigate the ways in which known molecular defects affect visual performance. Because molecular defects in retinal signalling invariably alter the speed of visual processing, our strategy has been to measure the resulting changes in flicker sensitivity. Flicker measurements provide not only straightforward clinical assessments of visual performance but also reveal fundamental details about the functioning of both abnormal and normal visual systems. Here, we bring together our past measurements of patients with pathogenic variants in the GNAT2, RGS9, GUCA1A, RPE65, OPA1, KCNV2 and NR2E3 genes and analyse the results using a standard model of visual processing. The model treats flicker sensitivity as the result of the actions of a sequence of simple processing steps, one or more of which is altered by the genetic defect. Our analyses show that most defects slow down the visual response directly, but some speed it up. Crucially, however, other steps in the processing sequence can make compensatory adjustments to offset the abnormality. For example, if the abnormal step slows down the visual response, another step is likely to speed up or attenuate the response to rebalance system performance. Such compensatory adjustments are probably made by steps in the sequence that usually adapt to changing light levels. Our techniques and modelling also allow us to tease apart stationary and progressive effects, and the localised molecular losses help us to unravel and characterise individual steps in the normal and abnormal processing sequences.

Light adaptation controls visual sensitivity by adjusting the speed and gain of the response to light

The range of c. 10¹² ambient light levels to which we can be exposed massively exceeds the <10³ response range of neurons in the visual system, but we can see well in dim starlight and bright sunlight. This remarkable ability is achieved largely by a speeding up of the visual response as light levels increase, causing characteristic changes in our sensitivity to different rates of flicker. Here, we account for over 65 years of flicker-sensitivity measurements with an elegantly-simple, physiologically-relevant model built from first-order low-pass filters and subtractive inhibition. There are only two intensity-dependent model parameters: one adjusts the speed of the visual response by shortening the time constants of some of the filters in the direct cascade as well as those in the inhibitory stages; the other parameter adjusts the overall gain at higher light levels. After reviewing the physiological literature, we associate the variable gain and three of the variable-speed filters with biochemical processes in cone photoreceptors, and a further variable-speed filter with processes in ganglion cells. The variable-speed but fixed-strength subtractive inhibition is most likely associated with lateral connections in the retina. Additional fixed-speed filters may be more central. The model can explain the important characteristics of human flicker-sensitivity including the approximate dependences of low-frequency sensitivity on contrast (Weber’s law) and of high-frequency sensitivity on amplitude (“high-frequency linearity”), the exponential loss of high-frequency sensitivity with increasing frequency, and the logarithmic increase in temporal acuity with light level (Ferry-Porter law). In the time-domain, the model can account for several characteristics of flash sensitivity including changes in contrast sensitivity with light level (de Vries-Rose and Weber’s laws) and changes in temporal summation (Bloch’s law). The new model provides fundamental insights into the workings of the visual system and gives a simple account of many visual phenomena.

Rod Photoresponse Kinetics Limit Temporal Contrast Sensitivity in Mesopic Vision

The mammalian visual system operates over an extended range of ambient light levels by switching between rod and cone photoreceptors. Rod-driven vision is sluggish, highly sensitive, and operates in dim or scotopic lights, whereas cone-driven vision is brisk, less sensitive, and operates in bright or photopic lights. At intermediate or mesopic lights, vision transitions seamlessly from rod-driven to cone-driven, despite the profound differences in rod and cone response dynamics. The neural mechanisms underlying such a smooth handoff are not understood. Using an operant behavior assay, electrophysiological recordings, and mathematical modeling we examined the neural underpinnings of the mesopic visual transition in mice of either sex. We found that rods, but not cones, drive visual sensitivity to temporal light variations over much of the mesopic range. Surprisingly, speeding up rod photoresponse recovery kinetics in transgenic mice improved visual sensitivity to slow temporal variations, in the range where perceptual sensitivity is governed by Weber's law of sensation. In contrast, physiological processes acting downstream from phototransduction limit sensitivity to high frequencies and temporal resolution. We traced the paradoxical control of visual temporal sensitivity to rod photoresponses themselves. A scenario emerges where perceptual sensitivity is limited by: (1) the kinetics of neural processes acting downstream from phototransduction in scotopic lights, (2) rod response kinetics in mesopic lights, and (3) cone response kinetics as light levels rise into the photopic range.SIGNIFICANCE STATEMENT Our ability to detect flickering lights is constrained by the dynamics of the slowest step in the visual pathway. Cone photoresponse kinetics limit visual temporal sensitivity in bright (photopic) lights, whereas mechanisms in the inner retina limit sensitivity in dim (scotopic) lights. The neural mechanisms underlying the transition between scotopic and photopic vision in mesopic lights, when both rods are cones are active, are unknown. This study provides a missing link in this mechanism by establishing that rod photoresponse kinetics limit temporal sensitivity during the mesopic transition. Surprisingly, this range is where Weber's Law of Sensation governs temporal contrast sensitivity in mouse. Our results will help guide future studies of complex and dynamic interactions between rod-cone signals in the mesopic retina.

Efficient assessment of the time course of perceptual sensitivity change

Perceptual sensitivity is usually estimated over trials and time intervals, which results in imprecise and biased estimates when it changes rapidly over time. We develop a novel procedure, the quick Change-Detection (qCD) method, to accurately, precisely, and efficiently assess the trial-by-trial time course of perceptual sensitivity change. Based on Bayesian adaptive testing, qCD selects the optimal stimulus, and updates, trial by trial, a joint probability distribution of the parameters that quantify perceptual sensitivity change over time. We demonstrate the utility of the method in measuring the time course of dark adaptation. Simulations showed that the accuracy and precision of the estimated dark adaptation curve after one qCD run (root mean squared error (RMSE): 0.002; the half width of the 68.2% credible interval (HWCI): 0.016; standard deviation (SD): 0.020; all in log₁₀ units) was higher than those obtained by ten runs of the quick Forced-Choice (qFC) procedure (RMSE: 0.020; HWCI: 0.032; SD: 0.031) and ten runs of a weighted up-down staircase procedure (RMSE: 0.026; SD: 0.031). Further, the dark adaptation curve obtained from one qCD run in a psychophysics experiment was highly consistent with the average of four qFC runs (RMSE = 0.076 log₁₀ units). Overall, qCD provides a procedure to characterize the detailed time course of perceptual sensitivity change in both basic research and clinical applications.

Negative feedback adjustment challenges reconstruction study from tree rings: A study case of response of Populus euphratica to river discontinuous flow and ecological water conveyance

Drought stress changes the relationship between the growth of tree rings and variations in ambient temperature. However, it is not clear how the growth of trees changes in response to drought of varying intensities, especially in arid areas. Therefore, Tree rings were studied for 6years in Populus euphratica to assess the impacts of abrupt changes in environment on tree rings using the theories and methods in dendrohydrology, ecology and phytophysiology. The width of tree rings increased by 8.7% after ecological water conveyance downstream of Tarim River compared to that when the river water had been cut off. However, during intermediate drought, as the depth of the groundwater increases, the downward trend in the tree rings was reversed because of changes in the physiology of the tree. Therefore, the growth of tree rings shows a negative feedback to intermediate drought stress, an observation that challenges the homogenization theory of tree ring reconstruction based on the traditional methods. Owing to the time lag, the cumulative effect and the negative feedback between the growth of tree rings and drought stress, the reconstruction of past environment by studying the patterns of tree rings is often inaccurate. Our research sets out to verify the hypothesis that intermediate drought stress results in a negative feedback adjustment and thus to answers two scientific questions: (1) How does the negative feedback adjustment promote the growth of tree rings as a result of intermediate drought stress? (2) How does the negative feedback adjustment lower the accuracy with which the past is reconstructed based on tree rings? This research not only enriches the connotations of intermediate disturbance hypothesis and reconstruction theory of tree rings, but also provides a scientific basis for the conservation of desert riparian forests worldwide.

A Computational Framework for Realistic Retina Modeling

Computational simulations of the retina have led to valuable insights about the biophysics of its neuronal activity and processing principles. A great number of retina models have been proposed to reproduce the behavioral diversity of the different visual processing pathways. While many of these models share common computational stages, previous efforts have been more focused on fitting specific retina functions rather than generalizing them beyond a particular model. Here, we define a set of computational retinal microcircuits that can be used as basic building blocks for the modeling of different retina mechanisms. To validate the hypothesis that similar processing structures may be repeatedly found in different retina functions, we implemented a series of retina models simply by combining these computational retinal microcircuits. Accuracy of the retina models for capturing neural behavior was assessed by fitting published electrophysiological recordings that characterize some of the best-known phenomena observed in the retina: adaptation to the mean light intensity and temporal contrast, and differential motion sensitivity. The retinal microcircuits are part of a new software platform for efficient computational retina modeling from single-cell to large-scale levels. It includes an interface with spiking neural networks that allows simulation of the spiking response of ganglion cells and integration with models of higher visual areas.

Dynamical adaptation in photoreceptors

Adaptation is at the heart of sensation and nowhere is it more salient than in early visual processing. Light adaptation in photoreceptors is doubly dynamical: it depends upon the temporal structure of the input and it affects the temporal structure of the response. We introduce a non-linear dynamical adaptation model of photoreceptors. It is simple enough that it can be solved exactly and simulated with ease; analytical and numerical approaches combined provide both intuition on the behavior of dynamical adaptation and quantitative results to be compared with data. Yet the model is rich enough to capture intricate phenomenology. First, we show that it reproduces the known phenomenology of light response and short-term adaptation. Second, we present new recordings and demonstrate that the model reproduces cone response with great precision. Third, we derive a number of predictions on the response of photoreceptors to sophisticated stimuli such as periodic inputs, various forms of flickering inputs, and natural inputs. In particular, we demonstrate that photoreceptors undergo rapid adaptation of response gain and time scale, over ∼ 300[Formula: see text] ms-i. e., over the time scale of the response itself-and we confirm this prediction with data. For natural inputs, this fast adaptation can modulate the response gain more than tenfold and is hence physiologically relevant.

Origin and effect of phototransduction noise in primate cone photoreceptors

Noise in the responses of cone photoreceptors sets a fundamental limit to visual sensitivity, yet the origin of noise in mammalian cones and its relation to behavioral sensitivity are poorly understood. Our work here on primate cones improves understanding of these issues in three ways. First, we find that cone noise is not dominated by spontaneous photopigment activation or by quantal fluctuations in photon absorption but instead by other sources, namely channel noise and fluctuations in cGMP. Second, we find that adaptation in cones, unlike that in rods, affects signals and noise differently. This difference helps explain why thresholds for rod- and cone-mediated signals have different dependencies on background light level. Third, past estimates of noise in mammalian cones are too high to explain behavioral sensitivity. Our measurements indicate a lower level of cone noise, and thus help reconcile physiological and behavioral estimates of cone noise and sensitivity.

The challenges natural images pose for visual adaptation

Advances in our understanding of natural image statistics and of gain control within the retinal circuitry are leading to new insights into the classic problem of retinal light adaptation. Here we review what we know about how rapid adaptation occurs during active exploration of the visual scene. Adaptational mechanisms must balance the competing demands of adapting quickly, locally, and reliably, and this balance must be maintained as lighting conditions change. Multiple adaptational mechanisms in different locations within the retina act in concert to accomplish this task, with lighting conditions dictating which mechanisms dominate.

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.

Retinal bipolar cells: temporal filtering of signals from cone photoreceptors

The temporal dynamics of the response of neurons in the outer retina were investigated by intracellular recording from cones, bipolar, and horizontal cells in the intact, light-adapted retina of the tiger salamander (Ambystoma tigrinum), with special emphasis on comparing the two major classes of bipolars cells, the ON depolarizing bipolars (Bd) and the OFF hyperpolarizing bipolars (Bh). Transfer functions were computed from impulse responses evoked by a brief light flash on a steady background of 20 cd/m(2). Phase delays ranged from about 89 ms for cones to 170 ms for Bd cells, yielding delays relative to that of cones of about 49 ms for Bh cells and 81 ms for Bd cells. The difference between Bd and Bh cells, which may be due to a delay introduced by the second messenger G-protein pathway unique to Bd cells, was further quantified by latency measurements and responses to white noise. The amplitude transfer functions of the outer retinal neurons varied with light adaptation in qualitative agreement with results for other vertebrates and human vision. The transfer functions at 20 cd/m(2) were predominantly low pass with 10-fold attenuation at about 13, 14, 9.1, and 7.7 Hz for cones, horizontal, Bh, and Bd cells, respectively. The transfer function from the cone voltage to the bipolar voltage response, as computed from the above measurements, was low pass and approximated by a cascade of three low pass RC filters ("leaky integrators"). These results for cone-->bipolar transmission are surprisingly similar to recent results for rod-->bipolar transmission in salamander slice preparations. These and other findings suggest that the rate of vesicle replenishment rather than the rate of release may be a common factor shaping synaptic signal transmission from rods and cones to bipolar cells.

Light adaptation in cone vision involves switching between receptor and post-receptor sites

We see over an enormous range of mean light levels, greater than the range of output signals retinal neurons can produce. Even highlights and shadows within a single visual scene can differ approximately 10,000-fold in intensity-exceeding the range of distinct neural signals by a factor of approximately 100. The effectiveness of daylight vision under these conditions relies on at least two retinal mechanisms that adjust sensitivity in the approximately 200 ms intervals between saccades. One mechanism is in the cone photoreceptors (receptor adaptation) and the other is at a previously unknown location within the retinal circuitry that benefits from convergence of signals from multiple cones (post-receptor adaptation). Here we find that post-receptor adaptation occurs as signals are relayed from cone bipolar cells to ganglion cells. Furthermore, we find that the two adaptive mechanisms are essentially mutually exclusive: as light levels increase the main site of adaptation switches from the circuitry to the cones. These findings help explain how human cone vision encodes everyday scenes, and, more generally, how sensory systems handle the challenges posed by a diverse physical environment.

Independence of luminance and contrast in natural scenes and in the early visual system

The early visual system is endowed with adaptive mechanisms that rapidly adjust gain and integration time based on the local luminance (mean intensity) and contrast (standard deviation of intensity relative to the mean). Here we show that these mechanisms are matched to the statistics of the environment. First, we measured the joint distribution of luminance and contrast in patches selected from natural images and found that luminance and contrast were statistically independent of each other. This independence did not hold for artificial images with matched spectral characteristics. Second, we characterized the effects of the adaptive mechanisms in lateral geniculate nucleus (LGN), the direct recipient of retinal outputs. We found that luminance gain control had the same effect at all contrasts and that contrast gain control had the same effect at all mean luminances. Thus, the adaptive mechanisms for luminance and contrast operate independently, reflecting the very independence encountered in natural images.

Spatiotemporal integration of light by the cat X-cell center under photopic and scotopic conditions

Visual responses to stimulation at high temporal frequency are generally considered to result from signals that avoid light adaptive gain adjustment, simply reflecting linear summation of luminance. Under conditions of high photopic illuminance, the center of the receptive field of the cat X-cell has been shown to expand in size when stimulated at high temporal frequency, raising the possibility that there is spatiotemporal interaction in luminance summation. Here we show that this expansion maintains constant the product of the center's luminance summing area and the temporal period of luminance modulation, implying that spatial and temporal integration of luminance can be traded for one another by the X-cell center. As such the X-cell has a spatiotemporal window for luminance integration that fuses the classical concepts of a spatial window of luminance integration (Ricco's Law) with a temporal window of luminance integration (Bloch's Law). We were interested to determine whether this tradeoff between spatial and temporal summation of luminance occurs also at lower light levels, where the temporal-frequency bandwidth of the X-cell is narrower. We found that it does not. Center radius does not expand with temporal frequency under either low photopic or scotopic conditions. These results are discussed within the context of the known retinal circuitry that underlies the X-cell center for photopic and scotopic conditions.

ENU-induced late-onset night blindness associated with rod photoreceptor cell degeneration in zebrafish

We describe a dominant mutation, night blindness d (nbd), that causes late-onset rod photoreceptor cell degeneration in zebrafish. The mutation was induced by treating male zebrafish with N-ethyl-N-nitrosourea (ENU). Visual sensitivity was tested using a behavioral assay based on a visually mediated escape response. At a young age, the heterozygous (nbd+/-) fish did not show any signs of night blindness or retinal degeneration. At 2 years, their behaviorally assessed visual sensitivity was decreased, albeit no alterations in the electroretinogram (ERG) were detected. Histology revealed that in the mutant retinas the rod photoreceptor cell outer segments (ROS) were thinned out. In homozygous larvae (nbd-/-), mass neural degeneration was detectable at about 2 days post fertilization (dpf). They died at an early age, usually no later than 8 dpf. In conclusion, nbd is a dominant mutation that causes late-onset night blindness with slow progression. However, nbd is not photoreceptor cell-specific, as becomes clear from the systemic dysfunctions of the homozygous larvae.

Vision: how to catch fast signals with slow detectors

The visual system is equipped with highly sensitive but slow detectors, yet it can resolve light changes up to 60 Hz. Processes taking place in retinal circuits go beyond the intrinsic limits of the transduction machinery by an unconventional exploitation of voltage-dependent conductances, cleverly lined up to generate a cascade of band-pass amplification stages.

Relation between potassium-channel kinetics and the intrinsic dynamics in isolated retinal bipolar cells

Characterization of the intrinsic dynamics of isolated retinal bipolar cells by a whole-cell patch-clamp technique combined with estimation of effective impulse responses across a range of mean injected currents reveals strikingly adaptive behavior. At resting potential, bipolar cells' effective impulse response is slow, high gain, and low pass. Depolarization speeds up response, decreases gain, and, in most cells, induces bandpass behavior. This adaptive behavior involves two K(+) currents. The delayed-rectifier accounts for the observed gain reduction, speed increase, and bandpass behavior. The A-channel further shortens the impulse responses but suppresses bandpass features. Computer simulations of model neurons with a delayed-rectifier and varying A-channel conductances reveal that impulse responses largely reflect the flux of electrical charge through the two K(+) channels. The A-channel broadens the frequency response and preempts the action of the delayed-rectifier, thereby reducing the associated bandpass features. Admixtures of the two K(+) channels produce the observed variety of dynamics of retinal bipolar cells.

The dynamics of primate retinal ganglion cells

A knowledge of the dynamics (temporal properties) of neuronal populations is essential for an understanding of their function, and is also crucial when one attempts to develop computational or mathematical models of the neurons. Here we review the temporal properties of the receptive fields (RFs) of the two best-studied types of ganglion cells in the primate retina, those that project to the parvocellular (P) and magnocellular (M) layers of the dorsal lateral geniculate nucleus. The center and surround mechanisms of the P RFs are approximately linear, and their impulse responses are very similar, although the surround lags the center by a few milliseconds. The center and surround are chromatically opponent. With the appropriate stimulus, one can find significant nonlinearities in their responses, and also in the interaction between the center and surround. The phase lag between the responses of the center and surround depends on the temporal frequency, so that at high temporal frequency the antagonism between them is reduced or abolished. The temporal responses of M cells are nonlinear, and with increasing contrast they show the effects of a contrast gain control. The different dynamical properties of the two populations suggest that M cells participate in motion analysis, while P cells are used for the analysis of form, texture, and perhaps color.

Noise and its effects on photoreceptor temporal contrast sensitivity at low light levels

We studied photoreceptors in the locust (Schistocerca americanus) visual system to determine the extent to which quantal noise and intrinsic neural noise limit temporal sensitivity. Typical computational models of the temporal contrast sensitivity function are deterministic, reflect only filter characteristics, and lack explicit noise sources [J. Opt. Soc. Am. 58, 1133 (1968); Vision Res. 32, 1373 (1992)]. We report here that the temporal contrast sensitivity function, at low light levels, is not simply the reflection of a filter function. Our evidence suggests that, at low backgrounds, noise, in conjunction with temporal filtering, plays a role in shaping the temporal contrast sensitivity function. At a given low adaptation level, quantal noise limits sensitivity at low temporal frequencies, while intrinsic noise limits sensitivity at relatively higher temporal frequencies.

The effects of temporal noise and retinal illuminance on foveal flicker sensitivity

We measured foveal flicker sensitivity with and without external added temporal noise at various levels of retinal illuminance and described the data with our model of flicker sensitivity comprising: (i) low-pass filtering of the flickering signal plus external temporal and/or quantal noise by the modulation transfer function (MTF) of the retina (R): (ii) high-pass filtering in proportion to temporal frequency by the MTF of the postreceptoral neural pathways (P): (iii) addition of internal white neural noise; and (iv) detection by a temporal matched filter. Without temporal noise flicker sensitivity had a band-pass frequency-dependence at high and medium illuminances but changed towards a low-pass shape above 0.5 Hz at low luminances, in agreement with earlier studies. In strong external temporal noise, however, the flicker sensitivity function had a low-pass shape even at high and medium illuminances and flicker sensitivity was consistently lower with noise than without. At low luminances flicker sensitivity was similar with and without noise. An excellent fit of the model was obtained under the assumption that the only luminance-dependent changes were increases in the cut-off frequency (fc) and maximum contrast transfer of R with increasing luminance. The results imply the following: (i) performance is consistent with detection by a temporal matched filter, but not with a thresholding process based on signal amplitude; (ii) quantal fluctuations do not at any luminance level become a source of dominant noise present at the detector; (iii) the changes in the maximum contrast transfer reflect changes in retinal gain, which at low to moderate luminances implement less-than-Weber adaptation, with a 'square-root' law at the lowest levels; (iv) the changes of fc as function of mean luminance closely parallels time scale changes in cones, but the absolute values of fc are lower than expected from the kinetics of monkey cones at all luminances; (v) the constancy of the high-pass filtering function P indicates that surround antagonism does not weaken significantly with decreasing light level.

Lower-level visual processing and models of light adaptation

Before there was a formal discipline of psychology, there were attempts to understand the relationship between visual perception and retinal physiology. Today, there is still uncertainty about the extent to which even very basic behavioral data (called here candidates for lower-level processing) can be predicted based upon retinal processing. Here, a general framework is proposed for developing models of lower-level processing. It is argued that our knowledge of ganglion cell function and retinal mechanisms has advanced to the point where a model of lower-level processing should include a testable model of ganglion cell function. This model of ganglion cell function, combined with minimal assumptions about the role of the visual cortex, forms a model of lower-level processing. Basic behavioral and physiological descriptions of light adaptation are reviewed, and recent attempts to model lower-level processing are discussed.

Light adaptation of cone photoresponses studied at the photoreceptor and ganglion cell levels in the frog retina

The sensitivity and time scale of the dominant (562 nm) cone system of the frog, Rana temporaria, were studied as functions of steady adapting illuminance (IB). Photoreceptor responses to brief flashes of light were recorded as aspartate-isolated ERG mass potentials from the isolated retina. The characteristics of the cone signal after transmission through the retina were derived from response thresholds and stimulus--intensity-response--latency functions for extracellularly recorded spike discharges of single ganglion cells in the eyecup. At 14 degrees C, the single-photon response of dark-adapted cones, extrapolated from ERG intensity-response functions, had an amplitude of 0.5% of the saturated response (Umax) and peaked at tp approximately 0.4 sec. Steady background illumination decreased both tp and flash sensitivity (SF), starting from apparent "dark lights" of, respectively, less than 10 (for time scale) and about 100 (for sensitivity) photoisomerisations per cone per second [P*sec-1]. From there upwards, two distinct ranges of background adaptation were apparent. Under moderate backgrounds (up to IB approximately 10(4) - 10(5) P*sec-1), sensitivity fell according to the relation SF alpha IB-0.64 and time scale shortened according to tp alpha IB-0.16. Under brighter backgrounds, from approx. 10(5) P*sec-1 up to the limit of our light source at 10(7) P*sec-1, the decrease in SF was significantly stronger than predicted by the Weber relation (SF alpha IB-1), while the decrease in tp levelled out and even tended to reverse. All these changes were virtually identical at the photoreceptor and ganglion cell levels, although the absolute time scale of cone signals apparent at the latter level was 2-fold longer. Our general conclusion is that photoreceptors have several distinct regimes for light adaptation, and traditional descriptions of functional changes (in sensitivity and kinetics) relevant to vision need to be restated with higher resolution, in view also of recent insights into the diversity of underlying mechanisms.

Rapid sensitivity changes on flickering backgrounds: tests of models of light adaptation

To investigate mechanisms underlying sensitivity changes that are capable of following rapid variations in intensity of the background field, we measured the threshold radiance needed to detect a 2-ms probe flash presented at various phases relative to a sinusoidally flickering background. The temporal frequency, mean luminance, and modulation of the background were systematically varied. The sensitivity change consisted of two components: a phase-insensitive increase in threshold that occurs at all the phases of the background field (a change in the dc level of the threshold), and a phase-dependent variation in threshold. Both components can reliably be measured at temporal frequencies up to approximately 50 Hz. On a 30-Hz background, the threshold varied with phase over roughly 0.5 log unit within a half-cycle (17 ms). For background flicker rates of 20-40 Hz the probe threshold increased with increasing instantaneous background radiance, following a typical threshold-versus-radiance template, and approaching Weber-law behavior during the peak of the background flicker. This pattern of threshold elevation was measured at mean background illuminances from 580 to 9100 Td (trolands), with the dimmer backgrounds being slightly less effective in producing threshold elevations. The measured increase in the dc level commenced as soon as the modulation of the background flicker began, and the amount of threshold elevation followed the envelope of the background flicker, ruling out modulation gain control explanations for the change in sensitivity on flickering backgrounds. The threshold elevations measured on a 30-Hz, 25% modulation background were lower than those measured on a 30-Hz, 100% modulation background at all phases. The measured changes in threshold with changes in background modulation rule out all adaptation models consisting of a multiplicative and a subtractive adaptation processes followed by a single, late, static nonlinearity.

A neural model of foveal light adaptation and afterimage formation

Psychophysical research has documented the existence of three processes in light adaptation: a fast subtractive process, a divisive process that is fast at light onset and slower at light offset, and a very slow subtractive process (Hayhoe et al., 1987). In the neural model developed here, the fast subtractive process is identified with horizontal cell feedback onto cones and the divisive process with amacrine cell feedback onto bipolar cells. The very slow subtractive process is identified with the modulatory feedback circuit from amacrines via interplexiform cells to horizontal cells. A nonlinear dynamical model is developed incorporating these aspects of retinal circuitry along with both ON- and OFF-center M and P pathways. This model is shown to account for many aspects of foveal light adaptation, including negative afterimage formation, and to explain a number of the physiological differences between M and P ganglion cells, including their differing contrast-response functions.

Probed-sinewave paradigm: a test of models of light-adaptation dynamics

Studies of light adaptation have, in general, employed either aperiodic or periodic stimuli. In earlier work, models originally developed to predict the results from one tradition failed to predict results from the other but the models from the two traditions could be merged to predict phenomena from both. To further test these merged models, a paradigm combining both types of stimuli was used. The threshold for a brief flash (the probe) was measured at various phases on a background that was varied sinusoidally in time. The probe threshold depends upon the phase at which it is presented for all background frequencies used, 0-16 Hz. These threshold variations are not well described by a sinewave; the peak threshold is > 180 deg out of phase with the trough threshold. Further, the positions of the peaks and troughs shift fairly abruptly at background modulations of 4-8 Hz. The difference between the peak and trough thresholds varies as a function of temporal frequency in a manner approximating the temporal contrast sensitivity function. The dc level (mean threshold) does not. The peak-trough difference dominates at low frequencies of background modulation, while the dc level dominates for higher frequencies. Existing models of light adaptation do not predict the key features of the data.

Phototransduction: modeling the primate cone flash response

We have developed a new model of phototransduction that accounts for the dynamics of primate and human cone flash responses in both their linear and saturating range. The model incorporates many of the known elements of the phototransduction cascade in vertebrate photoreceptors. The input stage is a new analytic expression for the activation and inactivation of cGMP-phosphodiesterase (PDE). Although the Lamb and Pugh (1992) model (of a delayed ramp for the rising phase of the PDE response in amphibian rods) provided a good fit for the first 2 log units of stimulus intensity without parameter adjustments, the remaining 4 log units of the data required nonlinear modifications of both delay and gain (slope). We show that this nonlinear behavior is a consequence of the delay approximation and develop a completely linear model to account for the rising phase of amphibian rod photocurrent responses over the full intensity range (approximately 6 log units). We use the same dynamic model to account for primate cone responses by decreasing the time constants of PDE activation and introducing an enhanced inactivation process. This PDE response activates a nonlinear calcium feedback stage that modulates guanylate cyclase synthesis of cyclic GMP. By adjustment of the throughput and feedback parameters, the full model successfully captures most of the features of the primate and human cone flash responses throughout their dynamic range. Our analysis suggests that initial processes in the transduction cascade may be qualitatively different from comparable processes in rods.

Background contrast modulates kinetics and lateral spread of responses to superimposed stimuli in outer retina

Surround enhancement (sensitization) is a poorly understood form of network adaptation in which the kinetics of the responses of retinal neurons to test stimuli become faster, and absolute sensitivity of the responses increases with increasing level of steady, surrounding light. Surround enhancement has been observed in all classes of retinal neurons in lower vertebrates except cones, in some primate retinal ganglion cells, and in human psychophysical studies. In theory, surround enhancement could be mediated by two broad classes of mechanisms, which are not mutually exclusive: one in which the kinetics of the transduction linking cone voltage to postsynaptic current in second-order neurons is modulated, and another in which the transformation of postsynaptic current to membrane voltage is modulated. We report here that both classes of mechanism play a role in surround enhancement measured in turtle horizontal cells (HCs). We stimulated the retina by modulating sinusoidally the illuminance of a bar placed at various positions in the HC receptive field. The bar was surrounded by either equally luminant or dim, steady light. Interpretation of responses in the context of a model for the cone-HC network led to the conclusion that the speeding up of response kinetics--due to selective increase in response gain at high temporal frequencies--by surround illuminance is almost completely accounted for by the change in the kinetics of the transduction linking cone membrane potential to HC postsynaptic current. However, surround illuminance also had an additional, surprising effect on the transformation between postsynaptic current and voltage: the space constant for signal spread in the HC network for the dim-surround condition was roughly twice as large as that for the bright-surround condition. Thus, increasing surround illuminance had analogous effects in the spatial and temporal domains: it restricted the time course and the spatial spread of signal. Both effects were dependent on the contrast between the mean bar illuminance and that of the surround, rather than on overall light level. When the stimulus with the bright surround was dimmed uniformly by a neutral density filter, the space constant did not increase, and response gain at high temporal frequencies did not decrease. Pharmacological experiments performed with dopamine and various agonists and antagonists indicated that, although exogenous dopamine can influence surround enhancement, endogenous dopamine does not play an important role in surround enhancement. We conclude that contrast in background light modulates the spatiotemporal properties of signal processing in the outer retina, and does so by a non-dopaminergic mechanism.

The influence of center-surround antagonism on light adaptation in cones in the retina of the turtle

The influence of center-surround antagonism on light adaptation in cone photoreceptors was investigated by intracellular recording from red-sensitive cones in the retina of the turtle, Pseudemys scripta elegans. Test flashes of 0.15-mm diameter were applied at the center of background fields of 0.25-mm or 2.2-mm diameter. Immediately upon expanding the background from 0.25 to 2.2 mm, the membrane potential depolarized by about 1-4 mV. The test flash response was enhanced if the depolarization was primarily due to synaptic feedback from horizontal cells, whereas the response was attenuated if the prolonged depolarization, an intrinsic response of the cone, was the dominant source of the depolarization. After several seconds, however, only the synaptic depolarization was maintained so maintained illumination of the large background field produced an enhancement of the cone's incremental sensitivity. The enhancement was examined in detail in steady-state conditions by obtaining amplitude-intensity measurements for centered test flashes on steady background fields over a large range of intensity. The effect of the large background field at any fixed intensity was fairly well described as a vertical (upward) shift of the amplitude-intensity curve obtained on the small field. This operation constitutes a quasi-subtractive mechanism of light adaptation and might provide a basis for the sort of subtractive mechanisms inferred from psychophysical studies of human vision. The enhancement was quantified by measuring the incremental sensitivity over four decades of background illumination. The magnitude of the enhancement increased with background intensity and then tended to stabilize at higher background intensities. The maximum difference in incremental sensitivity obtained on the large vs. small background field averaged 0.46 log unit (+/- 0.12 S.D.). At higher background intensities, incremental sensitivity conformed to Weber's Law behavior about equally well for flashes applied on either small or large background fields. In sum, the present results provide evidence for an additional mechanism of light adaptation in cone photoreceptors by showing that the incremental light sensitivity, initially set by mechanisms in the outer segment, can be modulated some three-fold by synaptic feedback at the inner segment of the cone.

The processing of temporal modulation at different levels of retinal illuminance

How does our temporal vision change as the mean illuminance reduces? We have examined the processing of near-threshold temporal information for a range of illuminance values (2850--0.15 phot td). At high illuminance, the modulation transfer function can be shown to be mediated via three underlying temporal filters that vary in sensitivity with spatial frequency. As the mean illuminance decreases these channels appear to change their sensitivity. Even at the lowest (scotopic) illuminance levels we were able to find evidence for at least two channels mediating detection threshold. There are also changes in the tuning properties of these channels such that the processing of high temporal frequencies is differentially compromised, resulting in a reduction in the flicker fusion limit of each channel, and a shift in the peak of the band-pass channel. The slope of the fall-off in sensitivity at high temporal frequencies is unaffected by test spatial frequency at each illuminance level, suggesting its limiting factor is one that is insensitive to spatial frequency. We propose that the changes in the tuning of the temporal filters occur because of an early (e.g. photoreceptor) change in the response dynamics, or by interactions between photoreceptors, rather than changes at or beyond the level of the channel response.

White noise analysis of a chromatic type horizontal cell in the Xenopus retina

The dynamics of color-coded signal transmission in the light-adapted Xenopus retina were studied by a combination of white noise (Wiener) analysis and simultaneous recordings from two types of horizontal cells: chromatic-type horizontal cells (C-HCs) are hyperpolarized by blue light and depolarized by red light, whereas luminosity-type horizontal cells (L-HCs) are hyperpolarized by all wave-lengths. The retina was stimulated by two superimposed fields of red and blue light modulated by two independent white noise signals, and the resulting intracellular responses were decomposed into red and blue components (first-order kernels). The first-order kernels predict the intracellular responses with a small degree of error (3.5-9.5% in terms of mean square error) under conditions where modulated responses exceeded 30 mV in amplitude peak-to-peak, thus demonstrating that both red and blue modulation responses are linear. Moreover, there is little or no interaction between the red- and blue-evoked responses; i.e., nearly identical first-order kernels were obtained for one color whether the other color was modulated or not. In C-HCs (but not L-HCs), there were consistent differences in the dynamics of the red and blue responses. In the C-HC, the cutoff frequency of the red response was higher than for the blue (approximately 12 vs 5 Hz), and the red kernel was more bandpass than the blue. In the L-HC, kernel waveform and cutoff frequencies were similar for both colors (approximately 12 Hz or greater), and the time-to-peak of the L-HC kernel was always shorter than either the red or blue C-HC kernel. These results have implications for the mechanisms underlying color coding in the distal retina, and they further suggest that nonlinear phenomena, such as voltage-dependent conductances in HCs, do not contribute to the generation of modulation responses under the experimental conditions used here.

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.

Voltage- and time-dependent potassium conductances enhance the frequency response of horizontal cells in the turtle retina

The contribution of voltage- and time-dependent potassium conductances to visual information processing in the distal turtle retina was studied in the isolated retina preparation. The effects of specific potassium channel blockers; tetraethylammonium (TEA) and 4-aminopyridine (4-AP) on the membrane potential and photoresponses of L-cones and L-type horizontal cells were monitored with intracellular microelectrodes. Both drugs produced a large depolarization of the L-type horizontal cells though the effect of 4-AP was more transient than that of TEA. While TEA produced response augmentation associated with negligible changes in the kinetics of the photoresponses, 4-AP induced profound changes in response kinetics which were seen as an overshoot of the resting potential at stimulus offset and a pronounced slowing down in the return of the membrane potential toward the prestimulus level. The effects of TEA on horizontal cells could be accounted for by the action of the drug on cone photoreceptors. The effects of 4-AP on the horizontal cells could not be attributed to an indirect action mediated by either the cone photoreceptors or by GABAergic and/or glycinergic neurons in the inner retina. These results suggest that voltage- and time-dependent potassium conductances act to speed up the recovery of the turtle horizontal cell membrane potential from the effects of bright light stimuli. Such a role was supported by the effects of potassium channel blockers on the frequency response curves of horizontal cells: the corner frequency was reduced on the average by 25%.

The dynamics of light adaptation in cat horizontal cell responses

In order to model the dynamic properties of light adaptation processes in cat horizontal (H-) cells, the time course of the gain adjustment following changes in the mean illumination level was studied. H-cell responses were recorded intracellularly in the optically intact, in vivo, eye of the cat. The light stimulus consisted of two spots, a large background spot (8.8 deg diameter) and a concentrically arranged smaller test spot (3.9 deg). The background was either square wave or sine wave modulated in intensity at a frequency of 0.2-1 Hz. The instantaneous value of the response gain was measured with brief flashes (10 msec) of the test spot, generated repetitively at a frequency of 5 or 10 Hz. Modulation of the background intensity, at a contrast of 0.6 and in the photopic range, effectively induces a modulation of the gain. The readjustment of the gain by a stepwise increase or decrease in background illumination is completed within about 200 msec. The amplitude of the gain modulation due to a 0.5 Hz background flicker is quantitatively comparable to that measured between steady illumination levels. Dynamic changes of the gain at low frequency stimuli therefore, have to be taken into account in modelling H-cell responses. For sinusoidal modulations of the background luminance the time course of gain adjustment is quantified by the phase shift of the gain modulation relative to background intensity modulation. The results, together with those described in two preceding papers, are used to test and discuss several light adaptation models that have been proposed previously. It was found that light adaptation in cat H-cells is described more adequately by a de Vries-Rose type of adaptation model than by a Weber type of light adaptation.

Temporal frequency dependent adaptation at the level of the outer retina in humans

The focal electroretinogram (FERG) was used to examine temporal frequency tuning at the outer retinal level in humans by measuring temporal modulation thresholds. Changes in FERG thresholds as a function of ambient light level were compared to temporal modulation thresholds obtained psychophysically using the same stimuli. At lower temporal frequencies, both FERG and psychophysical thresholds changed sensitivity proportional to the mean illuminance level. At higher illuminance levels, both threshold measures were relatively independent of illuminance. The comparison of the FERG to the behavioral data suggest that most of the adaptation-dependent changes in temporal sensitivity in humans occur at the level of the photoreceptor complex.

Modeling the dynamics of light adaptation: the merging of two traditions

Light adaptation has been studied using both aperiodic and periodic stimuli. Two well-documented phenomena are described: the background-onset effect (from an aperiodic-stimulus tradition) and high-temporal-frequency linearity (from the periodic-stimulus tradition). These phenomena have been explained within two different theoretical frameworks. Here we briefly review those frameworks. We then show that the models developed to predict the phenomenon from one tradition cannot predict the phenomenon from the other tradition, but that the models from the two traditions can be merged into a class of models that predicts both phenomena.

Mutual rod-cone suppression within the central visual field

Under mesopic conditions the contrast sensitivity of the central visual field is reduced as the result of a non-linear interaction between rod- and cone-mediated signals, each of which is capable of higher sensitivity in isolation. The interaction is produced only when the rod-mediated system is driven at flicker rates above 6 Hz. This finding bears upon how rod and cone signals are combined and therefore affects our interpretation of the significance of the relationship between retinal illuminance and both contrast sensitivity and temporal resolution.

A molecular basis for Weber's law

A mathematical model is presented that obeys a strong form of Weber's law--over a range of adapting and stimulus intensities, equal contrast stimuli evoke identical responses. To account for the strong Weber's law, the adaptive stage in the proposed model employs a "delayed" reverse reaction along with a power-law input. It is suggested that this Weber's law mechanism is responsible for a slow, voltage-uncorrelated component of adaptation in the vertebrate photoreceptor. A plausible biochemical mechanism is the G-protein cycle with phosphorylation of photoactivated photopigment (and binding of arrestin to the phosphorylated photopigment) as the adaptive process. In an Appendix, features of the general model and implications of a specific biochemical model are examined by computer simulation.

Light adaptation in turtle cones. Testing and analysis of a model for phototransduction

Light adaptation in cones was characterized by measuring the changes in temporal frequency responses to sinusoidal modulation of light around various mean levels spanning a range of four log units. We have shown previously that some aspects of cone adaptation behavior can be accounted for by a biochemical kinetic model for phototransduction in which adaptation is mediated largely by a sigmoidal dependence of guanylate cyclase activity on the concentration of free cytoplasmic Ca2+, ([Ca2+]i) (Sneyd and Tranchina, 1989). Here we extend the model by incorporating electrogenic Na+/K+ exchange, and the model is put to further tests by simulating experiments in the literature. It accounts for (a) speeding up of the impulse response, transition from monophasic to biphasic waveform, and improvement in contrast sensitivity with increasing background light level, I0; (b) linearity of the response to moderate modulations around I0; (c) shift of the intensity-response function (linear vs. log coordinates) with change in I0 (Normann and Perlman, 1979); the dark-adapted curve adheres closely to the Naka-Rushton equation; (d) steepening of the sensitivity vs. I0 function with [Ca2+]i fixed at its dark level, [Ca2+]i dark; (Matthews et al., 1988, 1990); (e) steepening of the steady-state intensity-response function when [Ca2+]i is held fixed at its dark level (Matthews et al., 1988; 1990); (f) shifting of a steep template saturation curve for normalized photocurrent vs. light-step intensity when the response is measured at fixed times and [Ca2+]i is held fixed at [Ca2+]i dark (Nakatani and Yau, 1988). Furthermore, the predicted dependence of guanylate cyclase activity on [Ca2+] closely matches a cooperative inhibition equation suggested by the experimental results of Koch and Stryer (1988) on cyclase activity in bovine rods. Finally, the model predicts that some changes in response kinetics with background light will still be present, even when [Ca2+]i is held fixed at [Ca2]i dark.

Light adaptation and frequency transfer properties of cat horizontal cells

The frequency transfer properties of horizontal cells in the cat retina were studied as a function of the mean light intensity level and stimulus contrast. To this end, horizontal cell responses to sinusoidally modulated light stimuli were recorded intracellularly in the optically intact, in vivo eye. The light stimulus consisted of a 3.9 deg dia. spot superimposed on a steady background (8.8 deg dia.). A discrete Fourier analysis was performed in order to describe the amplitude and phase characteristics of the linear response component and in order to specify the nonlinear distortion of the response. The amplitude of the fundamental Fourier component was found to increase linearly with the contrast of the sinusoidal light intensity modulation. Increasing the mean light level while keeping the contrast constant caused a frequency dependent increase in response amplitude. The increase was most pronounced at high temporal frequencies and resulted in a conspicuous increase of the flicker fusion frequency. Steady background illumination caused a reduction of the response amplitudes at the lower temporal frequencies. Responses in the high frequency range, however, were not affected. The phase shifts of the fundamental Fourier components were found to diminish at increasing mean illumination levels. The harmonic distortion of horizontal cell responses to sinewave flicker was studied as a function of stimulus frequency and stimulus contrast. By comparing the data obtained using sinusoidal light intensity modulation with the intensity profiles described in a preceding paper it was investigated to what extent the harmonic distortion can be explained by the nonlinearity expressed in the response vs intensity profiles.

Simulation of movement detection by direction-selective ganglion cells in the rabbit and squirrel retina

A veto-gate model of movement detection by direction-selective ganglion cells in the vertebrate retina, first proposed by Barlow and Levick (1965), provides the basis for a model described in this study. The model is a simple network consisting basically of (1) two subunits that have receptive fields with a center-surround organization and an adaptational gain control, (2) a lateral inhibitory pathway, (3) a site of nonlinear interaction, followed by (4) a leaky temporal integrator. The model is tested by comparing its basic properties to those reported in the physiological literature on rabbit and squirrel direction-selective retinal ganglion cells. It is shown that the physiological findings on sensitivity to flashes, moving spots or slits, and phi-movement stimuli, can be mimicked quite well by our model. Similarities between the component processes of the subunits and known retinal processes are pointed out. The simulation studies shed a new light on some of the known properties and suggest several new, more revealing, physiological experiments. Such experiments are necessary to develop a full specification of this type of model and to fix more parameter values than is possible at present. Results of some critical experiments are predicted to enable physiologists to falsify or corroborate the model. The simulation studies also help to distinguish use from abuse of this type of model in explanations of psychophysical findings. For example, neither the most complete Barlow-Levick detector nor any stripped-down versions that retain a temporally extended lateral inhibition (which is essential to mimick the physiological findings), respond well to moving random-pixel arrays.

Light adaptation in the primate retina: analysis of changes in gain and dynamics of monkey retinal ganglion cells

The responses of monkey retinal ganglion cells to sinusoidal stimuli of various temporal frequencies were measured and analyzed at a number of mean light levels. Temporal modulation tuning functions (TMTFs) were measured at each mean level by varying the drift rate of a sine-wave grating of fixed spatial frequency and contrast. The changes seen in ganglion cell temporal responses with changes in adaptation state were similar to those observed in human subjects and in turtle horizontal cells and cones tested with sinusoidally flickering stimuli; "Weber's Law" behavior was seen at low temporal frequencies but not at higher temporal frequencies. Temporal responses were analyzed in two ways: (1) at each light level, the TMTFs were fit by a model consisting of a cascade of low- and high-pass filters; (2) the family of TMTFs collected over a range of light levels for a given cell was fit by a linear negative feedback model in which the gain of the feedback was proportional to the mean light level. Analysis (1) revealed that the temporal responses of one class of monkey ganglion cells (M cells) were more phasic at both photopic and mesopic light levels than the responses of P ganglion cells. In analysis (2), the linear negative feedback model accounted reasonably well for changes in gain and dynamics seen in three P cells and one M cell. From the feedback model, it was possible to estimate the light level at which the dark-adapted gain of the cone pathways in the primate retina fell by a factor of two. This value was two to three orders of magnitude lower than the value estimated from recordings of isolated monkey cones. Thus, while a model which includes a single stage of negative feedback can account for the changes in gain and dynamics associated with light adaptation in the photopic and mesopic ranges of vision, the underlying physical mechanisms are unknown and may involve elements in the primate retina other than the cone.

Phototransduction in cones: an inverse problem in enzyme kinetics

Phototransduction is a process which links the absorption of photons by a rod or cone to the modulation of voltage across the cell membrane. An important feature of many vertebrate photoreceptors is a mechanism that adjusts the sensitivity and dynamics of the response to light according to the level of illumination. We construct a system of ordinary differential equations that models what are currently thought to be the important molecule mechanisms involved in phototransduction: this includes consideration of both intracellular enzyme kinetics and the properties of light-insensitive and light-sensitive conductances in the cone membrane. The system contains negative feedback whose functional form is determined by constraining the steady-state behaviour of the system. Despite the highly nonlinear nature of the system of ordinary differential equations, our methods permit us to derive an analytic expression for the first-order frequency response parametric in the steady-state value of only one dynamic variable, the light input. Various unknown kinetic parameters are found by fitting the model to experimental data on the first-order frequency response of cones measured at several mean light levels spanning a range of four log units. Good fits are obtained to the data, and the computed shape of the feedback function agrees qualitatively with recent experiment. Moreover, the model accounts for the dramatic speeding up of the response kinetics and the decrease in response gain with increasing light level.

Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations

Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.

Light adaptation in the turtle retina: embedding a parametric family of linear models in a single nonlinear model

A method for constructing nonlinear models for light adaptation in the retina is introduced. The components of the models are linear filters and static (instantaneous) nonlinear elements configured in a feedback arrangement. The signals in the models are combined through algebraic addition or multiplication. We apply the method to model light adaptation measured in turtle horizontal cells. Given a particular wiring diagram for the components, the functional forms of the static nonlinearities and frequency responses of the linear filters are determined by constraining the model to give temporal frequency responses (linear regime behavior) consistent with a family of linear feedback models which has been shown to provide a good description of adaptation in these cells. Two particular models, quite different in structure, are presented. Each model responds to perturbations around a mean light level as a feedback circuit in which the gain (strength) of feedback is adjusted to be proportional to the mean light level, but neither model has a separate pathway for measuring the mean light level. Thus, each of these nonlinear models embeds an entire family of linear models parametric in mean light level. Harmonic distortion in the responses of these models to sinusoidal input is found to be qualitatively consistent with physiological data. An alternative class of nonlinear models in which feedback gain is set by a separate slow pathway which tracks the mean light level is ruled out on the basis of its incorrect steady-state input-output behavior. The methods presented can be used to develop specific physical models for light adaptation based on the chemical kinetics of phototransduction or on nonlinear neural feedback. The relevance of the nonlinear models and construction techniques to modeling phototransduction is discussed.

White-noise analysis in visual neuroscience

In 1827, plant biologist Robert Brown discovered what is known as Brownian motion, a class of chaos. Formal derivative of Brownian motion is Gaussian white-noise. In 1938, Norbert Wiener proposed to use the Gaussian white-noise as an input probe to identify a system by a series of orthogonal functionals known as the Wiener G-functionals. White-noise analysis is uniquely suited for studying the response dynamics of retinal neurons because (1) white-noise light stimulus is a modulation around a mean luminance, as are the natural photic inputs, and it is a highly efficient input; and (2) the analysis defines the response dynamics and can be extended to spike trains, the final output of the retina. Demonstrated here are typical examples and results from applications of white-noise analysis to a visual system.

Biophysical evidence that light adaptation in Limulus photoreceptors is due to a negative feedback

The steady-state stimulus-response curve of the Limulus ventral photoreceptor comprises a linear portion followed by a less-than-unity power law dependence, which is maintained over at least 4 decades of intensity. This progressive desensitization corresponds to light adaptation. For flash stimulation of dark-adapted cells, the stimulus-response curve again has an initial linear portion, but this is followed by a region of supralinearity before the curve saturates. In a previous article, we showed that the distribution of time integrals of the single-photon responses is consistent with a model of a single chain of first-order reactions. Starting with such a model, we have looked at relevant elementary nonlinear biochemical mechanisms to determine which of them can modulate the enzymatic amplifications of the chain in such a way as to lead to these behaviors. We assume that each of the two phenomena, adaptation and supralinearity, derives from a single mechanism that acts on a single enzymatic stage. We then conclude that the adaptation must be a cooperative negative feedback, in which an accessory material activated by a late stage of the transduction chain acts cooperatively to inhibit an earlier enzymatic amplification. In Limulus, the number of molecules that cooperate is between 3 and 5. We were not able to discard any of the mechanisms tested for the supralinearity, except to say that they must act at a stage of the chain later than that on which the adaptive material acts. If we assume the conclusions of a previous work which shows that the supralinearity mechanism is active during the steady state, we can also conclude that the supralinearity stage must precede the stage that is the source of the adaptive material.