Lateral geniculate neurons in behaving primates. II. Encoding of visual information in the temporal shape of the response

A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area

What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.

A Temporal Sampling Basis for Visual Processing in Developmental Dyslexia

Knowledge of oscillatory entrainment and its fundamental role in cognitive and behavioral processing has increasingly been applied to research in the field of reading and developmental dyslexia. Growing evidence indicates that oscillatory entrainment to theta frequency spoken language in the auditory domain, along with cross-frequency theta-gamma coupling, support phonological processing (i.e., cognitive encoding of linguistic knowledge gathered from speech) which is required for reading. This theory is called the temporal sampling framework (TSF) and can extend to developmental dyslexia, such that inadequate temporal sampling of speech-sounds in people with dyslexia results in poor theta oscillatory entrainment in the auditory domain, and thus a phonological processing deficit which hinders reading ability. We suggest that inadequate theta oscillations in the visual domain might account for the many magno-dorsal processing, oculomotor control and visual deficits seen in developmental dyslexia. We propose two possible models of a magno-dorsal visual correlate to the auditory TSF: (1) A direct correlate that involves "bottom-up" magnocellular oscillatory entrainment of the visual domain that occurs when magnocellular populations phase lock to theta frequency fixations during reading and (2) an inverse correlate whereby attending to text triggers "top-down" low gamma signals from higher-order visual processing areas, thereby organizing magnocellular populations to synchronize to a theta frequency to drive the temporal control of oculomotor movements and capturing of letter images at a higher frequency.

Optogenetic activation of corticogeniculate feedback stabilizes response gain and increases information coding in LGN neurons

In spite of their anatomical robustness, it has been difficult to establish the functional role of corticogeniculate circuits connecting primary visual cortex with the lateral geniculate nucleus of the thalamus (LGN) in the feedback direction. Growing evidence suggests that corticogeniculate feedback does not directly shape the spatial receptive field properties of LGN neurons, but rather regulates the timing and precision of LGN responses and the information coding capacity of LGN neurons. We propose that corticogeniculate feedback specifically stabilizes the response gain of LGN neurons, thereby increasing their information coding capacity. Inspired by early work by McClurkin et al. (1994), we manipulated the activity of corticogeniculate neurons to test this hypothesis. We used optogenetic methods to selectively and reversibly enhance the activity of corticogeniculate neurons in anesthetized ferrets while recording responses of LGN neurons to drifting gratings and white noise stimuli. We found that optogenetic activation of corticogeniculate feedback systematically reduced LGN gain variability and increased information coding capacity among LGN neurons. Optogenetic activation of corticogeniculate neurons generated similar increases in information encoded in LGN responses to drifting gratings and white noise stimuli. Together, these findings suggest that the influence of corticogeniculate feedback on LGN response precision and information coding capacity could be mediated through reductions in gain variability.

Information-Theoretic Bounds and Approximations in Neural Population Coding

While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality. This article focuses on effective approximation methods for evaluating mutual information in the context of neural population coding. For large but finite neural populations, we derive several information-theoretic asymptotic bounds and approximation formulas that remain valid in high-dimensional spaces. We prove that optimizing the population density distribution based on these approximation formulas is a convex optimization problem that allows efficient numerical solutions. Numerical simulation results confirmed that our asymptotic formulas were highly accurate for approximating mutual information for large neural populations. In special cases, the approximation formulas are exactly equal to the true mutual information. We also discuss techniques of variable transformation and dimensionality reduction to facilitate computation of the approximations.

The multifunctional lateral geniculate nucleus

Providing the critical link between the retina and visual cortex, the well-studied lateral geniculate nucleus (LGN) has stood out as a structure in search of a function exceeding the mundane 'relay'. For many mammals, it is structurally impressive: Exquisite lamination, sophisticated microcircuits, and blending of multiple inputs suggest some fundamental transform. This impression is bolstered by the fact that numerically, the retina accounts for a small fraction of its input. Despite such promise, the extent to which an LGN neuron separates itself from its retinal brethren has proven difficult to appreciate. Here, I argue that whereas retinogeniculate coupling is strong, what occurs in the LGN is judicious pruning of a retinal drive by nonretinal inputs. These nonretinal inputs reshape a receptive field that under the right conditions departs significantly from its retinal drive, even if transiently. I first review design features of the LGN and follow with evidence for 10 putative functions. Only two of these tend to surface in textbooks: parsing retinal axons by eye and functional group and gating by state. Among the remaining putative functions, implementation of the principle of graceful degradation and temporal decorrelation are at least as interesting but much less promoted. The retina solves formidable problems imposed by physics to yield multiple efficient and sensitive representations of the world. The LGN applies context, increasing content, and gates several of these representations. Even if the basic concentric receptive field remains, information transmitted for each LGN spike relative to each retinal spike is measurably increased.

Contrast induced changes in response latency depend on stimulus specificity

Neurones in visual cortex show increasing response latency with decreasing stimulus contrast. Neurophysiological recordings from neurones in inferior temporal cortex (IT) and the superior temporal sulcus (STS), show that the increment in response latency with decreasing stimulus contrast is considerably greater in higher visual areas than that seen in primary visual cortex. This suggests that the majority of the latency change is not retinal or V1 in origin, instead each cortical processing area adds latency at low contrast. I show that, as in earlier visual areas, response latency is more strongly dependent on stimulus contrast than stimulus identity. There is large variation in the extent to which response latency increases with decreasing stimulus contrast. I show that this between cell variability is, at least in part, related to the stimulus specificity of the neurones: the increase in response latency as stimulus contrast decreases is greater for neurones that respond to few stimuli compared to neurones that respond to many stimuli.

Impact of noise on retinal coding of visual signals

Neural noise introduces uncertainty about the signals encoded in neural spike trains. Because of the uncertainty neurons can reliably transmit a limited amount of information. This amount is difficult to quantify for neurons that combine signals and noise in a complex manner, as many trials would be needed to estimate the joint probability distribution of stimulus and neural response accurately. The task is experimentally tractable, however, for neurons that combine signals with additive Gaussian noise. For such neurons, the joint probability distribution is well defined and information transmission rates can be computed from estimates of signal-to-noise ratio. Here we use power spectral analysis to specify the contributions of signal and noise to retinal coding of visual information. We show that in the spike trains of cat ganglion cells noise power is minimal and constant at temporal frequencies from 0.3 to 20 Hz and that it increases at higher frequencies to a plateau level that generally depends on stimulus contrast. We also show that trial-to-trial fluctuations in noise amplitude at different frequencies are uncorrelated and normally distributed. Although the contrast dependence indicates that noise at high temporal frequencies contributes nonlinearly to ganglion cell spike trains, cells in the primary visual cortex are not known to respond to stimulus modulations >20 Hz. Hence, noise in the retinal output would appear additive, white, and Gaussian from their perspective. This greatly simplifies analysis of information transmission from the eye to the primary visual cortex and perhaps other regions of the brain.

Properties of a temporal population code

The temporal patterning of neuronal activity may play a substantial role in the representation of sensory stimuli. One particular hypothesis suggests that visual stimuli are represented by the temporal evolution of the instantaneous firing rate averaged over a whole population of neurons. Using an implementation in a cortical type network with lateral interactions, we could previously show that this scheme can be successfully applied to a pattern recognition task. Here, we use a large set of artificially generated stimuli to investigate the coding properties of the network in detail. The temporal population code generated by the network is intrinsically invariant to stimulus translations. We show that the encoding is invariant to small deformations of the stimuli and robust with respect to static and dynamic variations in synaptic strength of the lateral connections in the network. Furthermore, we present several measures which indicate that the encoding maps the stimuli into a high-dimensional space. These results show that a temporal population code is a promising approach for the encoding of relevant stimulus properties while simultaneously discarding the irrelevant information.

Neural coding of spatial phase in V1 of the macaque monkey

We examine the responses of single neurons and pairs of neurons, simultaneously recorded with a single tetrode in the primary visual cortex of the anesthetized macaque monkey, to transient presentations of stationary gratings of varying spatial phase. Such simultaneously recorded neurons tended to have similar tuning to the phase of the grating. To determine the response features that reliably discriminate these stimuli, we use the metric-space approach extended to pairs of neurons. We find that paying attention to the times of individual spikes, at a resolution of approximately 30 ms, and keeping track of which neuron fires which spike rather than just the summed local activity contribute substantially to phase coding. The contribution is both quantitative (increasing the fidelity of phase coding) and qualitative (enabling a 2-dimensional "response space" that corresponds to the spatial phase cycle). We use a novel approach, the extraction of "temporal profiles" from the metric space analysis, to interpret and compare temporal coding across neurons. Temporal profiles were remarkably consistent across a large subset of neurons. This consistency indicates that simple mechanisms (e.g., comparing the size of the transient and sustained components of the response) allow the temporal contribution to phase coding to be decoded.

One factor underlies individual differences in auditory informational masking within and across age groups

Masked threshold for a pure-tone signal can be substantially elevated whenever the listener is uncertain about the spectral or temporal properties of the masker, an effect referred to as auditory informational masking. Individual differences in the effect are large, with young children being most susceptible. When masker uncertainty is introduced by randomizing the frequencies of a multitone masker on each presentation, the function relating a child's pure-tone signal threshold to the number of masker components is found to be substantially elevated above that of most adults. The age effect and the individual differences among adults are not well understood, though a difference in the shapes of the masking functions suggests that different detection strategies may be involved. The present study reports results from a principal components analysis of informational masking functions obtained from 38 normal-hearing children ranging in age from 4 to 16 years and 46 normal-hearing adults ranging in age from 19 to 38 years. The premise underlying the analysis is that if different detection strategies are involved, they should add independent sources of variance to the masking functions. Hence, more than one principal component (PC) should be required to account for a substantial proportion of the variance in these functions. The results, instead, supported the operation of a single underlying strategy with all but 17% of the variance accounted for by the first PC within and across age groups. An analysis of variance on the first two PCs showed that only the first changed with age, and a cluster analysis of the masking functions showed complete separation of clusters along this PC for all but 1 listener. The results are taken to suggest that large individual differences informational masking at all ages reflect differences in the extent to which masker uncertainty adds variance to the decision variable of an otherwise optimal decision strategy.

Information-geometric measure for neural spikes

This study introduces information-geometric measures to analyze neural firing patterns by taking not only the second-order but also higher-order interactions among neurons into account. Information geometry provides useful tools and concepts for this purpose, including the orthogonality of coordinate parameters and the Pythagoras relation in the Kullback-Leibler divergence. Based on this orthogonality, we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders. As a result, purely pairwise, triple-wise, and higher-order interactions are singled out. We also demonstrate the benefits of our proposal by using several examples.

Surfing a spike wave down the ventral stream

Numerous theories of neural processing, often motivated by experimental observations, have explored the computational properties of neural codes based on the absolute or relative timing of spikes in spike trains. Spiking neuron models and theories however, as well as their experimental counterparts, have generally been limited to the simulation or observation of isolated neurons, isolated spike trains, or reduced neural populations. Such theories would therefore seem inappropriate to capture the properties of a neural code relying on temporal spike patterns distributed across large neuronal populations. Here we report a range of computer simulations and theoretical considerations that were designed to explore the possibilities of one such code and its relevance for visual processing. In a unified framework where the relation between stimulus saliency and spike relative timing plays the central role, we describe how the ventral stream of the visual system could process natural input scenes and extract meaningful information, both rapidly and reliably. The first wave of spikes generated in the retina in response to a visual stimulation carries information explicitly in its spatio-temporal structure: the most salient information is represented by the first spikes over the population. This spike wave, propagating through a hierarchy of visual areas, is regenerated at each processing stage, where its temporal structure can be modified by (i). the selectivity of the cortical neurons, (ii). lateral interactions and (iii). top-down attentional influences from higher order cortical areas. The resulting model could account for the remarkable efficiency and rapidity of processing observed in the primate visual system.

The temporal resolution of neural codes: does response latency have a unique role?

This article reviews the nature of the neural code in non-human primate cortex and assesses the potential for neurons to carry two or more signals simultaneously. Neurophysiological recordings from visual and motor systems indicate that the evidence for a role for precisely timed spikes relative to other spike times (ca. 1-10 ms resolution) is inconclusive. This indicates that the visual system does not carry a signal that identifies whether the responses were elicited when the stimulus was attended or not. Simulations show that the absence of such a signal reduces, but does not eliminate, the increased discrimination between stimuli that are attended compared with when the stimuli are unattended. The increased accuracy asymptotes with increased gain control, indicating limited benefit from increasing attention. The absence of a signal identifying the attentional state under which stimuli were viewed can produce the greatest discrimination between attended and unattended stimuli. Furthermore, the greatest reduction in discrimination errors occurs for a limited range of gain control, again indicating that attention effects are limited. By contrast to precisely timed patterns of spikes where the timing is relative to other spikes, response latency provides a fine temporal resolution signal (ca. 10 ms resolution) that carries information that is unavailable from coarse temporal response measures. Changes in response latency and changes in response magnitude can give rise to different predictions for the patterns of reaction times. The predictions are verified, and it is shown that the standard method for distinguishing executive and slave processes is only valid if the representations of interest, as evidenced by the neural code, are known. Overall, the data indicate that the signalling evident in neural signals is restricted to the spike count and the precise times of spikes relative to stimulus onset (response latency). These coding issues have implications for our understanding of cognitive models of attention and the roles of executive and slave systems.

Changes in response modulation of cat perigeniculate neurons related to EEG state and application of neuromodulators

Spike activity of single perigeniculate (PGN) neurons was recorded in the anaesthetized (N2O/halothane) and paralysed cat during presentation of moving gratings of optimal spatial frequency. Typically, the ongoing (tonic, spontaneous) activity of PGN cells increased during a rise in EEG delta power accompanied by a reduction and often a total loss of spike rate modulation by the moving grating. The opposite behaviour was found when the EEG delta power vanished. Micro-iontophoretically applied acetylcholine (ACh) had an effect similar to a decrease in EEG delta power, decreasing ongoing activity but increasing the response modulation depth. The opposite effect could be achieved with the excitatory action of serotonin (5-HT), mimicking a strengthened EEG delta power. These data support previous data indicating that PGN neurons contribute to spatio-temporal tuning of subcortical visual activity in a state-dependent way.

Temporal coding of visual information in the thalamus

The amount of information a sensory neuron carries about a stimulus is directly related to response reliability. We recorded from individual neurons in the cat lateral geniculate nucleus (LGN) while presenting randomly modulated visual stimuli. The responses to repeated stimuli were reproducible, whereas the responses evoked by nonrepeated stimuli drawn from the same ensemble were variable. Stimulus-dependent information was quantified directly from the difference in entropy of these neural responses. We show that a single LGN cell can encode much more visual information than had been demonstrated previously, ranging from 15 to 102 bits/sec across our sample of cells. Information rate was correlated with the firing rate of the cell, for a consistent rate of 3.6 +/- 0.6 bits/spike (mean +/- SD). This information can primarily be attributed to the high temporal precision with which firing probability is modulated; many individual spikes were timed with better than 1 msec precision. We introduce a way to estimate the amount of information encoded in temporal patterns of firing, as distinct from the information in the time varying firing rate at any temporal resolution. Using this method, we find that temporal patterns sometimes introduce redundancy but often encode visual information. The contribution of temporal patterns ranged from -3.4 to +25.5 bits/sec or from -9.4 to +24.9% of the total information content of the responses.

Encoding of tactile stimulus location by somatosensory thalamocortical ensembles

The exquisite modular anatomy of the rat somatosensory system makes it an excellent model to test the potential coding strategies used to discriminate the location of a tactile stimulus. Here, we investigated how ensembles of simultaneously recorded single neurons in layer V of primary somatosensory (SI) cortex and in the ventral posterior medial (VPM) nucleus of the thalamus of the anesthetized rat may encode the location of a single whisker stimulus on a single trial basis. An artificial neural network based on a learning vector quantization algorithm, was used to identify putative coding mechanisms. Our data suggest that these neural ensembles may rely on a distributed coding scheme to represent the location of single whisker stimuli. Within this scheme, the temporal modulation of neural ensemble firing rate, as well as the temporal interactions between neurons, contributed significantly to the representation of stimulus location. The relative contribution of these temporal codes increased with the number of whiskers that the ensembles must discriminate among. Our results also indicated that the SI cortex and the VPM nucleus may function as a single entity to encode stimulus location. Overall, our data suggest that the representation of somatosensory features in the rat trigeminal system may arise from the interactions of neurons within and between the SI cortex and VPM nucleus. Furthermore, multiple coding strategies may be used simultaneously to represent the location of tactile stimuli.

Single units and sensation: a retrospect

The single-neuron doctrine is reexamined, and the search for causal links between single units and sensation reviewed. Although several decades of single-unit recording have been very successful in elucidating physiological mechanisms, linking signals from a single cell and perception has progressed at a slower rate. Nevertheless, analysing the activity of single neurons has achieved significant gains and remains the most promising level for elucidation of processing algorithms in the visual system. At the subcortical level, the conclusion that signals from just a single cell can carry enough information for some kinds of performance remains (almost) valid. Under carefully controlled conditions, just a few impulses in a few retinal ganglion cells are an adequate signal for the cortex to initiate a behavioural response. Elucidating cortical codes has been more difficult, and evidence exists suggesting the sharing of responsibility for a task among cell assemblies; how large these assemblies are, and how to test for them neurophysiologically, remains a challenge.

Using response models to estimate channel capacity for neuronal classification of stationary visual stimuli using temporal coding

Both spike count and temporal modulation are known to carry information about which of a set of stimuli elicited a response; but how much information temporal modulation adds remains a subject of debate. This question usually is addressed by examining the results of a particular experiment that depend on the specific stimuli used. Developing a response model allows us to ask how much more information is carried by the best use of response strength and temporal modulation together (that is, the channel capacity using a code incorporating both) than by the best use of spike count alone (the channel capacity using the spike count code). This replaces dependence on a particular data set with dependence on the accuracy of the model. The model is constructed by finding statistical rules obeyed by all the observed responses and assuming that responses to stimuli not presented in our experiments obey the same rules. We assume that all responses within the observed dynamic range, even if not elicited by a stimulus in our experiment, could be elicited by some stimulus. The model used here is based on principal component analysis and includes both response strength and a coarse (+/-10 ms) representation of temporal modulation. Temporal modulation at finer time scales carries little information about the identity of stationary visual stimuli (although it may carry information about stimulus motion or change), and we present evidence that, given its variability, it should not be expected to do so. The model makes use of a linear relation between the logarithms of mean and variance of responses, similar to the widely seen relation between mean and variance of spike count. Responses are modeled using truncated Gaussian distributions. The amount of stimulus-related information carried by spike count in our data are 0.35 and 0.31 bits in primary visual and inferior temporal cortices, respectively, rising to 0.52 and 0.37 bits for the two-principal-component code. The response model estimates that the channel capacity is 1.1 and 1.4 bits, respectively, using the spike count only, rising to 2.0 and 2.2 bits using two principal components. Thus using this representation of temporal modulation is nearly equivalent to adding a second independent cell using the spike count code. This is much more than estimated using transmitted information but far less than would be expected if all degrees of freedom provided by the individual spike times carried independent information.

Stochastic nature of precisely timed spike patterns in visual system neuronal responses

It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as spike count or latency. We examined exactly timed (1-ms precision) triplets and quadruplets of spikes in the stimulus-elicited responses of lateral geniculate nucleus (LGN) and primary visual cortex (V1) neurons of the awake fixating rhesus monkey. Large numbers of these precisely timed spike patterns were found. Information theoretical analysis showed that the precisely timed spike patterns carried only information already available from spike count, suggesting that the number of precisely timed spike patterns was related to firing rate. We therefore examined statistical models relating precisely timed spike patterns to response strength. Previous statistical models use observed properties of neuronal responses such as the peristimulus time histogram, interspike interval, and/or spike count distributions to constrain the parameters of the model. We examined a new stochastic model, which unlike previous models included all three of these constraints and unlike previous models predicted the numbers and types of observed precisely timed spike patterns. This shows that the precise temporal structures of stimulus-elicited responses in LGN and V1 can occur by chance. We show that any deviation of the spike count distribution, no matter how small, from a Poisson distribution necessarily changes the number of precisely timed spike patterns expected in neural responses. Overall the results indicate that the fine temporal structure of responses can only be interpreted once all the coarse temporal statistics of neural responses have been taken into account.

Computing with self-excitatory cliques: A model and an application to hyperacuity-scale computation in visual cortex

We present a model of visual computation based on tightly inter-connected cliques of pyramidal cells. It leads to a formal theory of cell assemblies, a specific relationship between correlated firing patterns and abstract functionality, and a direct calculation relating estimates of cortical cell counts to orientation hyperacuity. Our network architecture is unique in that (1) it supports a mode of computation that is both reliable and efficient; (2) the current-spike relations are modeled as an analog dynamical system in which the requisite computations can take place on the time scale required for an early stage of visual processing; and (3) the dynamics are triggered by the spatiotemporal response of cortical cells. This final point could explain why moving stimuli improve vernier sensitivity.

Spatial phase and the temporal structure of the response to gratings in V1

We recorded single-unit activity of 25 units in the parafoveal representation of macaque V1 to transient appearance of sinusoidal gratings. Gratings were systematically varied in spatial phase and in one or two of the following: contrast, spatial frequency, and orientation. Individual responses were compared based on spike counts, and also according to metrics sensitive to spike timing. For each metric, the extent of stimulus-dependent clustering of individual responses was assessed via the transmitted information, H. In nearly all data sets, stimulus-dependent clustering was maximal for metrics sensitive to the temporal pattern of spikes, typically with a precision of 25-50 ms. To focus on the interaction of spatial phase with other stimulus attributes, each data set was analyzed in two ways. In the "pooled phases" approach, the phase of the stimulus was ignored in the assessment of clustering, to yield an index Hpooled. In the "individual phases" approach, clustering was calculated separately for each spatial phase and then averaged across spatial phases to yield an index Hindiv. Hpooled expresses the extent to which a spike train represents contrast, spatial frequency, or orientation in a manner which is not confounded by spatial phase (phase-independent representation), whereas Hindiv expresses the extent to which a spike train represents one of these attributes, provided spatial phase is fixed (phase-dependent representation). Here, representation means that a stimulus attribute has a reproducible and systematic influence on individual responses, not a neural mechanism for decoding this influence. During the initial 100 ms of the response, contrast was represented in a phase-dependent manner by simple cells but primarily in a phase-independent manner by complex cells. As the response evolved, simple cell responses acquired phase-independent contrast information, whereas complex cells acquired phase-dependent contrast information. Simple cells represented orientation and spatial frequency in a primarily phase-dependent manner, but also they contained some phase-independent information in their initial response segment. Complex cells showed primarily phase-independent representation of orientation but primarily phase-dependent representation of spatial frequency. Joint representation of two attributes (contrast and spatial frequency, contrast and orientation, spatial frequency and orientation) was primarily phase dependent for simple cells, and primarily phase independent for complex cells. In simple and complex cells, the variability in the number of spikes elicited on each response was substantially greater than the expectations of a Poisson process. Although some of this variation could be attributed to the dependence of the response on the spatial phase of the grating, variability was still markedly greater than Poisson when the contribution of spatial phase to response variance was removed.

Sensory coding in cortical neurons. Recent results and speculations

We described a novel approach to the study of how spike trains encode sensory information. This approach emphasizes the idea that spike trains are sequences of discrete events, rather than approximations to continuous signals. Aided by some simple heuristics, such as a caricature of neurons as coincidence detectors, we constructed candidate notions of "distances" between spike trains, considered as points in an abstract space. Each candidate distance was evaluated for relevance to biological encoding by determining whether it led to systematic, stimulus-dependent, clustering of the neural responses. We showed here that these distance can also be used to construct a "response space" for the neuron. The response space, which is typically not Euclidean, can represent two or three stimulus attributes. We also introduced the notion of a "consensus spike train," defined as the spike train with minimum average distance from a set of observed responses. For the distances we considered, the consensus spike train (for a particular stimulus) contained only those spikes that were present at consistent times across the observed responses to that stimulus, and thus contained fewer spikes than the typical observed responses. Nevertheless, these consensus spike trains provided an equivalent (or even superior) representation of the stimulus array.

On the significance of temporally structured activity in the dorsal lateral geniculate nucleus (LGN)

Higher organisms perceive information about external or internal physical or chemical stimuli with specialized sensors that encode characteristics of that stimulus by a train of action potentials. Usually, the location and modality of the stimulus is represented by the location and specificity of the receptor and the intensity of the stimulus and its temporal modulation is thought to be encoded by the instantaneous firing rate. Recent studies have shown that, primarily in cortical structures, special features of a stimulus also are represented in the temporal pattern of spike activity. Typical attributes of this time structure are oscillatory patterns of activity and synchronous discharges in spatially distributed neurons that respond to inputs evoked by a coherent object. The origin and functional significance of this kind of activity is less clear. Cortical, subcortical and even very peripheral sources seem to be involved. Most of the relevant studies were devoted to the mammalian visual system and cortical findings on temporally structured activity were reviewed recently (Eckhorn, 1994, Progr. Brain Res., Vol. 102, pp. 405-426; Singer and Gray, 1995, Annu. Rev. Neurosci., Vol. 18, pp. 555-586). Therefore, this article is designed to give an overview, especially of those studies concerned with the temporal structure of visual activity in subcortical centers of the primary visual pathway, which are the retina and the dorsal lateral geniculate nucleus (LGN). We discuss the mechanisms that possibly contribute to the generation and modulation of the subcortical activity time structure and we try to relate to each other the subcortical and cortical patterns of sensory activity.

Analytical estimates of limited sampling biases in different information measures

Measuring the information carried by neuronal activity is made difficult, particularly when recording from mammalian cells, by the limited amount of data usually available, which results in a systematic error. While empirical ad hoc procedures have been used to correct for such error, we have recently proposed a direct procedure consisting of the analytical calculation of the average error, its estimation (up to subleading terms) from the data, and its subtraction from raw information measures to yield unbiased measures. We calculate here the leading correction terms for both the average transmitted information and the conditional information and, since usually one must first regularize the data, we specify the expressions appropriate to different regularizations. Computer simulations indicate a broad range of validity of the analytical results, suggest the effectiveness of regularizing by simple binning and illustrate the advantage of this over the previously used 'bootstrap' procedure.

Latency variability of responses to visual stimuli in cells of the cat's lateral geniculate nucleus

We constructed average histograms from responses evoked by flashing stimuli and noted previously described variations in the shape of the response profile, particularly with respect to sharpness of the peak. To express this variable, we measured the half-rise latency, which is the latency from stimulus onset required to reach half the maximum response. A short half-rise latency, which is characteristic of nonlagged cells, is associated with a brisk response and sharp peak; a long half-rise latency, characteristic of lagged cells, is associated with a sluggish response and broad peak. Nonlagged cells were readily seen; we attempted to identify cells with long latencies as lagged, but we were unable to do so unambiguously due to failure to observe lagged properties other than latency. We thus refer to these latter cells as having "lagged-like" responses to indicate that we are not certain whether these are indeed lagged cells. In addition to the histograms, we analyzed the individual response trials that were summed to create each histogram, and we used spike density analysis to estimate the initial response latency to the flashing spot for each trial. We found that lagged-like responses were associated with more variability in initial response latency than were nonlagged responses. We then employed an alignment procedure to eliminate latency variation from individual trials; that is, responses during individual trials were shifted in time as needed so that each had a latency equal to the average latency of all trials. We used these "aligned" trials to create a second, "aligned" response histogram for each cell. The alignment procedure had little effect on nonlagged responses, because these were already well aligned due to consistent response latencies amongst trials. For lagged-like responses, however, the alignment made a dramatic difference. The aligned histograms looked very much like those for nonlagged responses: the responses appeared brisk, with a sharply rising peak that was fairly high in amplitude. We thus conclude that the slow build up to a relatively low peak of firing of the lagged-like response histogram is not an accurate reflection of responses on single trials. Instead, the sluggishness of lagged-like responses inferred from average response histograms results from temporal smearing due to latency variability amongst trials. We thus conclude that there is relatively little difference in briskness between nonlagged and lagged-like responses to single stimuli.

Temporal structure in the light response of relay cells in the dorsal lateral geniculate nucleus of the cat

1. The spike interval pattern during the light responses of 155 on- and 81 off-centre cells of the dorsal lateral geniculate nucleus (LGN) was studied in anaesthetized and paralysed cats by the use of a novel analysis. Temporally localized interval distributions were computed from a 100 ms time window, which was shifted along the time axis in 10 ms steps, resulting in a 90% overlap between two adjacent windows. For each step the interval distribution was computed inside the time window with 1 ms resolution, and plotted as a greyscale-coded pixel line orthogonal to the time axis. For visual stimulation, light or dark spots of different size and contrast were presented with different background illumination levels. 2. Two characteristic interval patterns were observed during the sustained response component of the cells. Mainly on-cells (77%) responded with multimodal interval distributions, resulting in elongated 'bands' in the 2-dimensional time window plots. In similar situations, the interval distributions for most (71%) off-cells were rather wide and featureless. In those cases where interval bands (i.e. multimodal interval distributions) were observed for off-cells (14%), they were always much wider than for the on-cells. This difference between the on- and off-cell population was independent of the background illumination and the contrast of the stimulus. Y on-cells also tended to produce wider interval bands than X on-cells. 3. For most stimulation situations the first interval band was centred around 6-9 ms, which has been called the fundamental interval; higher order bands are multiples thereof. The fundamental interval shifted towards larger sizes with decreasing stimulus contrast. Increasing stimulus size, on the other hand, resulted in a redistribution of the intervals into higher order bands, while at the same time the location of the fundamental interval remained largely unaffected. This was interpreted as an effect of the increasing surround inhibition at the geniculate level, by which individual retinal EPSPs were cancelled. A changing level of adaptation can result in a mixed shift/redistribution effect because of the changing stimulus contrast and changing level of tonic inhibition. 4. The occurrence of interval bands is not directly related to the shape of the autocorrelation function, which can be flat, weakly oscillatory or strongly oscillatory, regardless of the interval band pattern. 5. A simple computer model was devised to account for the observed cell behaviour. The model is highly robust against parameter variations.(ABSTRACT TRUNCATED AT 400 WORDS)

Fine structure analysis of temporal patterns in the light response of cells in the lateral geniculate nucleus of cat

This study focuses on the analysis of temporal patterns in the spike train of cells in the lateral geniculate nucleus (LGN) of cat. Two-hundred eighty-three units have been recorded extracellularly in anesthetized animals during visual stimulation with flashing spot stimuli of different size. We used a novel method of temporally local computed interval distributions (intervalogram; Funke & Wörgötter, 1995) to visualize the statistical distribution of interspike intervals during different phases of the visual response. Multimodal interval distributions were observed mainly in X- and Y-ON cells, reflecting the tendency of these cells to fire with preferred intervals during the sustained light response. The shortest preferred interval is called the fundamental interval and the longer ones (higher-order intervals) are, in general, multiples thereof. During increasing surround inhibition a redistribution of the intervals towards the higher orders was observed. We regarded the different in the interval distributions as different components of possible temporal spike sequences and performed a pattern search up to the level of five subsequent intervals. While it is obvious, that the dominant peak is most strongly represented in any interval sequence, we also show that a significant overrepresentation of short sequences of similar intervals exists. The repetition rate is rather small (4-5 intervals) and, therefore, no long-lasting oscillatory pattern was observed in the autocorrelograms. Power spectral analysis of the peristimulus-time histograms, however, revealed that the sequential firing pattern is strongly stimulus locked at least for the majority of sweeps in the records. The mean firing rate of an LGN cell decreases with increasing stimulus size as well as with decreasing contrast. Therefore, the mean rate cannot be used to distinguish between these situations. While in the whole network this tradeoff can be resolved by the combined activity of multiple cells, our findings additionally suggest that contrast and size can be distinguished already at the single-cell level using different temporal patterns.

Pharmacological inactivation of pretectal nuclei reveals different modulatory effects on retino-geniculate transmission by X and Y cells in the cat

The modulatory influence of pretectal neurons on retino-geniculate transmission in the cat was studied by cross-correlation analysis of single-unit activity simultaneously recorded from the dorsal lateral geniculate nucleus (dLGN) and the pretectum (PT) and with reversible inactivation of the PT by GABA microiontophoresis during simultaneous visual stimulation of PT and dLGN neurons. Visually induced population activity in PT nuclei was achieved by a moving (or counterphasing) grating which was presented in the background of the light spot used to stimulate the dLGN neuron. As a control, the light spot was presented on a stationary grating to avoid stimulation of PT neurons but to yield the same illumination of the background. Extracellularly recorded dLGN relay cells of the X- and Y-type were found to be differentially affected by the PT-dLGN projection. During visual stimulation of PT cells, X cells were strongly inhibited and this effect was significantly reduced during PT inactivation. By contrast, the visual responses of most Y cells were affected neither by PT stimulation nor by PT inactivation. In addition, the temporal structure of spike patterns during the light response was examined with autocorrelograms and spike-interval distributions. X-on cells often exhibited a multimodal interval distribution and oscillatory type of activity. During stimulation of the PT interval distributions changed in a characteristic manner and oscillations disappeared. Both effects could be almost totally cancelled by PT inactivation. By contrast, the temporal structure of Y-cell responses was not affected. Our results demonstrate for the first time a pretectal modulation of retino-geniculate transmission in cat dLGN which is clearly different for X and Y cells. This influence seems to be mediated via (inhibitory) interneurons, since we found no indication for a direct coupling between PT and dLGN units. This projection might contribute to the well-known phenomenon of saccadic suppression.

Cortical feedback increases visual information transmitted by monkey parvocellular lateral geniculate nucleus neurons

We studied the effect of cooling the striate cortex on parvocellular lateral geniculate nucleus (PLGN) neurons in awake monkeys. Cooling the striate cortex produced both facilitation and inhibition of the responses of all neurons, depending on the stimulus presented. Cooling the striate cortex also altered the temporal distribution of spikes in the responses of PLGN neurons. Shannon's information measure revealed that cooling the striate cortex reduced the average stimulus-related information transmitted by all PLGN neurons. The reduction in transmitted information was associated with both facilitation and inhibition of the response. Cooling the striate cortex reduced the amount of information transmitted about all of the stimulus parameters tested: pattern, luminance, spatial contrast, and sequential contrast. The effect of cooling was nearly the same for codes based on the number of spikes in the response as for codes based on their temporal distribution. The reduction in transmitted information occurred because the differences among the responses to different stimuli (signal separation) were reduced, not because the variability of the responses to individual stimuli (noise) was increased. We conclude that one function of corticogeniculate feedback is to improve the ability of PLGN neurons to discriminate among stimuli by enhancing the differences among their responses.

Coding for stimulus velocity by temporal patterning of spike discharges in visual cells of cat superior colliculus

Statistical analyses, performed on extracellularly recorded spike trains generated by 69 single motion sensitive visual cells in the intermediate layers of superior colliculi of pretrigeminal cat preparations, revealed that--even in the unstimulated condition (38/69)--most neuronal spike discharge patterns tended to switch between two stochastically distinct states, in the form of rapidly alternating "bursting" (high frequency) and "resting" (low frequency) episodes. The numbers of consecutive interspike intervals within a given state were, as a rule, independent integer-valued random variables with discrete probability distributions, in essential agreement with the semi-Markov model proposed by Ekholm and Hyvärinen [(1970) Biophysical Journal, 10, 773-796]. The introduction of visual stimuli (47/69) moving with velocities of 2-160 deg/sec caused systematic and reproducible changes in the ratio of bursting to resting activities, decreases in overall discharge variability, and increases in signal transinformation flow. Moreover, with one group of stimulated cells (28/47), increasing stimulus velocity caused increasingly precise ("stimulus-forced") synchronization of bursting episodes with specific phases of stimulus movement; while for a smaller group (12/47), stimulus-related alternations between bursting and resting states assumed the form of semi-rhythmical burst discharges within the characteristic 60-80 Hz "gamma oscillation" range ("stimulus-induced" synchronization). For a minority of cells (7/47), switching between bursting and resting states--although characteristically modified by stimulus velocity--remained largely desynchronized with all phases of stimulus transit. It was argued that such temporal patterns of discharge may constitute elements of a candidate "distribution" code for movement detection by the cat visual system.

Concurrent processing and complexity of temporally encoded neuronal messages in visual perception

The intrinsic neuronal code that carries visual information and the perceptual mechanism for decoding that information are not known. However, multivariate statistics and information theory show that neurons in four visual areas simultaneously carry multiple, stimulus-related messages by utilizing multiplexed temporal codes. The complexity of these temporal messages increases progressively across the visual system, yet the temporal codes overlap in time. Thus, visual perception may depend on the concurrent processing of multiplexed temporal messages from all visual areas.