The spatiotemporal transfer function of the Limulus lateral eye

Contrast adaptation in the Limulus lateral eye

Luminance and contrast adaptation are neuronal mechanisms employed by the visual system to adjust our sensitivity to light. They are mediated by an assortment of cellular and network processes distributed across the retina and visual cortex. Both have been demonstrated in the eyes of many vertebrates, but only luminance adaptation has been shown in invertebrate eyes to date. Since the computational benefits of contrast adaptation should apply to all visual systems, we investigated whether this mechanism operates in horseshoe crab eyes, one of the best-understood neural networks in the animal kingdom. The spike trains of optic nerve fibers were recorded in response to light stimuli modulated randomly in time and delivered to single ommatidia or the whole eye. We found that the retina adapts to both the mean luminance and contrast of a white-noise stimulus, that luminance- and contrast-adaptive processes are largely independent, and that they originate within an ommatidium. Network interactions are not involved. A published computer model that simulates existing knowledge of the horseshoe crab eye did not show contrast adaptation, suggesting that a heretofore unknown mechanism may underlie the phenomenon. This mechanism does not appear to reside in photoreceptors because white-noise analysis of electroretinogram recordings did not show contrast adaptation. The likely site of origin is therefore the spike discharge mechanism of optic nerve fibers. The finding of contrast adaption in a retinal network as simple as the horseshoe crab eye underscores the broader importance of this image processing strategy to vision.

Predicting perfect adaptation motifs in reaction kinetic networks

Adaptation and compensation mechanisms are important to keep organisms fit in a changing environment. "Perfect adaptation" describes an organism's response to an external stepwise perturbation by resetting some of its variables precisely to their original preperturbation values. Examples of perfect adaptation are found in bacterial chemotaxis, photoreceptor responses, or MAP kinase activities. Two concepts have evolved for how perfect adaptation may be understood. In one approach, so-called "robust perfect adaptation", the adaptation is a network property (due to integral feedback control), which is independent of rate constant values. In the other approach, which we have termed "nonrobust perfect adaptation", a fine-tuning of rate constant values is needed to show perfect adaptation. Although integral feedback describes robust perfect adaptation in general terms, it does not directly show where in a network perfect adaptation may be observed. Using control theoretic methods, we are able to predict robust perfect adaptation sites within reaction kinetic networks and show that a prerequisite for robust perfect adaptation is that the network is open and irreversible. We applied the method on various reaction schemes and found that new (robust) perfect adaptation motifs emerge when considering suggested models of bacterial and eukaryotic chemotaxis.

Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli

Functional models of the early visual system should predict responses not only to simple artificial stimuli but also to sequences of complex natural scenes. An ideal testbed for such models is the lateral geniculate nucleus (LGN). Mechanisms shaping LGN responses include the linear receptive field and two fast adaptation processes, sensitive to luminance and contrast. We propose a compact functional model for these mechanisms that operates on sequences of arbitrary images. With the same parameters that fit the firing rate responses to simple stimuli, it predicts the bulk of the firing rate responses to complex stimuli, including natural scenes. Further improvements could result by adding a spiking mechanism, possibly one capable of bursts, but not by adding mechanisms of slow adaptation. We conclude that up to the LGN the responses to natural scenes can be largely explained through insights gained with simple artificial stimuli.

Theoretical analysis of reverse-time correlation for idealized orientation tuning dynamics

A theoretical analysis is presented of a reverse-time correlation method used in experimentally investigating orientation tuning dynamics of neurons in the primary visual cortex. An exact mathematical characterization of the method is developed, and its connection with the Volterra-Wiener nonlinear systems theory is described. Various mathematical consequences and possible physiological implications of this analysis are illustrated using exactly solvable idealized models of orientation tuning.

A Neural Model of the Scintillating Grid Illusion: Disinhibition and Self-Inhibition in Early Vision

A stationary display of white discs positioned on intersecting gray bars on a dark background gives rise to a striking scintillating effect—the scintillating grid illusion. The spatial and temporal properties of the illusion are well known, but a neuronal-level explanation of the mechanism has not been fully investigated. Motivated by the neurophysiology of the Limulus retina, we propose disinhibition and self-inhibition as possible neural mechanisms that may give rise to the illusion. In this letter, a spatiotemporal model of the early visual pathway is derived that explicitly accounts for these two mechanisms. The model successfully predicted the change of strength in the illusion under various stimulus conditions, indicating that low-level mechanisms may well explain the scintillating effect in the illusion.

Do we know what the early visual system does?

We can claim that we know what the visual system does once we can predict neural responses to arbitrary stimuli, including those seen in nature. In the early visual system, models based on one or more linear receptive fields hold promise to achieve this goal as long as the models include nonlinear mechanisms that control responsiveness, based on stimulus context and history, and take into account the nonlinearity of spike generation. These linear and nonlinear mechanisms might be the only essential determinants of the response, or alternatively, there may be additional fundamental determinants yet to be identified. Research is progressing with the goals of defining a single "standard model" for each stage of the visual pathway and testing the predictive power of these models on the responses to movies of natural scenes. These predictive models represent, at a given stage of the visual pathway, a compact description of visual computation. They would be an invaluable guide for understanding the underlying biophysical and anatomical mechanisms and relating neural responses to visual perception.

How the brain uses time to represent and process visual information(1)

Information theory provides a theoretical framework for addressing fundamental questions concerning the nature of neural codes. Harnessing its power is not straightforward, because of the differences between mathematical abstractions and laboratory reality. We describe an approach to the analysis of neural codes that seeks to identify the informative features of neural responses, rather than to estimate the information content of neural responses per se. Our analysis, applied to neurons in primary visual cortex (V1), demonstrates that the informative precision of spike times varies with the stimulus modality being represented. Contrast is represented by spike times on the shortest time scale, and different kinds of pattern information are represented on longer time scales. The interspike interval distribution has a structure that is unanticipated from the firing rate. The significance of this structure is not that it contains additional information, but rather, that it may provide a means for simple synaptic mechanisms to decode the information that is multiplexed within a spike train. Extensions of this analysis to the simultaneous responses of pairs of neurons indicate that neighboring neurons convey largely independent information, if the decoding process is sensitive to the neuron of origin and not just the average firing rate. In summary, stimulus-related information is encoded into the precise times of spikes fired by V1 neurons. Much of this information would be obscured if individual spikes were merely taken to be estimators of the firing rate. Additional information would be lost by averaging across the responses of neurons in a local population. We propose that synaptic mechanisms sensitive to interspike intervals and dendritic processing beyond simple summation exist at least in part to enable the brain to take advantage of this extra information.

Cell-based model of the Limulus lateral eye

We present a cell-based model of the Limulus lateral eye that computes the eye's input to the brain in response to any specified scene. Based on the results of extensive physiological studies, the model simulates the optical sampling of visual space by the array of retinal receptors (ommatidia), the transduction of light into receptor potentials, the integration of excitatory and inhibitory signals into generator potentials, and the conversion of generator potentials into trains of optic nerve impulses. By simulating these processes at the cellular level, model ommatidia can reproduce response variability resulting from noise inherent in the stimulus and the eye itself, and they can adapt to changes in light intensity over a wide operating range. Programmed with these realistic properties, the model eye computes the simultaneous activity of its ensemble of optic nerve fibers, allowing us to explore the retinal code that mediates the visually guided behavior of the animal in its natural habitat. We assess the accuracy of model predictions by comparing the response recorded from a single optic nerve fiber to that computed by the model for the corresponding receptor. Correlation coefficients between recorded and computed responses were typically >95% under laboratory conditions. Parametric analyses of the model together with optic nerve recordings show that animal-to-animal variation in the optical and neural properties of the eye do not alter significantly its response to objects having the size and speed of horseshoe crabs. The eye appears robustly designed for encoding behaviorally important visual stimuli. Simulations with the cell-based model provide insights about the design of the Limulus eye and its encoding of the animal's visual world.

Directionality and inhibition in crayfish tangential cells

The purpose of this study was to characterize the inhibitory mechanism(s) associated with directionally selective motion detection (DS) in nonspiking tangential cells of crayfish optic lobe. The experiments employed intracellular recording of synaptic potentials elicited with sinewave gratings and pharmacological techniques. Previous studies established that tangential cells are subject to bicuculline-sensitive GABA-mediated inhibition. In this study DS was reduced by 90% by bicuculline. The reduction in DS was accompanied by a substantial increase in the response to null-direction motion. Bicuculline also altered the response to pulses of illumination. The magnitude and time course of inhibition were derived from the time varying difference between the control light response and that elicited during bicuculline perfusion. Both the inhibitory delay (relative to excitation) and the inhibitory amplitude are close to the expectations of a linear model of DS. The inhibition is not prolonged with respect to excitation but its risetime is approximately 2.5 times longer. The result implies a longer time constant in the inhibitory pathway relative to that in the excitatory pathway and places limits on the frequency response of inhibition and DS. The velocity-dependence of DS is related to the time course of inhibition. The stimulus drift velocity eliciting maximum directionality is inversely proportional to the inhibitory delay. Bicuculline did not influence orientation selectivity. It is concluded that the quantitative features of bicuculline-sensitive, GABA-mediated inhibition are consistent with a linear model of DS.

Deciphering a neural code for vision

Deciphering the information that eyes, ears, and other sensory organs transmit to the brain is important for understanding the neural basis of behavior. Recordings from single sensory nerve cells have yielded useful insights, but single neurons generally do not mediate behavior; networks of neurons do. Monitoring the activity of all cells in a neural network of a behaving animal, however, is not yet possible. Taking an alternative approach, we used a realistic cell-based model to compute the ensemble of neural activity generated by one sensory organ, the lateral eye of the horseshoe crab, Limulus polyphemus. We studied how the neural network of this eye encodes natural scenes by presenting to the model movies recorded with a video camera mounted above the eye of an animal that was exploring its underwater habitat. Model predictions were confirmed by simultaneously recording responses from single optic nerve fibers of the same animal. We report here that the eye transmits to the brain robust "neural images" of objects having the size, contrast, and motion of potential mates. The neural code for such objects is not found in ambiguous messages of individual optic nerve fibers but rather in patterns of coherent activity that extend over small ensembles of nerve fibers and are bound together by stimulus motion. Integrative properties of neurons in the first synaptic layer of the brain appear well suited to detecting the patterns of coherent activity. Neural coding by this relatively simple eye helps explain how horseshoe crabs find mates and may lead to a better understanding of how more complex sensory organs process information.

Limulus vision in the ocean day and night: effects of image size and contrast

Male horseshoe crabs, Limulus polyphemus, use their eyes to locate mates day and night. We investigated their ability to detect targets of different size and contrast in a mating area of Buzzards Bay, Cape Cod, MA. We found that males can see large, high-contrast targets better than small, low-contrast ones. For targets of the same size, animals must be about 0.1 m closer to a low-contrast target to see it as well as a high-contrast one. For targets of the same contrast, animals must be approximately 0.2 m closer to a small target to see it as well as one twice as large. A decrease of 0.05 steradians in the size of the retinal image of a target can be compensated by a four-fold increase in contrast. About 60% of the animals detect black targets subtending 0.110 steradians (equivalent to an adult female viewed from about 0.56 m), while only 20% detect targets subtending 0.039 steradians. This study shows that horseshoe crabs maintain about constant contrast sensitivity under diurnal changes in light intensity in their natural environment. As a consequence of circadian and adaptive mechanisms in the retina, male horseshoe crabs can detect female-size objects about equally well day and night.

Motion detection and adaptation in crayfish photoreceptors. A spatiotemporal analysis of linear movement sensitivity

Impulse and sine wave responses of crayfish photoreceptors were examined to establish the limits and the parameters of linear behavior. These receptors exhibit simple low pass behavior which is well described by the transfer function of a linear resistor-capacitor cascade of three to five stages, each with the same time constant (tau). Additionally, variations in mean light intensity modify tau twofold and the contrast sensitivity by fourfold. The angular sensitivity profile is Gaussian and the acceptance angle (phi) increases 3.2-fold with dark adaptation. The responses to moving stripes of positive and negative contrast were measured over a 100-fold velocity range. The amplitude, phase, and waveform of these responses were predicted from the convolution of the receptor's impulse response and angular sensitivity profile. A theoretical calculation based on the convolution of a linear impulse response and a Gaussian sensitivity profile indicates that the sensitivity to variations in stimulus velocity is determined by the ratio phi/tau. These two parameters are sufficient to predict the velocity of the half-maximal response over a wide range of ambient illumination levels. Because phi and tau vary in parallel during light adaptation, it is inferred that many arthropods can maintain approximately constant velocity sensitivity during large shifts in mean illumination and receptor time constant. The results are discussed relative to other arthropod and vertebrate receptors and the strategies that have evolved for movement detection in varying ambient illumination.

Implementation of the template model of vision

Adopting principles learnt from insect vision we have constructed model of a general-purpose front-end visual system for motion detection that is designed to operate in parallel along each photoreceptor axis with only local connections. The model is also designed to assist electrophysiological analysis of visual processing because it puts the response to a moving scene into sets of template responses similar to the distribution of activity among different neurons. An earlier template model divided the visual image into the fields of adjacent receptors, measured as intensity or receptor modulation at small increments of time. As soon as we used this model with natural scenes, however, we found that we had to look at changes in intensity, not intensity itself. Running the new model also generated new insights into the effects of very fast motion, of blurring the image, and the value of lateral inhibition. We also experimented with ways of measuring the angular velocity of the image moving across the eye. The camera eye is moved at a known speed and the range to objects is calculated from the angular velocity of contrasts moving across the receptor array. The original template model is modified so that contrast is saturated in a new representation of the original image data. This reduces the 8-bit grey-scale image to a log, 3 = 1.6-bit image, which becomes the input to a look-up table of templates. The output consists of groups of responding templates in specific ratios that define the input features, and these ratios lead into types of invariance at a higher level of further logic. At any stage, there can be persistent parallel inputs from all earlier stages. This design would enable groups of templates to be tuned to different expected situations, such as different velocities, different directions and different types of edges.

Efferent control of temporal response properties of the Limulus lateral eye

The sensitivity of the Limulus lateral eye exhibits a pronounced circadian rhythm. At night a circadian oscillator in the brain activates efferent fibers in the optic nerve, inducing multiple changes in the physiological and anatomical characteristics of retinal cells. These changes increase the sensitivity of the retina by about five orders of magnitude. We investigated whether this increase in retinal sensitivity is accompanied by changes in the ability of the retina to process temporal information. We measured the frequency transfer characteristic (FTC) of single receptors (ommatidia) by recording the response of their optic nerve fibers to sinusoidally modulated light. We first measured the FTC in the less sensitive daytime state and then after converting the retina to the more sensitive nighttime state by electrical stimulation of the efferent fibers. The activation of these fibers shifted the peak of the FTC to lower frequencies and reduced the slope of the low-frequency limb. These changes reduce the eye's ability to detect rapid changes in light intensity but enhance its ability to detect dim flashes of light. Apparently Limulus sacrifices temporal resolution for increased visual sensitivity at night.

Linear information processing in the retina: a study of horizontal cell responses

A basic question about visual perception is whether the retina produces a faithful or a distorted neural representation of the visual image. It is now well known that in some retinal pathways there are significant nonlinear transductions which distort the neural image. The next natural question is, What are the locations of the nonlinear stages within the retinal network? We report here on an investigation of linearity and nonlinearity of responses of horizontal cells in the turtle retina as an assay of the degree of nonlinearity in the outer plexiform layer of the retina. The visual stimuli were sinusoidal gratings; these patterns were modulated by contrast reversal with a sinusoidal time course. The conclusion from our experiments is that the turtle's horizontal cell responses show evidence only of linear spatial summation even at moderately high contrasts on moderately high background levels. Our work thus indicates that there is no significant distortion of the visual image by the photoreceptors or by the neural summation of photoreceptor signals by horizontal cells under normal physiological conditions. These results are consistent with the view that the major nonlinearities of the retina are proximal to the outer plexiform layer.

Neuroanatomy of the visual afferents in the horseshoe crab (Limulus polyphemus)

The central nervous system of Limulus consists of a circumesophageal ring of fused ganglia and a paired ventral nerve cord. The anterior portion, the protocerebrum, receives sensory inputs including visual information. Three optic nerves, one each from the lateral eye, median ocellus, and ventral eye enter each side of the protocerebrum. The central connections of each optic nerve were determined by staining cut nerve trunks with cobalt chloride. The lateral optic nerve innervates the lamina, medulla, optic tract, ventral central body, and ocellar ganglion. The branching patterns of single axons, probably those of eccentric cells in the lateral eye retina, were observed. Single, large-diameter axons in the lateral optic nerve ramify at seven loci including sites in each of the structures innervated by the lateral optic nerve as a whole. The median optic nerve innervates the ocellar ganglion, central body, optic tract, and medulla. Three types of branching patterns were observed for single, large-diameter fibers in the median optic nerve. One type bypasses the ocellar ganglion and innervates the central body. A second type passes through the ocellar ganglion and optic tract without branching and innervates the posterior medulla. A third type innervates the ocellar ganglion, ventral central body, optic tract, and medulla. The ventral optic nerve is composed of large-diameter axons of ventral photoreceptors. Each axon enters the ganglion cell layer of the medulla and branches over a planar area less than 150 micrograms in diameter. We also observed that axons from mechanoreceptors on the anterior carapace innervate the posterior neuropil of the medulla, and that about 5% of the neurons in the medullar ganglion cell layer send axons to the ipsilateral circumesophageal connective.

Spatiotemporal filtering and the interpolation effect in apparent motion

A target moving in discrete spatial steps with an appropriate interstep interval (ISI) can appear visually as if it is in continuous motion. The momentary spatial position of such a target is interpolated by the observer between its real physical positions. The extent of this interpolation was measured by a vernier alignment technique, and was found to decrease as the ISI was lengthened. A discretely moving target may be described as a continuously moving target on which is superimposed a periodic modulation of spatial position. It is shown that the traditional "staircase" stimulus for apparent motion can be generalized to include other kinds of periodic modulation. With the use of various analog-filtered and digitally filtered versions of staircase stimuli with different ISIs, it was shown that the pehnomenal interpolation of a periodically modulated moving target was affected only when the frequencies of modulation were less than about 25 Hz. The spatial amplitude of the modulation also has some effect.

Electrical coupling of photoreceptors in retinal network models

The spatial width of photoreceptor receptive fields affects the processing of signals in neural networks of the retina. This effect has been examined using the simple recurrent and non-recurrent network models, where lateral interaction strength was adjusted to approximate a prescribed receptive field profile. The results indicate that the optimal performance of the networks is obtained with photoreceptor receptive fields wider than the ganglion cell sepration. It is thus concluded that while electrical coupling of photoreceptors in the retina reduces the intrinsic noise in the system, it also improves the sampling efficiency of the laterally coupled neural network of the retina.

Effect of boundaries on the response of a neural network

The effect an abrupt boundary has upon the dynamical response of a neural network is investigated. The retina of the Limulus eye is used as a model system for studying this effect. A theoretical technique is presented for the quantitative prediction of the manner in which this neural network responds in the vicinity of its boundary. Corresponding experimental measurements of the response to moving stimuli by single optic neurons located near retinal boundaries are presented. Theory and experiment show detailed quantitative agreement.

Treatment of nerve impulse data for comparison with theory

A procedure is given for the comparison of nerve impulse data with model predictions. This method utilizes information in the nerve impulse train that is ignored by the post-stimulus-onset histogram and thereby gives an improved signal-to-noise ratio. Comparison of observed responses in the Limulus retina with predictions derived from a detailed model gives good agreement.

Nonlinear spatial summation and the contrast gain control of cat retinal ganglion cells

1. We studied how responses to visual stimuli at spatially separated locations were combined by cat retinal ganglion cells. 2. The temporal signal which modulated the stimuli was a sum of sinusoids. Fourier analysis of the ganglion cell impulse train yielded first order responses at the modulation frequencies, and second order responses at sums and differences of the input frequencies. 3. Spatial stimuli were spots in the centre and periphery of the cell's receptive field. Four conditions of stimulation were used: centre alone, periphery alone, centre and periphery in phase, centre and periphery out of phase. 4. The effective first order response of the centre was defined as the response due to centre stimulation in the presence of periphery stimulation, but independent of the relative phases of the two regions. Likewise, the effective first order response of the periphery was defined as the response due to periphery in the presence of centre stimulation, but independent of the relative phases of the two regions. These effective responses may be calculated by addition and subtraction of the measured responses to the combined stimuli. 5. There was a consistent difference between the first order frequency kernal of the effective centre and the first order kernel of the centre alone. The amplitudes of the effective centre responses were diminished at low frequencies of modulation compared to the isolated centre responses. Also, the phase of the effective centre's response to high frequencies was advanced. Such non-linear interaction occurred in all ganglion cells, X or Y, but the effects were larger in Y cells. 6. In addition to spatially uniform stimuli in the periphery, spatial grating patterns were also used. These peripheral gratings affected the first order kernal of the centre even though the peripheral gratings produced no first order responses by themselves. 7. The temporal properties of the non-linear interaction of centre and periphery were probed by modulation in the periphery with single sinusoids. The most effective temporal frequencies for producing non-linear summation were: (a) 4-15 Hz when all the visual stimuli were spatially uniform, (b) 2-8 Hz when spatial grating patterns were used in the periphery. 8. The characteristics of non-linear spatial summation observed in these experiments are explained by the properties of the contrast gain control mechanism which we have previously postulated.