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M W Levine

Publications and source records attributed to M W Levine.

At least 19 recordsLinked to original sources
PubMed2001

An analysis of the effect of retinal ganglion cell impulses upon the firing probability of neurons in the dorsal lateral geniculate nucleus of the cat.

This study examines the probabilistic way in which LGN cells produce impulses. Simultaneous extracellular recordings were made from a single lateral geniculate nucleus (LGN) relay cell and the one retinal cell that triggered most of its impulses during vigorous responses. Impulses in the retinal train were classified as 'successful' in triggering an LGN impulse, or 'unsuccessful'. Similarly, the impulses in the LGN train were either 'Triggered' by a successful retinal impulse, or were 'Anonymous'. These impulses delimited various intervals whose distributions were compared to the relevant distribution of all intervals to determine whether short or long intervals tended to dominate in each case. Intervals between unsuccessful and successful impulses tended to be shorter than other retinal intervals, with their probability declining exponentially with duration. These data imply a decaying excitation produced by each impulse, but with a short refractory period following each Triggered impulse. Short intervals between Anonymous impulses were relatively common; Anonymous impulses thus lack the same refractoriness and tend to occur in bursts. The exponential excitation following an unsuccessful retinal impulse also facilitates Anonymous impulses, while Anonymous impulses (during visual stimulation) render the LGN slightly refractory for subsequent retinal impulses.

Action Potentials↗
PubMed1998

Models for the cross-correlation between retinal ganglion cells.

Neighboring ganglion cells in the vertebrate retina not only respond to the same stimuli but also display cross-correlated activity on a millisecond time scale. Recent studies of this cross-correlation have indicated that simple linear addition of common variability to each ganglion cell signal does not account for the observations (Levine 1997). In this report, Monte Carlo simulations of various linear and nonlinear models are presented that confirm the earlier speculations. Models in which common variability alters the leakages of a pair of leaky integrate-and-fire neurons account for the data and predict the cross-correlogram lag without invoking temporal delay lines.

Animals↗
PubMed1996

Tailoring of variability in the lateral geniculate nucleus of the cat.

Variability is usually considered an unwanted component in a sensory signal, yet the visual system does not seem to filter out the noise. On the contrary, noise is 'tailored' to scale with the signal size. We show that this tailoring occurs in the lateral geniculate nucleus, preferentially in X-cells, which are the cells most likely to transmit pattern information. Tailoring the variability to the signal size may be the visual system's way of providing the right amount of variability for a signal of any magnitude at all times during the computation.

Animals↗
PubMed1992

Modeling the variability of firing rate of retinal ganglion cells.

Impulse trains simulating the maintained discharges of retinal ganglion cells were generated by digital realizations of the integrate-and-fire model. If the mean rate were set by a "bias" level added to "noise," the variability of firing would be related to the mean firing rate as an inverse square root law; the maintained discharges of retinal ganglion cells deviate systematically from such a relationship. A more realistic relationship can be obtained if the integrate-and-fire mechanism is "leaky"; with this refinement, the integrate-and-fire model captures the essential features of the data. However, the model shows that the distribution of intervals is insensitive to that of the underlying variability. The leakage time constant, threshold, and distribution of the noise are confounded, rendering the model unspecifiable. Another aspect of variability is presented by the variance of responses to repeated discrete stimuli. The variance of response rate increases with the mean response amplitude; the nature of that relationship depends on the duration of the periods in which the response is sampled. These results have defied explanation. But if it is assumed that variability depends on mean rate in the way observed for maintained discharges, the variability of responses to abrupt changes in lighting can be predicted from the observed mean responses. The parameters that provide the best fits for the variability of responses also provide a reasonable fit to the variability of maintained discharges.

Action Potentials↗
PubMed1992

Variability of responses of cat retinal ganglion cells.

Previous studies of the variability of firing of retinal ganglion cells have led to apparently contradictory conclusions. To a first approximation, the variance of rate of maintained discharges of ganglion cells in cat is independent of the mean firing rate. On the other hand, the variability of responses to abrupt changes in lighting of ganglion cells in goldfish increases with increasing firing rate. To examine whether the difference is due to differences between species, we examined the variability of responses of cat ganglion cells, and find it similar to that of goldfish ganglion cells. The variance of rate of ganglion cells is neither independent of mean rate, as might be expected from maintained discharges, nor directly proportional to the mean rate, as it is for cat cortical cells. Rather, there is a nonlinear relationship between variance of rate and mean rate.

Animals↗
PubMed1991

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells.

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1991

A model for the variability of maintained discharges and responses to flashes of light.

Previous studies of the variability of firing of retinal ganglion cells have led to apparently contradictory conclusions. To a first approximation, maintained discharges derive their variability from a noise source that is linearly added to the signal setting the mean firing rate. On the other hand, the variability of responses to abrupt changes in lighting seems to result from a nonlinear interaction between signal and noise. In both the cat and the goldfish retinae, the variance of rate is a fractional power function of the mean response amplitude (impulses/s). The exponent of that power function depends on the duration of the period in which the response is sampled after each transition in luminance; longer durations have a larger exponent. These results are difficult to explain with any simple model. The variability of the maintained discharges also deviates from the predictions of simple additivity. We propose a model for the variability of responses to abrupt changes in lighting that incorporates variability of the form observed for maintained discharges. The parameters of our model that provide the best fits to the variability of responses also provide a reasonable fit to the variability of maintained discharges. Thus, a single explanation can account for the variability of maintained discharges and responses of ganglion cells.

Animals↗
PubMed1991

Complicated substructure from simple circularly symmetric Gaussian processes within the centers of goldfish ganglion cell receptive fields.

The center of the receptive field of some retinal ganglion cells exhibits an interesting fine structure: the relative amplitudes of responses to onset and responses to offset of a small spot of light varies systematically as the spot is positioned at various places within the center. Although this pattern may appear complicated, a simple model can account for it in detail. The model postulates that the ganglion cell receives input from separate ON and OFF processes within the center of its receptive field. These processes have the form of Gaussian functions and are laterally displaced from each other. These central ON and OFF input processes are not associated with the additional antagonistic surround of the receptive field. The model is examined for various parameters of the input processes. The observed systematic variation in the ratio of offset to onset responses is predicted when the two processes are of nearly equal width (standard deviation of the Gaussians). Receptive fields made of more than two Gaussians produce various patterns, depending on the relative standard deviations of the Gaussians. Oblong fields, reminiscent of those found in visual cortex, may be generated from a relatively small number of circularly symmetric Gaussian processes.

Animals↗
PubMed1988

Statistical properties of the maintained discharge of chemically isolated ganglion cells in goldfish retina.

Action potentials were recorded from isolated goldfish retinae maintained in a superfusate of Ringer's solution. Responses to flashes of light and maintained discharges were obtained from 84 cells. The properties of these cells were compared to those in two other goldfish preparations: the isolated retina maintained in a flow of moist oxygen and the self-respiring fish. Maintained discharges of cells in the superfused retinae tended to have lower mean firing rates, higher variability, and weaker high-pass properties than had been observed in the previous preparations. These properties seemed insensitive to the particular formulae used to superfuse the retinae. Cobalt, which disables synapses, dramatically reduced maintained firing and eliminated photic responses. Cells that did fire in the presence of cobalt generally had low variabilities before cobalt was added; their firing in cobalt was considerably more variable than the baseline. Nevertheless, cobalt did not seem to change the temporal dependency (high-pass properties) of the maintained discharges. The cholinergic agonist carbachol had an excitatory effect upon 71% of the cells tested. Bursty or oscillatory firing in cobalt was rendered more regular by the addition of carbachol. With the exception of the mean firing rate, none of the statistical properties of the maintained discharge differed in cobalt plus carbachol from those in normal Ringer's solution. There was a tendency for the statistical properties of the maintained discharge after the treatment to approach those of the previously reported preparations; the treatment was at least partially responsible for the drift in properties. The results are discussed in terms of the possible sources of variability in the ganglion cell's discharge, with particular reference to the high-pass filter that appears to act upon it.

Action Potentials↗
PubMed1988

Evidence for local circuits within the receptive fields of retinal ganglion cells in goldfish.

A new form of receptive field map, the response-component map, was developed to identify points within a receptive field that produce similar response patterns. The fields were probed with discretely flashed small spots of light. The magnitudes of the responses to stimulus onset and to stimulus offset elicited at each point were represented on the map by a vector radiating from the position representing the location of that point. Thus, response-component maps preserve the spatial distributions of responsivity and temporal nonlinearities. Points with similar response patterns were identified from a scatterplot in which the response at each spatial position was located in a plane representing the angles of the response-component vectors. Points with similar response characteristics that were also spatially contiguous were considered as a distinct response subregion within the receptive field. Barely 10% of the receptive fields of goldfish ganglion cells mapped with this technique proved as simple as the traditional concentric field described for retinal cells. In at least 17% of the cases, the field showed three concentric rings, with a very small "inner center" within the center of the field. In at least 50% of the cases, response subregions of different type lay side by side, rather than in a concentric configuration. Some subregions could be differentiated by the relative strengths of the responses to onset and offset of the stimulus spot, supporting the hypothesis that a push-pull system generates ganglion cell responses. Subregions were evident in successive mappings of the same cell, demonstrating they are not due to the vagaries of individual responses. They probably represent the spatial domains (or their intersections) of individual interneurons distal to the retinal ganglion cells. It is possible that position within the receptive field may be coded by the temporal pattern of the responses.

Animals↗
PubMed1988

Variability in responses of retinal ganglion cells.

Changes in the maintained discharge of retinal ganglion cells have been modeled by addition of noise to a rate-setting signal, whereas the responses of cortical cells have been reported to indicate a nonlinear relationship between noise and signal. To determine whether this represents a difference between retinal cells and cortical cells, the variance of light-evoked responses of ganglion cells in the retinas of goldfish was compared with the magnitude of the responses. Variance increased for higher firing rates. These results are discussed in terms of mechanisms by which light-evoked signals might interact with the variability of maintained discharges.

Analysis of Variance↗
PubMed1987

Interactions between the rod and the cone pathways in the cat retina.

The receptive field centers of 21 on-center X retinal ganglion cells in cat were tested with stimuli designed to detect nonlinear interactions between the rod and the cone systems. One red and one green stimulus light were always present, at a level such that modulation of the red light essentially affected only cones, and that of the green light only rods. The two lights could be superimposed spatially (overlapped configuration) or fall on separate subareas of the receptive field center (nonoverlapped configuration). In most cases, there was less complete summation of the responses to modulation of the lights in the overlapped than in the nonoverlapped configuration, with a corresponding difference in the summation of sensitivities. In 1/6 of the experiments, there was more complete summation of the responses to the lights in the overlapped configuration, with a corresponding difference in the summation of sensitivities. The mean magnitude of the interaction for all experiments was equivalent to an antagonistic interaction between the rod and cone pathways such that the signal in each was diminished by a quantity slightly greater than 30% of the signal in the other.

Animals↗
PubMed1987

Variability in the maintained discharges of retinal ganglion cells.

The statistics of maintained discharges of goldfish and cat retinal ganglion cells are examined, and simulations are made with integrate-and-fire models. Actual interval distributions are best fitted with a hyperbolic gamma distribution; however, interval distributions derived from simulations demonstrate that this need not imply a skewed variable signal. The high-pass filtering in the maintained discharges of ganglion cells is weaker than would be expected from the transfer function for photic signals; this phenomenon, as well as the observation of two peaks in some of the interval distributions, is modeled by transient changes in the firing threshold after each impulse. Increases in firing rate owing to changes in the level of background illumination are accompanied by declines in the coefficient of variation; simulations predict an inverse-square-root relationship between the rate and the coefficient of variation, an approximation that may be improved by again assuming changes in the firing threshold.

Action Potentials↗
PubMed1986

The variability of the maintained discharge of cat dorsal lateral geniculate cells.

Maintained discharge in the presence of a steady background luminance was analysed from forty-eight cells in the A laminae of the dorsal lateral geniculate nucleus of cat. Cells were categorized as XG or YG and, in most cases, as on-or off-centre. The temporal contrast sensitivity function of twenty-seven of the cells was measured using drifting gratings of the optimal spatial frequency. The maintained discharge was characterized by several simple descriptors, including the interval distribution, mean firing rate, and coefficient of variability. Its temporal organization was revealed by two indicators of correlational properties, the normalized autocovariance and the serial correlogram, and more effectively, by the less familiar plot of the standard deviation of firing rate versus sample duration. The statistics revealing temporal organization of the maintained discharge indicated that the variability of firing was nearly, but not quite, derived from a renewal process. The maintained discharges of seven cells were studied for more than one luminance level. Mean luminance did not appear to have any consistent effect upon the statistics of the maintained discharge. The temporal filtering properties of lateral geniculate cells were deduced from a comparison of the temporal contrast sensitivities of geniculate neurones (Troy, 1983b) and retinal ganglion cells (Lennie, 1980). Analyses showed that the maintained discharge of retinal neurones passed through this filter could not account for the observed statistics of the maintained discharge of geniculate neurones. It is proposed that additional noise is added to the retinal signal at the level of the lateral geniculate. Models are presented to explain how the signals might be filtered in a way that does not also affect the added noise.

Action Potentials↗
PubMed1984

Common noise in the firing of neighbouring ganglion cells in goldfish retina.

Pairs of goldfish retinal ganglion cells with overlapping receptive fields were recorded during stimulation with repeated light flashes. Cross-correlation histograms for 'maintained' discharge, 'on' responses, and 'off' responses were computed with a correction for the systematic responses to the stimuli; cross-covariances were derived from these. If stimulus-induced signals and noise combine linearly, then the cross-covariances are independent of differences in mean firing rate. Cross-covariances of pairs of cells with the same response polarity displayed a positive peak near zero lag; pairs with complementary responses showed a negative peak. 'On-off' cells could generally be classified as on-like or off-like, based on the plateau of firing during a prolonged flash and the relative magnitudes of the on and off peak responses; the cross-covariances of these cells were as one would predict if they were pure on- or off-centre neurones. The cross-covariances derived from the on period usually differed in magnitude from those derived in the dark (either maintained or off response). In general, cross-covariances for off responses were nearly identical to those for the maintained discharges of the same pair, although the mean rates at off were usually quite different from the maintained. The change in magnitude of the cross-covariances from on responses therefore appears to be a non-linear effect of light, and not of the changes in firing rate induced by the light. Other features of the cross-covariances were not affected by stimulation. The general shapes remained fairly constant, and the lags at which the peaks occurred were not consistently affected. We estimated the variance of the firing rate of each unit in three ways, and used two methods of portioning the variance implied by the cross-covariances; from these estimates, we obtained an upper bound for the proportion of the variance of firing of a cell which is due to the common noise that affects both members of a pair. We found that the common influence accounts for less than 20% of the total variance. During stimulation, both the magnitude of the cross-covariance and the variance of the rates change; however, the percentage of total variance contributed by the common noise source is constant. We conclude that light has the effect of changing the gain of the pathway after the introduction of both the common and unshared (private) noise sources but before the ganglion cell.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗
PubMed1983

Statistics of the maintained discharge of cat retinal ganglion cells.

Action potentials were recorded from single fibres in the optic tracts of anaesthetized cats. Continuous records were obtained at various levels of scotopic and mesopic retinal illumination. In some cases, the light intensity was modulated by a pseudorandom Gaussian white-noise signal. The maintained discharge of on-centre neurones increased while the maintained discharge of off-centre neurons decreased with increased illumination of the receptive field centre. For both cell types, the coefficient of variation declined with increased rate of discharge. There was minimal short-term dependency in the firing patterns, and it was unaffected by the level of retinal illumination. Virtually all of the structure revealed by the normalized autocovariance functions could be attributed to the shape of the interval distributions. The first few coefficients of the serial correlogram were slightly negative. The magnitude of this negativity was not related to illumination. Long-term dependency in the firing pattern was also quite small; the standard deviations of the mean rate in samples of about 1 sec duration were only slightly less than would be predicted from the interval distributions. This dependency tended to increase at higher retinal illuminations. Neural discharges elicited by Gaussian modulation of the light were strikingly different from those elicited by steady light. Modulation caused the first coefficient of the serial correlogram to become more positive, while the next several coefficients became more negative. A corresponding pattern could be seen in the normalized autocovariance functions, and in the differences between the normalized autocovariance and normalized autoconvolution. Long-term dependency also increased dramatically, such that the standard deviations of mean rate were about 60% of what would be expected given the interval distributions observed. These results place a number of constraints upon the ways in which intrinsic noise in the retina may enter the visual processing network. Two alternative models consistent with the data are presented.

Animals↗
PubMed1983

Correlation of activity in neighbouring goldfish ganglion cells: relationship between latency and lag.

Pairs of retinal ganglion cells in the isolated goldfish retina were recorded simultaneously with a single electrode. Repeated flashes of light were delivered to evaluate the response latency of each of the units. The cross-correlation histogram for the maintained discharge of each pair of cells was examined, and its temporal relationships (lags) were compared with the differences in response latencies of the two units. There was a strong correlation between these measures; however, the differences between latencies were often at least twice as great as the lags. The differences between the times to the peaks of the responses of the two units were less reliably related to the lags of the pairs, although the correlation was positive and the differences in time-to-peak generally greater than the lags. The weaker relationship between the difference in time-to-peak and lag than between latency difference and lag is apparently a manifestation of a negative correlation between latency and rise time (from first response to peak). This indicates that cells with a longer latency compensate with a faster rise time. There was a negative correlation between the mean maintained rate of a neurone and its response latency. That is, cells with faster maintained discharge rates respond sooner than those with slower maintained rates. There was virtually no relationship between the lags or the differences in latency and the differences between the magnitudes of the responses to light. Thus, it is unlikely that differences in latency (or lags) could be attributed to unequal effectiveness of the stimuli for the two units. The relationship between differences in latency and lags did not depend on the response categorizations of the two units. Specifically, it did not matter whether the members of the pair were on centre, off centre or on-off centre; neither did it matter whether they were X-like or not-X-like neurones. Consideration of these data leads to the conclusion that there must be 'marked' pathways of differential conduction velocity through the retina.

Action Potentials↗