How much the eye tells the brain

In the classic "What the frog's eye tells the frog's brain," Lettvin and colleagues showed that different types of retinal ganglion cell send specific kinds of information. For example, one type responds best to a dark, convex form moving centripetally (a fly). Here we consider a complementary question: how much information does the retina send and how is it apportioned among different cell types? Recording from guinea pig retina on a multi-electrode array and presenting various types of motion in natural scenes, we measured information rates for seven types of ganglion cell. Mean rates varied across cell types (6-13 bits . s(-1)) more than across stimuli. Sluggish cells transmitted information at lower rates than brisk cells, but because of trade-offs between noise and temporal correlation, all types had the same coding efficiency. Calculating the proportions of each cell type from receptive field size and coverage factor, we conclude (assuming independence) that the approximately 10(5) ganglion cells transmit on the order of 875,000 bits . s(-1). Because sluggish cells are equally efficient but more numerous, they account for most of the information. With approximately 10(6) ganglion cells, the human retina would transmit data at roughly the rate of an Ethernet connection.     

Neural coding properties based on spike timing and pattern correlation of retinal ganglion cells

Correlation between spike trains or neurons sometimes indicates certain neural coding rules in the visual system. In this paper, the relationship between spike timing correlation and pattern correlation is discussed, and their ability to represent stimulus features is compared to examine their coding strategies not only in individual neurons but also in population. Two kinds of stimuli, natural movies and checkerboard, are used to arouse firing activities in chicken retinal ganglion cells. The spike timing correlation and pattern correlation are calculated by cross-correlation function and Lempel–Ziv distance respectively. According to the correlation values, it is demonstrated that spike trains with similar spike patterns are not necessarily concerted in firing time. Moreover, spike pattern correlation values between individual neurons’ responses reflect the difference of natural movies and checkerboard; neurons cooperate with each other with higher pattern correlation values which represent spatiotemporal correlations during response to natural movies. Spike timing does not reflect stimulus features as obvious as spike patterns, caused by their particular coding properties or physiological foundation. As a result, separating the pattern correlation out of traditional timing correlation concept uncover additional insight in neural coding.     

Retino-cortical information transmission achievable with a retina implant

Blind subjects with photoreceptor degeneration perceive phosphenes when their intact retinal ganglion cells are stimulated electrically. Is this approach suitable for transmitting enough information to the visual cortex for partially restoring vision? We stimulated the retina of anesthetized cats electrically and visually while recording the responses in the visual cortex. Transmission of retino-cortical information T was quantified by information theory. T was 20-160 bit/s (per stimulation and recording site) with random electrical or visual impulse stimulation at rates between 20 and 40 s-1. While increasing spatial density of independent electrical stimulation channels T did not saturate with 7 electrodes/mm2 retina. With seven electrodes up to 500 bit/s was transmitted to 15 cortical recording sites. Electrical stimulation basically employs temporal stimulus patterns. They are intimately linked with intensity/contrast information coded by the spike density of retinal ganglion cells. From the cortical information spread we estimated the spatial resolution as 0.5mm cortex corresponding to 0.5-1.0 degrees visual angle. If the human cortex can receive and decode the information transmitted by a retina implant, our quantitative results measured in cats suggest that visuo-motor coordination and object recognition in many in- and out-door situations will be possible.     

Distribution Coding in the Visual Pathway

Although a variety of types of spike interval histograms have been reported, little attention has been given to the spike interval distribution as a neural code and to how different distributions are transmitted through neural networks. In this paper we present experimental results showing spike interval histograms recorded from retinal ganglion cells of the cat. These results exhibit a clear correlation between spike interval distribution and stimulus condition at the retinal ganglion cell level. The averaged mean rates of the cells studied were nearly the same in light as in darkness whereas the spike interval histograms were much more regular in light than in darkness. We present theoretical models which illustrate how such a distribution coding at the retinal level could be “interpreted” or recorded at some higher level of the nervous system such as the lateral geniculate nucleus. Interpretation is an essential requirement of a neural code which has often been overlooked in modeling studies. Analytical expressions are derived describing the role of distribution coding in determining the transfer characteristics of a simple interaction model and of a lateral inhibition network. Our work suggests that distribution coding might be interpreted by simply interconnected neural networks such as relay cell networks, in general, and the primary thalamic sensory nuclei in particular.     

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runsn times as often as learned, wheren is a positive integer (n 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.     

Visual pattern discrimination by population retinal ganglion cells’ activities during natural movie stimulation

In the visual system, neurons often fire in synchrony, and it is believed that synchronous activities of group neurons are more efficient than single cell response in transmitting neural signals to down-stream neurons. However, whether dynamic natural stimuli are encoded by dynamic spatiotemporal firing patterns of synchronous group neurons still needs to be investigated. In this paper we recorded the activities of population ganglion cells in bullfrog retina in response to time-varying natural images (natural scene movie) using multi-electrode arrays. In response to some different brief section pairs of the movie, synchronous groups of retinal ganglion cells (RGCs) fired with similar but different spike events. We attempted to discriminate the movie sections based on temporal firing patterns of single cells and spatiotemporal firing patterns of the synchronous groups of RGCs characterized by a measurement of subsequence distribution discrepancy. The discrimination performance was assessed by a classification method based on Support Vector Machines. Our results show that different movie sections of the natural movie elicited reliable dynamic spatiotemporal activity patterns of the synchronous RGCs, which are more efficient in discriminating different movie sections than the temporal patterns of the single cells’ spike events. These results suggest that, during natural vision, the down-stream neurons may decode the visual information from the dynamic spatiotemporal patterns of the synchronous group of RGCs’ activities.     

See globally, spike locally: oscillations in a retinal model encode large visual features

We show that coherent oscillations among neighboring ganglion cells in a retinal model encode global topological properties, such as size, that cannot be deduced unambiguously from their local, time-averaged firing rates. Whereas ganglion cells may fire similar numbers of spikes in response to both small and large spots, only large spots evoke coherent high frequency oscillations, potentially allowing downstream neurons to infer global stimulus properties from their local afferents. To determine whether such information might be extracted over physiologically realistic spatial and temporal scales, we analyzed artificial spike trains whose oscillatory correlations were similar to those measured experimentally. Oscillatory power in the upper gamma band, extracted on single-trials from multi-unit spike trains, supported good to excellent size discrimination between small and large spots, with performance improving as the number of cells and/or duration of the analysis window was increased. By using Poisson distributed spikes to normalize the firing rate across stimulus conditions, we further found that coincidence detection, or synchrony, yielded substantially poorer performance on identical size discrimination tasks. To determine whether size encoding depended on contiguity independent of object shape, we examined the total oscillatory activity across the entire model retina in response to random binary images. As the ON-pixel probability crossed the percolation threshold, which marks the sudden emergence of large connected clusters, the total gamma-band activity exhibited a sharp transition, a phenomena that may be experimentally observable. Finally, a reanalysis of previously published oscillatory responses from cat ganglion cells revealed size encoding consistent with that predicted by the retinal model.     

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.     

Information flow and temporal coding in primate pattern vision

We perform time-resolved calculations of the information transmitted about visual patterns by neurons in primary visual and inferior temporal cortices. All measurable information is carried in an effective time-varying firing rate, obtained by averaging the neuronal response with a resolution no finer than about 25 ms in primary visual cortex and around twice that in inferior temporal cortex. We found no better way for a neuron receiving these messages to decode them than simply to count spikes for this long. Most of the information tends to be concentrated in one or, more often, two brief packets, one at the very beginning of the response and the other typically 100 ms later. The first packet is the most informative part of the message, but the second one generally contains new information. A small but significant part of the total information in the message accumulates gradually over the entire course of the response. These findings impose strong constraints on the codes used by these neurons.     

Interaction of excitatory and depressant amino acids in the frog retina

(1) Application of excitatory or depressant amino acids (concentrations from 10(-4) to 10(-2) M) could modify response patterns of the retinal ganglion cells to photic stimulus. Excitatory amino acids gave rise to spontaneous discharge while depressant amino acids inhibited spike discharge in response to test flashes. (2) Application of excitatory amino acids of more than 10(-3) M resulted in irreversible termination of spike discharges while recovery was always observed in the case of depressant amino acids even when the concentration of the applied solution was as high as 10(-2) M. No effect was observed when one exciting and one depressant amino acid were properly combined. (3) There is a mixture of four amino acids (two excitatory and two depressant) which could enhance the spike discharge in response to test flashes without giving rise to spontaneous firing. (4) It is implied that proper balance of excitatory and depressant amino acids is important in regulating the excitability of a number of neurons.     

Computing Complex Visual Features with Retinal Spike Times

Neurons in sensory systems can represent information not only by their firing rate, but also by the precise timing of individual spikes. For example, certain retinal ganglion cells, first identified in the salamander, encode the spatial structure of a new image by their first-spike latencies. Here we explore how this temporal code can be used by downstream neural circuits for computing complex features of the image that are not available from the signals of individual ganglion cells. To this end, we feed the experimentally observed spike trains from a population of retinal ganglion cells to an integrate-and-fire model of post-synaptic integration. The synaptic weights of this integration are tuned according to the recently introduced tempotron learning rule. We find that this model neuron can perform complex visual detection tasks in a single synaptic stage that would require multiple stages for neurons operating instead on neural spike counts. Furthermore, the model computes rapidly, using only a single spike per afferent, and can signal its decision in turn by just a single spike. Extending these analyses to large ensembles of simulated retinal signals, we show that the model can detect the orientation of a visual pattern independent of its phase, an operation thought to be one of the primitives in early visual processing. We analyze how these computations work and compare the performance of this model to other schemes for reading out spike-timing information. These results demonstrate that the retina formats spatial information into temporal spike sequences in a way that favors computation in the time domain. Moreover, complex image analysis can be achieved already by a simple integrate-and-fire model neuron, emphasizing the power and plausibility of rapid neural computing with spike times.     

Spike amplitude modulation at high stimulation frequencies

Summary A technique of mathematical analysis has been developed for studying spike amplitude variations, during natural sinusoidal stimulation. This technique is suitable even when stimulation frequency is of the same order as, or higher than, the cell firing rate.We used this technique for the cat's retinal ganglion cells. The results agree with the previous ones (Gestri et al., 1967) at low stimulation frequencies and show that the spike amplitude modulation occur even at high frequencies, the phase shift between spike amplitude and firing probability being a function of the stimulation frequency.     

On the complex dynamics of intracellular ganglion cell light responses in the cat retina

We recorded intracellular responses from cat retinal ganglion cells to sinusoidal flickering lights, and compared the response dynamics with a theoretical model based on coupled nonlinear oscillators. Flicker responses for several different spot sizes were separated in a smooth generator (G) potential and corresponding spike trains. We have previously shown that the G-potential reveals complex, stimulus-dependent, oscillatory behavior in response to sinusoidally flickering lights. Such behavior could be simulated by a modified van der Pol oscillator. In this paper, we extend the model to account for spike generation as well, by including extended Hodgkin-Huxley equations describing local membrane properties. We quantified spike responses by several parameters describing the mean and standard deviation of spike burst duration, timing (phase shift) of bursts, and the number of spikes in a burst. The dependence of these response parameters on stimulus frequency and spot size could be reproduced in great detail by coupling the van der Pol oscillator and Hodgkin-Huxley equations. The model mimics many experimentally observed response patterns, including non-phase-locked irregular oscillations. Our findings suggest that the information in the ganglion cell spike train reflects both intraretinal processing, simulated by the van der Pol oscillator, and local membrane properties described by Hodgkin-Huxley equations. The interplay between these complex processes can be simulated by changing the coupling coefficients between the two oscillators. Our simulations therefore show that irregularities in spike trains, which normally are considered to be noise, may be interpreted as complex oscillations that might carry information.To the memory of Prof. Otto-Joachim Grusser     

Auditory information coding by modeled cochlear nucleus neurons

In this paper we use information theory to quantify the information in the output spike trains of modeled cochlear nucleus globular bushy cells (GBCs). GBCs are part of the sound localization pathway. They are known for their precise temporal processing, and they code amplitude modulations with high fidelity. Here we investigated the information transmission for a natural sound, a recorded vowel. We conclude that the maximum information transmission rate for a single neuron was close to 1,050 bits/s, which corresponds to a value of approximately 5.8 bits per spike. For quasi-periodic signals like voiced speech, the transmitted information saturated as word duration increased. In general, approximately 80% of the available information from the spike trains was transmitted within about 20 ms. Transmitted information for speech signals concentrated around formant frequency regions. The efficiency of neural coding was above 60% up to the highest temporal resolution we investigated (20 μs). The increase in transmitted information to that precision indicates that these neurons are able to code information with extremely high fidelity, which is required for sound localization. On the other hand, only 20% of the information was captured when the temporal resolution was reduced to 4 ms. As the temporal resolution of most speech recognition systems is limited to less than 10 ms, this massive information loss might be one of the reasons which are responsible for the lack of noise robustness of these systems.     

Spatiotemporal analysis of simultaneous single-unit activity in the dragonfly

The present work describes a new technique for the identification of functional connectivity between neural firing patterns. The simultaneous singleunit recordings obtained from over 50 individual cells in the dragonfly mesothoracic ganglion during three consecutive behavioral states: pre-flight, flight and postflight were evaluated. Each individual spike train was converted into a synthesized analog gradient designed to capture crucial physiological characteristics of the cell from which the spike train emanated. Estimates of network functional connectivity were calculated using correlations between analog gradient spike trains for all possible cell pairings. Both functional excitation and inhibition could be detected in the correlations. The detection of functional connectivity was relatively independent of cell firing rate. More detailed analyses indicated the existence of cellular firing histories and connectivity patterns during flight that strongly resembled the characteristics of a bi-stable oscillator. Such an oscillator, hypothetically, could drive the elevator and depressor motor neuron firing paterns that support wing kinematics. There was no evidence for the functional existence of such an oscillator within either preor post-flight spike records. The detected spatiotemporal patterns of neural activity are hypothesized to be consistent with neural command sequences that the dragonfly might use to control flight. The demonstrated capability to define short-time scale functional relationships between spike trains obtained from dragonfly ganglia should have valuable applications to the comparative study of neural information processing strategies in a variety of other neural systems.     

Visual pattern recognition based on spatio-temporal patterns of retinal ganglion cells’ activities

Neural information is processed based on integrated activities of relevant neurons. Concerted population activity is one of the important ways for retinal ganglion cells to efficiently organize and process visual information. In the present study, the spike activities of bullfrog retinal ganglion cells in response to three different visual patterns (checker-board, vertical gratings and horizontal gratings) were recorded using multi-electrode arrays. A measurement of subsequence distribution discrepancy (MSDD) was applied to identify the spatio-temporal patterns of retinal ganglion cells' activities in response to different stimulation patterns. The results show that the population activity patterns were different in response to different stimulation patterns, such difference in activity pattern was consistently detectable even when visual adaptation occurred during repeated experimental trials. Therefore, the stimulus pattern can be reliably discriminated according to the spatio-temporal pattern of the neuronal activities calculated using the MSDD algorithm.     

Ion conductances related to development of repetitive firing in mouse retinal ganglion neurons in situ

ABSTRACT: In the retina, the ability to encode graded depolarizations into spike trains of variable frequency appears to be a specific property of retinal ganglion neurons (RGNs). To deduce the developmental changes in ion conductances underlying the transition from single to repetitive firing, patch-clamp recordings were performed in the isolated mouse retina between embryonic day 15 (E15) and postnatal day 5 (P5). Immature neurons of the E15 retina were selected according to their capacity to generate voltage-activated Na+ currents (I(Na)(v)). Identification of P5 RGNs was based on retrograde labeling, visualization of the axon, or the amplitude of I(Na)(v). At E15, half of the cells were excitable but none of them generated more than one spike. At P5, all cells were excitable and a majority discharged in tonic fashion. Ion conductances subserving maintenance of repetitive discharge were identified at P5 by exposure to low extracellular Ca2+, Cd2+, and charybdotoxin, all of which suppressed repetitive discharge. omega-Conotoxin GVIA and nifedipine had no effect. We compared passive membrane properties and a variety of voltage-activated ion channels at E15 and P5. It was found that the density of high voltage-activated (HVA) Ca2+ currents increased in parallel with the development of repetitive firing, while the density of Ni2+-sensitive low voltage-activated (LVA) Ca2+ currents decreased. Changes in density and activation kinetics of tetrodotoxin-sensitive Na+ currents paralleled changes in firing thresholds and size of action potentials, but seemed to be unrelated to maintenance of repetitive firing. Densities of A-type K+ currents and delayed rectifier currents did not change. The results suggest that HVA Ca2+ channels, and among them a toxin-resistant subtype, are specifically engaged in activation of Ca2+-sensitive K+ conductance and thereby account for frequency coding in postnatal RGNs.     

Response dynamics of bullfrog ON-OFF RGCs to different stimulus durations

Stimulus duration is an important feature of visual stimulation. In the present study, response properties of bullfrog ON-OFF retinal ganglion cells (RGCs) in exposure to different visual stimulus durations were studied. By using a multi-electrode recording system, spike discharges from ON-OFF RGCs were simultaneously recorded, and the cells’ ON and OFF responses were analyzed. It was found that the ON response characteristics, including response latency, spike count, as well as correlated activity and relative latency between pair-wise cells, were modulated by different light OFF intervals, while the OFF response characteristics were modulated by different light ON durations. Stimulus information carried by the ON and OFF responses was then analyzed, and it was found that information about different light ON durations was more carried by transient OFF response, whereas information about different light OFF intervals were more carried by transient ON response. Meanwhile, more than 80 % information about stimulus durations was carried by firing rate. These results suggest that ON-OFF RGCs are sensitive to different stimulus durations, and they can efficiently encode the information about visual stimulus duration by firing rate.     

Phase-of-firing coding of natural visual stimuli in primary visual cortex

We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts. The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.     

The chronotron: a neuron that learns to fire temporally precise spike patterns

In many cases, neurons process information carried by the precise timings of spikes. Here we show how neurons can learn to generate specific temporally precise output spikes in response to input patterns of spikes having precise timings, thus processing and memorizing information that is entirely temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that provides high memory capacity (E-learning), and one that has a higher biological plausibility (I-learning). With I-learning, the neuron learns to fire the target spike trains through synaptic changes that are proportional to the synaptic currents at the timings of real and target output spikes. We study these learning rules in computer simulations where we train integrate-and-fire neurons. Both learning rules allow neurons to fire at the desired timings, with sub-millisecond precision. We show how chronotrons can learn to classify their inputs, by firing identical, temporally precise spike trains for different inputs belonging to the same class. When the input is noisy, the classification also leads to noise reduction. We compute lower bounds for the memory capacity of chronotrons and explore the influence of various parameters on chronotrons' performance. The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation. Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.