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.     

Conversion of Phase Information into a Spike-Count Code by Bursting Neurons

Single neurons in the cerebral cortex are immersed in a fluctuating electric field, the local field potential (LFP), which mainly originates from synchronous synaptic input into the local neural neighborhood. As shown by recent studies in visual and auditory cortices, the angular phase of the LFP at the time of spike generation adds significant extra information about the external world, beyond the one contained in the firing rate alone. However, no biologically plausible mechanism has yet been suggested that allows downstream neurons to infer the phase of the LFP at the soma of their pre-synaptic afferents. Therefore, so far there is no evidence that the nervous system can process phase information. Here we study a model of a bursting pyramidal neuron, driven by a time-dependent stimulus. We show that the number of spikes per burst varies systematically with the phase of the fluctuating input at the time of burst onset. The mapping between input phase and number of spikes per burst is a robust response feature for a broad range of stimulus statistics. Our results suggest that cortical bursting neurons could play a crucial role in translating LFP phase information into an easily decodable spike count code.     

Estimating the contribution of assembly activity to cortical dynamics from spike and population measures

The hypothesis that cortical networks employ the coordinated activity of groups of neurons, termed assemblies, to process information is debated. Results from multiple single-unit recordings are not conclusive because of the dramatic undersampling of the system. However, the local field potential (LFP) is a mesoscopic signal reflecting synchronized network activity. This raises the question whether the LFP can be employed to overcome the problem of undersampling. In a recent study in the motor cortex of the awake behaving monkey based on the locking of coincidences to the LFP we determined a lower bound for the fraction of spike coincidences originating from assembly activation. This quantity together with the locking of single spikes leads to a lower bound for the fraction of spikes originating from any assembly activity. Here we derive a statistical method to estimate the fraction of spike synchrony caused by assemblies—not its lower bound—from the spike data alone. A joint spike and LFP surrogate data model demonstrates consistency of results and the sensitivity of the method. Combining spike and LFP signals, we obtain an estimate of the fraction of spikes resulting from assemblies in the experimental data.     

Estimating Extracellular Spike Waveforms from CA1 Pyramidal Cells with Multichannel Electrodes

Extracellular (EC) recordings of action potentials from the intact brain are embedded in background voltage fluctuations known as the “local field potential” (LFP). In order to use EC spike recordings for studying biophysical properties of neurons, the spike waveforms must be separated from the LFP. Linear low-pass and high-pass filters are usually insufficient to separate spike waveforms from LFP, because they have overlapping frequency bands. Broad-band recordings of LFP and spikes were obtained with a 16-channel laminar electrode array (silicone probe). We developed an algorithm whereby local LFP signals from spike-containing channel were modeled using locally weighted polynomial regression analysis of adjoining channels without spikes. The modeled LFP signal was subtracted from the recording to estimate the embedded spike waveforms. We tested the method both on defined spike waveforms added to LFP recordings, and on in vivo-recorded extracellular spikes from hippocampal CA1 pyramidal cells in anaesthetized mice. We show that the algorithm can correctly extract the spike waveforms embedded in the LFP. In contrast, traditional high-pass filters failed to recover correct spike shapes, albeit produceing smaller standard errors. We found that high-pass RC or 2-pole Butterworth filters with cut-off frequencies below 12.5 Hz, are required to retrieve waveforms comparable to our method. The method was also compared to spike-triggered averages of the broad-band signal, and yielded waveforms with smaller standard errors and less distortion before and after the spike.     

Context matters: the illusive simplicity of macaque V1 receptive fields

Even in V1, where neurons have well characterized classical receptive fields (CRFs), it has been difficult to deduce which features of natural scenes stimuli they actually respond to. Forward models based upon CRF stimuli have had limited success in predicting the response of V1 neurons to natural scenes. As natural scenes exhibit complex spatial and temporal correlations, this could be due to surround effects that modulate the sensitivity of the CRF. Here, instead of attempting a forward model, we quantify the importance of the natural scenes surround for awake macaque monkeys by modeling it non-parametrically. We also quantify the influence of two forms of trial to trial variability. The first is related to the neuron's own spike history. The second is related to ongoing mean field population activity reflected by the local field potential (LFP). We find that the surround produces strong temporal modulations in the firing rate that can be both suppressive and facilitative. Further, the LFP is found to induce a precise timing in spikes, which tend to be temporally localized on sharp LFP transients in the gamma frequency range. Using the pseudo R(2) as a measure of model fit, we find that during natural scene viewing the CRF dominates, accounting for 60% of the fit, but that taken collectively the surround, spike history and LFP are almost as important, accounting for 40%. However, overall only a small proportion of V1 spiking statistics could be explained (R(2)～5%), even when the full stimulus, spike history and LFP were taken into account. This suggests that under natural scene conditions, the dominant influence on V1 neurons is not the stimulus, nor the mean field dynamics of the LFP, but the complex, incoherent dynamics of the network in which neurons are embedded.     

Covariation between Spike and LFP Modulations Revealed with Focal and Asynchronous Stimulation of Receptive Field Surround in Monkey Primary Visual Cortex

A focal visual stimulus outside the classical receptive field (RF) of a V1 neuron does not evoke a spike response by itself, and yet evokes robust changes in the local field potential (LFP). This subthreshold LFP provides a unique opportunity to investigate how changes induced by surround stimulation leads to modulation of spike activity. In the current study, two identical Gabor stimuli were sequentially presented with a variable stimulus onset asynchrony (SOA) ranging from 0 to 100 ms: the first (S1) outside the RF and the second (S2) over the RF of primary visual cortex neurons, while trained monkeys performed a fixation task. This focal and asynchronous stimulation of the RF surround enabled us to analyze the modulation of S2-evoked spike activity and covariation between spike and LFP modulation across SOA. In this condition, the modulation of S2-evoked spike response was dominantly facilitative and was correlated with the change in LFP amplitude, which was pronounced for the cells recorded in the upper cortical layers. The time course of covariation between the SOA-dependent spike modulation and LFP amplitude suggested that the subthreshold LFP evoked by the S1 can predict the magnitude of upcoming spike modulation.     

Non-parametric detection of temporal order across pairwise measurements of time delays

Neuronal synchronization is often associated with small time delays, and these delays can change as a function of stimulus properties. Investigation of time delays can be cumbersome if the activity of a large number of neurons is recorded simultaneously and neuronal synchronization is measured in a pairwise manner (such as the cross-correlation histograms) because the number of pairwise measurements increases quadratically. Here, a non-parametric statistical test is proposed with which one can investigate (i) the consistency of the delays across a large number of pairwise measurements and (ii) the consistency of the changes in the time delays as a function of experimental conditions. The test can be classified as non-parametric because it takes into account only the directions of the delays and thus, does not make assumptions about the distributions and the variances of the measurement errors.     

Coherence between Rat Sensorimotor System and Hippocampus Is Enhanced during Tactile Discrimination

Rhythms with time scales of multiple cycles per second permeate the mammalian brain, yet neuroscientists are not certain of their functional roles. One leading idea is that coherent oscillation between two brain regions facilitates the exchange of information between them. In rats, the hippocampus and the vibrissal sensorimotor system both are characterized by rhythmic oscillation in the theta range, 5–12 Hz. Previous work has been divided as to whether the two rhythms are independent or coherent. To resolve this question, we acquired three measures from rats—whisker motion, hippocampal local field potential (LFP), and barrel cortex unit firing—during a whisker-mediated texture discrimination task and during control conditions (not engaged in a whisker-mediated memory task). Compared to control conditions, the theta band of hippocampal LFP showed a marked increase in power as the rats approached and then palpated the texture. Phase synchronization between whisking and hippocampal LFP increased by almost 50% during approach and texture palpation. In addition, a greater proportion of barrel cortex neurons showed firing that was phase-locked to hippocampal theta while rats were engaged in the discrimination task. Consistent with a behavioral consequence of phase synchronization, the rats identified the texture more rapidly and with lower error likelihood on trials in which there was an increase in theta-whisking coherence at the moment of texture palpation. These results suggest that coherence between the whisking rhythm, barrel cortex firing, and hippocampal LFP is augmented selectively during epochs in which the rat collects sensory information and that such coherence enhances the efficiency of integration of stimulus information into memory and decision-making centers.     

Comparison of LFP-based and spike-based spectro-temporal receptive fields and cross-correlation in cat primary auditory cortex

Multi-electrode array recordings of spike and local field potential (LFP) activity were made from primary auditory cortex of 12 normal hearing, ketamine-anesthetized cats. We evaluated 259 spectro-temporal receptive fields (STRFs) and 492 frequency-tuning curves (FTCs) based on LFPs and spikes simultaneously recorded on the same electrode. We compared their characteristic frequency (CF) gradients and their cross-correlation distances. The CF gradient for spike-based FTCs was about twice that for 2-40 Hz-filtered LFP-based FTCs, indicating greatly reduced frequency selectivity for LFPs. We also present comparisons for LFPs band-pass filtered between 4-8 Hz, 8-16 Hz and 16-40 Hz, with spike-based STRFs, on the basis of their marginal frequency distributions. We find on average a significantly larger correlation between the spike based marginal frequency distributions and those based on the 16-40 Hz filtered LFP, compared to those based on the 4-8 Hz, 8-16 Hz and 2-40 Hz filtered LFP. This suggests greater frequency specificity for the 16-40 Hz LFPs compared to those of lower frequency content. For spontaneous LFP and spike activity we evaluated 1373 pair correlations for pairs with >200 spikes in 900 s per electrode. Peak correlation-coefficient space constants were similar for the 2-40 Hz filtered LFP (5.5 mm) and the 16-40 Hz LFP (7.4 mm), whereas for spike-pair correlations it was about half that, at 3.2 mm. Comparing spike-pairs with 2-40 Hz (and 16-40 Hz) LFP-pair correlations showed that about 16% (9%) of the variance in the spike-pair correlations could be explained from LFP-pair correlations recorded on the same electrodes within the same electrode array. This larger correlation distance combined with the reduced CF gradient and much broader frequency selectivity suggests that LFPs are not a substitute for spike activity in primary auditory cortex.     

Robustness of the significance of spike synchrony with respect to sorting errors

The aim of spike sorting is to reconstruct single unit spike times from extracellular multi-unit recordings. Failure in the identification of a spike (false negative) or assignment of a spike to a wrong unit (false positive) are typical examples of sorting errors. Their influence on cross-correlation measures has been addressed and it has been shown that correlation analysis of multi-unit signals may lead to incorrect interpretations. We formulate a model to study the influence of sorting errors on the significance of synchronized spikes, and thus are able to study if and how the significance changes in case of imperfect sorting. Here we explore the case of pairwise analysis of simultaneously recorded neurons. Interestingly, a decrease in the significance is observed in the presence of false positives, as well as for false negatives. Furthermore, false negative errors reduce the significance of synchronized spikes more strongly than false positives. Thus, conservative sorting strategies have a stronger tendency to lead to a loss of the significance of synchronization. We demonstrate that a detailed understanding of sorting techniques and their possible effects on subsequent data analyses is important in order to rule out inconsistencies in the interpretation of results. Action Editor: John P. Miller     

Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains

The statistical analysis of two simultaneously observed trains of neuronal spikes is described, using as a conceptual framework the theory of stochastic point processes.The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. If the null hypothesis is rejected—if dependence is attributed to the trains—the problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects of nonstationarities on the statistical measures for simultaneous spike trains are also discussed. For two-train comparisons of irregularly discharging nerve cells, moderate nonstationarities are shown to have little effect on the detection of interactions.Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons.A companion paper covers the analysis of single spike trains.     

Object selectivity of local field potentials and spikes in the macaque inferior temporal cortex

Local field potentials (LFPs) arise largely from dendritic activity over large brain regions and thus provide a measure of the input to and local processing within an area. We characterized LFPs and their relationship to spikes (multi and single unit) in monkey inferior temporal cortex (IT). LFP responses in IT to complex objects showed strong selectivity at 44% of the sites and tolerance to retinal position and size. The LFP preferences were poorly predicted by the spike preferences at the same site but were better explained by averaging spikes within approximately 3 mm. A comparison of separate sites suggests that selectivity is similar on a scale of approximately 800 microm for spikes and approximately 5 mm for LFPs. These observations imply that inputs to IT neurons convey selectivity for complex shapes and that such input may have an underlying organization spanning several millimeters.     

Measuring spike timing distance in the Hindmarsh–Rose neurons

In the present paper, a simple spike timing distance is defined which can be used to measure the degree of synchronization with the information only encoded in the precise timing of the spike trains. Via calculating the spike timing distance defined in this paper, the spike train similarity of uncoupled Hindmarsh–Rose neurons in bursting or spiking states with different initial conditions is investigated and the results are compared with other spike train distance measures. Later, the spike timing distance measure is applied to study the synchronization of coupled or common noise-stimulated neurons. Counterintuitively, the addition of weak coupling or common noise doesn’t enhance the degree of synchronization although after critical values, both of them can induce complete synchronizations. More interestingly, the common noise plays opposite roles for weak and strong enough couplings. Finally, it should be noted that the measure defined in this paper can be extended to measure large neuronal ensembles and the lag synchronization.     

Processing of sensory signals by a non-spiking neuron in the leech

The non-spiking neurons 151 are present as bilateral pairs in each midbody ganglion of the leech nervous system and they are electrically coupled to several motorneurons. Intracellular recordings were used to investigate how these neurons process input from the mechanosensory P neurons in isolated ganglia. Induction of spike trains (15 Hz) in single P cells evoked responses that combined depolarizing and hyperpolarizing phases in cells 151. The phasic depolarizations, transmitted through spiking interneurons, reversed at around -20 mV. The hyperpolarization had two components, both reversing at around -65 mV, and which were inhibited by strychnine (10 micromol l(-1)). The faster component was transmitted through spiking interneurons and the slower component through a direct P-151 interaction. Short trains (<400 ms) of P cell spikes (15 Hz) evoked the phasic depolarizations superimposed on the hyperpolarization, while long spike trains (>500 ms) produced a succession of depolarizations that masked the hyperpolarizing phase. The amplitude and duration of the hyperpolarization reached their maximum at the initial spikes in a train, while the depolarizations persisted throughout the duration of the stimulus train. Both phases of the response were relatively unaffected by the spike frequency (5-25 Hz). The non-spiking neurons 151 processed the sensory signals in the temporal rather than in the amplitude domain.     

Fast, scalable, Bayesian spike identification for multi-electrode arrays

We present an algorithm to identify individual neural spikes observed on high-density multi-electrode arrays (MEAs). Our method can distinguish large numbers of distinct neural units, even when spikes overlap, and accounts for intrinsic variability of spikes from each unit. As MEAs grow larger, it is important to find spike-identification methods that are scalable, that is, the computational cost of spike fitting should scale well with the number of units observed. Our algorithm accomplishes this goal, and is fast, because it exploits the spatial locality of each unit and the basic biophysics of extracellular signal propagation. Human interaction plays a key role in our method; but effort is minimized and streamlined via a graphical interface. We illustrate our method on data from guinea pig retinal ganglion cells and document its performance on simulated data consisting of spikes added to experimentally measured background noise. We present several tests demonstrating that the algorithm is highly accurate: it exhibits low error rates on fits to synthetic data, low refractory violation rates, good receptive field coverage, and consistency across users.     

Towards a unifying model of neural net activity in the visual cortex

A neural net model describing the non-linear interactions between axonal spikes is presented. It reconciles aspects of pattern recognition (as action of an associative memory) with those of spike synchronization and phase locking. The stability of the synchronized state is studied in detail.     

Stability of rapidly adapting afferent entrainment vs responsivity

Spike discharge activity was recorded from low-threshold, rapidly adapting, skin mechanoreceptive afferents (RA afferents) dissected from the median (forelimb) or tibial (hindlimb) nerves in anesthetized monkeys and cats. The spike activity was evoked by delivery of controlled sinusoidal vertical skin displacement ("flutter") stimuli to the receptive field (RF). The stimuli (15-30 Hz; 30-400 mum peak-to-peak amplitude; duration 0.8-15 s) were superimposed on a static skin indentation (0.5-1.0 mm) which was either maintained continuously throughout the run or applied trial-by-trial. The neural activity and the analog signal of the position of the stimulator probe were digitized at 10 kHz resolution and stored for off-line analysis. The main goal was to determine whether changes in the RA afferent response to skin flutter stimulation may be responsible for the enhanced capacity to discriminate stimulus frequency that accompanies a relatively brief (approximately equal to 1 min) pre-exposure to such stimulation in humans. To this end, the spike train data were evaluated using methods that enabled independent measurement of entrainment and responsivity. Responsivity (response intensity) was measured as the average number of spikes/stimulus cycle, while entrainment (the degree to which evoked spike train activity is phase-locked to the stimulus) was quantitatively assessed using statistical techniques developed for the analysis of "circular" (directional) data, supplemented by methods based on the calculation of power spectra from point process data. The methods are demonstrated to enable quantification of RA afferent entrainment over a range of stimulus durations and amplitudes substantially greater than reported in previous studies. While RA afferent responsivity was found to decline to a minor extent (10-20%) both across and within stimulus trials, entrainment remained consistently high and stable, and exhibited no temporal trends or dependence on any other measured factor. The average phase angle of the entrained RA afferent response also remained stable both within and across trials, showing only a tendency to increase slightly during the initial 100-500 ms after stimulus onset. The results imply that the improved capacity to discriminate stimulus frequency that develops in response to an exposure to cutaneous flutter stimulation is not attributable to a change in RA afferent entrainment per se.     

Predicting spike occurrence and neuronal responsiveness from LFPs in primary somatosensory cortex

Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neuronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role.     

Stability of rapidly adapting afferent entrainment vs responsivity

Spike discharge activity was recorded from low-threshold, rapidly adapting, skin mechanoreceptive afferents (RA afferents) dissected from the median (forelimb) or tibial (hindlimb) nerves in anesthetized monkeys and cats. The spike activity was evoked by delivery of controlled sinusoidal vertical skin displacement ("flutter") stimuli to the receptive field (RF). The stimuli (15-30 Hz; 30-400 microm peak-to-peak amplitude; duration 0.8-15 s) were superimposed on a static skin indentation (0.5-1.0 mm) which was either maintained continuously throughout the run or applied trial-by-trial. The neural activity and the analog signal of the position of the stimulator probe were digitized at 10 kHz resolution and stored for off-line analysis. The main goal was to determine whether changes in the RA afferent response to skin flutter stimulation may be responsible for the enhanced capacity to discriminate stimulus frequency that accompanies a relatively brief (approximately 1 min) pre-exposure to such stimulation in humans. To this end, the spike train data were evaluated using methods that enabled independent measurement of entrainment and responsivity. Responsivity (response intensity) was measured as the average number of spikes/stimulus cycle, while entrainment (the degree to which evoked spike train activity is phase-locked to the stimulus) was quantitatively assessed using statistical techniques developed for the analysis of "circular" (directional) data, supplemented by methods based on the calculation of power spectra from point process data. The methods are demonstrated to enable quantification of RA afferent entrainment over a range of stimulus durations and amplitudes substantially greater than reported in previous studies. While RA afferent responsivity was found to decline to a minor extent (10-20%) both across and within stimulus trials, entrainment remained consistently high and stable, and exhibited no temporal trends or dependence on any other measured factor. The average phase angle of the entrained RA afferent response also remained stable both within and across trials, showing only a tendency to increase slightly during the initial 100-500 ms after stimulus onset. The results imply that the improved capacity to discriminate stimulus frequency that develops in response to an exposure to cutaneous flutter stimulation is not attributable to a change in RA afferent entrainment per se.     

Cross-intensity functions and the estimate of spike-time jitter

Correlation measures are important tools for the analysis of simultaneously recorded spike trains. A well-known measure with probabilistic interpretation is the cross-intensity function (CIF), which is an estimate of the conditional probability that a neuron spikes as a function of the time lag to spikes in another neuron. The non-commutative nature of the CIF is particularly useful when different neuron classes are studied that can be distinguished based on their anatomy or physiology. Here we explore the utility of the CIF for estimating spike-time jitter in synaptic interactions between neuron pairs of connected classes. When applied to spike train pairs from sleeping songbirds, we are able to distinguish fast synaptic interactions mediated primarily by AMPA receptors from slower interactions mediated by NMDA receptors. We also find that spike jitter increases with the time lag between spikes, reflecting the accumulation of noise in neural activity sequences, such as in synfire chains. In conclusion, we demonstrate some new utility of the CIF as a spike-train measure.