Mutual temporal relationships among neuronal spike trains. Statistical techniques for display and analysis

Magnetoencephalography: physics, techniques, and applications in the basic and clinical neurosciences

Magnetoencephalography (MEG) is a technique used to measure the magnetic fields generated from neuronal activity in the brain. MEG has a high temporal resolution on the order of milliseconds and provides a more direct measure of brain activity when compared with hemodynamic-based neuroimaging methods such as magnetic resonance imaging and positron emission tomography. The current review focuses on basic features of MEG such as the instrumentation and the physics that are integral to the signals that can be measured, and the principles of source localization techniques, particularly the physics of beamforming and the techniques that are used to localize the signal of interest. In addition, we review several metrics that can be used to assess functional coupling in MEG and describe the advantages and disadvantages of each approach. Lastly, we discuss the current and future applications of MEG.

Survey of spiking in the mouse visual system reveals functional hierarchy

The anatomy of the mammalian visual system, from the retina to the neocortex, is organized hierarchically¹. However, direct observation of cellular-level functional interactions across this hierarchy is lacking due to the challenge of simultaneously recording activity across numerous regions. Here we describe a large, open dataset-part of the Allen Brain Observatory²-that surveys spiking from tens of thousands of units in six cortical and two thalamic regions in the brains of mice responding to a battery of visual stimuli. Using cross-correlation analysis, we reveal that the organization of inter-area functional connectivity during visual stimulation mirrors the anatomical hierarchy from the Allen Mouse Brain Connectivity Atlas³. We find that four classical hierarchical measures-response latency, receptive-field size, phase-locking to drifting gratings and response decay timescale-are all correlated with the hierarchy. Moreover, recordings obtained during a visual task reveal that the correlation between neural activity and behavioural choice also increases along the hierarchy. Our study provides a foundation for understanding coding and signal propagation across hierarchically organized cortical and thalamic visual areas.

A general method to generate artificial spike train populations matching recorded neurons

We developed a general method to generate populations of artificial spike trains (ASTs) that match the statistics of recorded neurons. The method is based on computing a Gaussian local rate function of the recorded spike trains, which results in rate templates from which ASTs are drawn as gamma distributed processes with a refractory period. Multiple instances of spike trains can be sampled from the same rate templates. Importantly, we can manipulate rate-covariances between spike trains by performing simple algorithmic transformations on the rate templates, such as filtering or amplifying specific frequency bands, and adding behavior related rate modulations. The method was examined for accuracy and limitations using surrogate data such as sine wave rate templates, and was then verified for recorded spike trains from cerebellum and cerebral cortex. We found that ASTs generated with this method can closely follow the firing rate and local as well as global spike time variance and power spectrum. The method is primarily intended to generate well-controlled spike train populations as inputs for dynamic clamp studies or biophysically realistic multicompartmental models. Such inputs are essential to study detailed properties of synaptic integration with well-controlled input patterns that mimic the in vivo situation while allowing manipulation of input rate covariances at different time scales.

Simultaneous electrophysiological and morphological assessment of functional damage to neural networks in vitro after 30-300 g impacts

An enigma of mild traumatic brain injury are observations of substantial behavior and performance deficits in the absence of bleeding or other observable structural damage. Altered behavior and performance reflect changes in action potential (AP) patterns within neuronal networks, which could result from subtle subcellular responses that affect synaptic efficacy and AP production. The aim of this study was to investigate and quantify network activity changes after simulated concussions in vitro and therewith develop a platform for simultaneous and direct observations of morphological and electrophysiological changes in neural networks. We used spontaneously active networks grown on microelectrode arrays (MEAs) to allow long-term multisite monitoring with simultaneous optical observations before and after impacts delivered by a ballistic pendulum (30 to 300 g accelerations). The monitoring of AP waveshape templates for long periods before and after impact provided an internal control for cell death or loss of cell-electrode coupling in the observed set of neurons. Network activity patterns were linked in real-time to high power phase contrast microscopy. There was no overt loss of glial or neuronal adhesion, even at high-g impacts. All recording experiments showed repeatable spike production responses: a loss of activity with recovery to near reference in 1 hr, followed by a slow activity decay to a stable, level plateau approximately 30–40% below reference. The initial recovery occurred in two steps: a rapid return of activity to an average 24% below reference, forming a level plateau lasting from 5 to 20 min, followed by a climb to within 10% of reference where a second plateau was established for 1 to 2 hrs. Cross correlation profiles revealed changes in firing hierarchy as well as in Phase 1 in spontaneous network oscillations that were reduced by as much as 20% 6–8 min post impact with only a partial recovery at 30 min. We also observed that normally stable nuclei developed irregular rotational motion after impact in 27 out of 30 networks. The evolution of network activity deficits and recovery can be linked with microscopically observable changes in the very cells that are generating the activity. The repeatable electrophysiological impact response profiles and oscillation changes can provide a quantitative basis for systematic evaluations of pharmacological intervention strategies. Future expansion to include fluorescent microscopy should allow detailed investigations of damage mechanisms on the subcellular level.

Task activations produce spurious but systematic inflation of task functional connectivity estimates

Most neuroscientific studies have focused on task-evoked activations (activity amplitudes at specific brain locations), providing limited insight into the functional relationships between separate brain locations. Task-state functional connectivity (FC) - statistical association between brain activity time series during task performance - moves beyond task-evoked activations by quantifying functional interactions during tasks. However, many task-state FC studies do not remove the first-order effect of task-evoked activations prior to estimating task-state FC. It has been argued that this results in the ambiguous inference "likely active or interacting during the task", rather than the intended inference "likely interacting during the task". Utilizing a neural mass computational model, we verified that task-evoked activations substantially and inappropriately inflate task-state FC estimates, especially in functional MRI (fMRI) data. Various methods attempting to address this problem have been developed, yet the efficacies of these approaches have not been systematically assessed. We found that most standard approaches for fitting and removing mean task-evoked activations were unable to correct these inflated correlations. In contrast, methods that flexibly fit mean task-evoked response shapes effectively corrected the inflated correlations without reducing effects of interest. Results with empirical fMRI data confirmed the model's predictions, revealing activation-induced task-state FC inflation for both Pearson correlation and psychophysiological interaction (PPI) approaches. These results demonstrate that removal of mean task-evoked activations using an approach that flexibly models task-evoked response shape is an important preprocessing step for valid estimation of task-state FC.

Identification of excitatory-inhibitory links and network topology in large-scale neuronal assemblies from multi-electrode recordings

Functional-effective connectivity and network topology are nowadays key issues for studying brain physiological functions and pathologies. Inferring neuronal connectivity from electrophysiological recordings presents open challenges and unsolved problems. In this work, we present a cross-correlation based method for reliably estimating not only excitatory but also inhibitory links, by analyzing multi-unit spike activity from large-scale neuronal networks. The method is validated by means of realistic simulations of large-scale neuronal populations. New results related to functional connectivity estimation and network topology identification obtained by experimental electrophysiological recordings from high-density and large-scale (i.e., 4096 electrodes) microtransducer arrays coupled to in vitro neural populations are presented. Specifically, we show that: (i) functional inhibitory connections are accurately identified in in vitro cortical networks, providing that a reasonable firing rate and recording length are achieved; (ii) small-world topology, with scale-free and rich-club features are reliably obtained, on condition that a minimum number of active recording sites are available. The method and procedure can be directly extended and applied to in vivo multi-units brain activity recordings.

The balance between excitation and inhibition is fundamental for proper brain functions and for this reason is precisely regulated in adult cortices. Impaired excitation/inhibition balance is often associated with several neurological disorders, such as epilepsy, autism and schizophrenia. However, estimating functional inhibitory connections is not an easy task and few methods are available to identify such connections from electrophysiological data. Here we present a cross-correlation based method to identify both excitatory and inhibitory functional connections in large-scale neuronal networks. The method is applicable to both in vitro and in vivo spike data recordings. Once a connectivity map (i.e. a graph) is obtained, we characterized the associated topology by means of classical graph theory metrics to unveil functional architecture. In this work, we analyze in vitro cortical networks probed by means of large-scale microelectrode arrays (i.e., 4096 sensors) and we derive network topologies from spike data. The functional organization found is called “small-world and scale-free” and is the same organization found in cortical in vivo brain regions by means of different experimental methods. We also show that to obtain reliable information about network architecture at least a network with a hundred of nodes-neurons is needed.

A Copula-Based Granger Causality Measure for the Analysis of Neural Spike Train Data

In systems neuroscience, it is becoming increasingly common to record the activity of hundreds of neurons simultaneously via electrode arrays. The ability to accurately measure the causal interactions among multiple neurons in the brain is crucial to understanding how neurons work in concert to generate specific brain functions. The development of new statistical methods for assessing causal influence between spike trains is still an active field of neuroscience research. Here, we suggest a copula-based Granger causality measure for the analysis of neural spike train data. This method is built upon our recent work on copula Granger causality for the analysis of continuous-valued time series by extending it to point-process neural spike train data. The proposed method is therefore able to reveal nonlinear and high-order causality in the spike trains while retaining all the computational advantages such as model-free, efficient estimation, and variability assessment of Granger causality. The performance of our algorithm can be further boosted with time-reversed data. Our method performed well on extensive simulations, and was then demonstrated on neural activity simultaneously recorded from primary visual cortex of a monkey performing a contour detection task.

Maintained avalanche dynamics during task-induced changes of neuronal activity in nonhuman primates

Sensory events, cognitive processing and motor actions correlate with transient changes in neuronal activity. In cortex, these transients form widespread spatiotemporal patterns with largely unknown statistical regularities. Here, we show that activity associated with behavioral events carry the signature of scale-invariant spatiotemporal clusters, neuronal avalanches. Using high-density microelectrode arrays in nonhuman primates, we recorded extracellular unit activity and the local field potential (LFP) in premotor and prefrontal cortex during motor and cognitive tasks. Unit activity and negative LFP deflections (nLFP) consistently changed in rate at single electrodes during tasks. Accordingly, nLFP clusters on the array deviated from scale-invariance compared to ongoing activity. Scale-invariance was recovered using ‘adaptive binning’, that is identifying clusters at temporal resolution given by task-induced changes in nLFP rate. Measures of LFP synchronization confirmed and computer simulations detailed our findings. We suggest optimization principles identified for avalanches during ongoing activity to apply to cortical information processing during behavior.

The Population Tracking Model: A Simple, Scalable Statistical Model for Neural Population Data

Our understanding of neural population coding has been limited by a lack of analysis methods to characterize spiking data from large populations. The biggest challenge comes from the fact that the number of possible network activity patterns scales exponentially with the number of neurons recorded ([Formula: see text]). Here we introduce a new statistical method for characterizing neural population activity that requires semi-independent fitting of only as many parameters as the square of the number of neurons, requiring drastically smaller data sets and minimal computation time. The model works by matching the population rate (the number of neurons synchronously active) and the probability that each individual neuron fires given the population rate. We found that this model can accurately fit synthetic data from up to 1000 neurons. We also found that the model could rapidly decode visual stimuli from neural population data from macaque primary visual cortex about 65 ms after stimulus onset. Finally, we used the model to estimate the entropy of neural population activity in developing mouse somatosensory cortex and, surprisingly, found that it first increases, and then decreases during development. This statistical model opens new options for interrogating neural population data and can bolster the use of modern large-scale in vivo Ca[Formula: see text] and voltage imaging tools.

Joint cross-correlation analysis reveals complex, time-dependent functional relationship between cortical neurons and arm electromyograms

Correlation between cortical activity and electromyographic (EMG) activity of limb muscles has long been a subject of neurophysiological studies, especially in terms of corticospinal connectivity. Interest in this issue has recently increased due to the development of brain-machine interfaces with output signals that mimic muscle force. For this study, three monkeys were implanted with multielectrode arrays in multiple cortical areas. One monkey performed self-timed touch pad presses, whereas the other two executed arm reaching movements. We analyzed the dynamic relationship between cortical neuronal activity and arm EMGs using a joint cross-correlation (JCC) analysis that evaluated trial-by-trial correlation as a function of time intervals within a trial. JCCs revealed transient correlations between the EMGs of multiple muscles and neural activity in motor, premotor and somatosensory cortical areas. Matching results were obtained using spike-triggered averages corrected by subtracting trial-shuffled data. Compared with spike-triggered averages, JCCs more readily revealed dynamic changes in cortico-EMG correlations. JCCs showed that correlation peaks often sharpened around movement times and broadened during delay intervals. Furthermore, JCC patterns were directionally selective for the arm-reaching task. We propose that such highly dynamic, task-dependent and distributed relationships between cortical activity and EMGs should be taken into consideration for future brain-machine interfaces that generate EMG-like signals.

Impact of spike train autostructure on probability distribution of joint spike events

The discussion whether temporally coordinated spiking activity really exists and whether it is relevant has been heated over the past few years. To investigate this issue, several approaches have been taken to determine whether synchronized events occur significantly above chance, that is, whether they occur more often than expected if the neurons fire independently. Most investigations ignore or destroy the autostructure of the spiking activity of individual cells or assume Poissonian spiking as a model. Such methods that ignore the autostructure can significantly bias the coincidence statistics. Here, we study the influence of the autostructure on the probability distribution of coincident spiking events between tuples of mutually independent non-Poisson renewal processes. In particular, we consider two types of renewal processes that were suggested as appropriate models of experimental spike trains: a gamma and a log-normal process. For a gamma process, we characterize the shape of the distribution analytically with the Fano factor (FFc). In addition, we perform Monte Carlo estimations to derive the full shape of the distribution and the probability for false positives if a different process type is assumed as was actually present. We also determine how manipulations of such spike trains, here dithering, used for the generation of surrogate data change the distribution of coincident events and influence the significance estimation. We find, first, that the width of the coincidence count distribution and its FFc depend critically and in a nontrivial way on the detailed properties of the structure of the spike trains as characterized by the coefficient of variation CV. Second, the dependence of the FFc on the CV is complex and mostly nonmonotonic. Third, spike dithering, even if as small as a fraction of the interspike interval, can falsify the inference on coordinated firing.

Scaled correlation analysis: a better way to compute a cross-correlogram

When computing a cross-correlation histogram, slower signal components can hinder the detection of faster components, which are often in the research focus. For example, precise neuronal synchronization often co-occurs with slow co-variation in neuronal rate responses. Here we present a method - dubbed scaled correlation analysis - that enables the isolation of the cross-correlation histogram of fast signal components. The method computes correlations only on small temporal scales (i.e. on short segments of signals such as 25 ms), resulting in the removal of correlation components slower than those defined by the scale. Scaled correlation analysis has several advantages over traditional filtering approaches based on computations in the frequency domain. Among its other applications, as we show on data from cat visual cortex, the method can assist the studies of precise neuronal synchronization.

THE USE OF NONPARAMETRIC METHODS OF STATIONARY POINT PROCESSES IN THE STUDY OF COMPLEX INTERACTIONS IN THE NEUROMUSCULAR SYSTEM

In this paper we study the complex interactions involved in the incoming stimulus, from a gamma (γ) and/or an alpha (α) motoneuron, and the outgoing response from the muscle spindle transmitted by the Ia sensory afferent neuron to the spinal cord. The most interesting case is the γ and α coactivation to the function of the muscle spindle, while the effect from a single (γ or α) motoneuron is also presented as a comparison. The mathematical background of this analysis is based on the theory of stationary point processes. A kernel type method of estimating second- and third-order conditional densities is used. Under certain conditions the asymptotic distributions of these estimates are Normal and the construction of 95% approximate confidence intervals is feasible. The application of these asymptotic results to the system of the muscle spindle enables us to detect and interpret its excitatory and/or inhibitory behavior.

Statistical technique for analysing functional connectivity of multiple spike trains

A new statistical technique, the Cox method, used for analysing functional connectivity of simultaneously recorded multiple spike trains is presented. This method is based on the theory of modulated renewal processes and it estimates a vector of influence strengths from multiple spike trains (called reference trains) to the selected (target) spike train. Selecting another target spike train and repeating the calculation of the influence strengths from the reference spike trains enables researchers to find all functional connections among multiple spike trains. In order to study functional connectivity an "influence function" is identified. This function recognises the specificity of neuronal interactions and reflects the dynamics of postsynaptic potential. In comparison to existing techniques, the Cox method has the following advantages: it does not use bins (binless method); it is applicable to cases where the sample size is small; it is sufficiently sensitive such that it estimates weak influences; it supports the simultaneous analysis of multiple influences; it is able to identify a correct connectivity scheme in difficult cases of "common source" or "indirect" connectivity. The Cox method has been thoroughly tested using multiple sets of data generated by the neural network model of the leaky integrate and fire neurons with a prescribed architecture of connections. The results suggest that this method is highly successful for analysing functional connectivity of simultaneously recorded multiple spike trains.

Macroscopic entrainment of periodically forced oscillatory ensembles

Large-amplitude oscillations of macroscopic neuronal signals, such as local field potentials and electroencephalography or magnetoencephalography signals, are commonly considered as being generated by a population of mutually synchronized neurons. In a computational study in generic networks of phase oscillators and bursting neurons, however, we show that this common belief may be wrong if the neuronal population receives an external rhythmic input. The latter may stem from another neuronal population or an external, e.g., sensory or electrical, source. In that case the population field potential may be entrained by the rhythmic input, whereas the individual neurons are phase desynchronized both mutually and with their field potential. Intriguingly, the corresponding large-amplitude oscillations of the population mean field are generated by pairwise desynchronized neurons oscillating at frequencies shifted far away from the frequency of the macroscopic field potential.

Mechanisms of synchronous activity in cerebellar Purkinje cells

Complex spike synchrony is thought to be a key feature of how inferior olive climbing fibre afferents make their vital contribution to cerebellar function. However, little is known about whether the other major cerebellar input, the mossy fibres (which generate simple spikes within Purkinje cells, PCs), exhibit a similar synchrony in impulse timing. We have used a multi-microelectrode system to record simultaneously from two or more PCs in the posterior lobe of the ketamine/xylazine-anaesthetized rat to examine the relationship between complex spike and simple spike synchrony in PC pairs located mainly in the A2 and C1 zones in crus II and the paramedian lobule. PC pairs displaying correlations in the occurrence of their complex spikes (coupled PCs) were usually located in the same zone and were also more likely to exhibit correlations in the timing of their spontaneous simple spikes and associated pauses in activity. In coupled PCs, synchrony in both complex spike and simple spike activity was enhanced and the relative timing in the occurrence of complex spikes could be altered by peripheral stimulation. We conclude that the functional coupling between PC pairs in their complex spike and simple spike activity can be significantly modified by sensory inputs, and that mechanisms besides electrotonic coupling are involved in generating PC synchrony. Synchronous activity in multiple PCs converging onto the same cerebellar nuclear cells is likely to have a significant impact on cerebellar output that could form important timing signals to orchestrate coordinated movements.

Are central pattern generators understandable?

Most rhythmic behaviors are produced by a specialized ensemble of neurons found in the central nervous system. These central pattern generators (CPGs) have become a cornerstone of neuronal circuit analysis. Studying simple invertebrate nervous systems may reveal the interactions of the neurons involved in the production of rhythmic motor output. There has recently been progress in this area, but due to certain intrinsic features of CPGs it is unlikely that present techniques will ever yield a complete understanding of any but the simplest of them. The chief impediment seems to be our inability to identify and characterize the total interneuronal pool making up a CPG. In addition, our general analytic strategy relies on a descriptive, reductionist approach, with no analytical constructs beyond phenomenological modeling. Detailed descriptive data are usually not of sufficient depth for specific model testing, giving rise instead to ad hoc explanations of mechanisms which usually turn out to be incorrect. Because they make too many assumptions, modeling studies have not added much to our understanding of CPCs; this is due not so much to inadequate simulations as to the poor quality and incomplete nature of the data provided by experimentalists.

A basic strategy that would provide sufficient information for neural modeling would include: (1) identifying and characterizing each element in the CPG network; (2) specifying the synaptic connectivity between the elements; and (3) analyzing nonlinear synaptic properties and interactions by means of the connectivity matrix. Limitations based on our present technical capabilities are also discussed.

Distributed fading memory for stimulus properties in the primary visual cortex

It is currently not known how distributed neuronal responses in early visual areas carry stimulus-related information. We made multielectrode recordings from cat primary visual cortex and applied methods from machine learning in order to analyze the temporal evolution of stimulus-related information in the spiking activity of large ensembles of around 100 neurons. We used sequences of up to three different visual stimuli (letters of the alphabet) presented for 100 ms and with intervals of 100 ms or larger. Most of the information about visual stimuli extractable by sophisticated methods of machine learning, i.e., support vector machines with nonlinear kernel functions, was also extractable by simple linear classification such as can be achieved by individual neurons. New stimuli did not erase information about previous stimuli. The responses to the most recent stimulus contained about equal amounts of information about both this and the preceding stimulus. This information was encoded both in the discharge rates (response amplitudes) of the ensemble of neurons and, when using short time constants for integration (e.g., 20 ms), in the precise timing of individual spikes (<or= approximately 20 ms), and persisted for several 100 ms beyond the offset of stimuli. The results indicate that the network from which we recorded is endowed with fading memory and is capable of performing online computations utilizing information about temporally sequential stimuli. This result challenges models assuming frame-by-frame analyses of sequential inputs.

Neural synchrony in ventral cochlear nucleus neuron populations is not mediated by intrinsic processes but is stimulus induced: implications for auditory brainstem implants

The aim of this investigation was to elucidate if neural synchrony forms part of the spike time-based theory for coding of sound information in the ventral cochlear nucleus (VCN) of the auditory brainstem. Previous research attempts to quantify the degree of neural synchrony at higher levels of the central auditory system have indicated that synchronized firing of neurons during presentation of an acoustic stimulus could play an important role in coding complex sound features. However, it is unknown whether this synchrony could in fact arise from the VCN as it is the first station in the central auditory pathway. Cross-correlation analysis was conducted on 499 pairs of multiunit clusters recorded in the urethane-anesthetized rat VCN in response to pure tones and combinations of two tones to determine the presence of neural synchrony. The shift predictor correlogram was used as a measure for determining the synchrony owing to the effects of the stimulus. Without subtraction of the shift predictor, over 65% of the pairs of multiunit clusters exhibited significant correlation in neural firing when the frequencies of the tones presented matched their characteristic frequencies (CFs). In addition, this stimulus-evoked neural synchrony was dependent on the physical distance between electrode sites, and the CF difference between multiunit clusters as the number of correlated pairs dropped significantly for electrode sites greater than 800 microm apart and for multiunit cluster pairs with a CF difference greater than 0.5 octaves. However, subtraction of the shift predictor correlograms from the raw correlograms resulted in no remaining correlation between all VCN pairs. These results suggest that while neural synchrony may be a feature of sound coding in the VCN, it is stimulus induced and not due to intrinsic neural interactions within the nucleus. These data provide important implications for stimulation strategies for the auditory brainstem implant, which is used to provide functional hearing to the profoundly deaf through electrical stimulation of the VCN.

Differential response patterns in the si barrel and septal compartments during mechanical whisker stimulation

A growing body of evidence suggests that the barrel and septal regions in layer IV of rat primary somatosensory (SI) cortex may represent separate processing channels. To assess this view, pairs of barrel and septal neurons were recorded simultaneously in the anesthetized rat while a 4x4 array of 16 whiskers was mechanically stimulated at 4, 8, 12, and 16 Hz. Compared with barrel neurons, regular-spiking septal neurons displayed greater increases in response latencies as the frequency of whisker stimulation increased. Cross-correlation analysis indicated that the incidence and strength of neuronal coordination varied with the relative spatial configuration (within vs. across rows) and compartmental location (barrel vs. septa) of the recorded neurons. Barrel and septal neurons were strongly coordinated if both neurons were in close proximity and resided in the same row. Some barrel neurons were weakly coordinated, but only if they resided in the same row. By contrast, the strength of coordination among pairs of septal neurons did not vary with their spatial proximity or their spatial configuration within the arcs and rows of the barrel field. These differential responses provide further support for the view that the barrel and septal regions represent the cortical gateway for processing streams that encode specific aspects of the sensorimotor information associated with whisking behavior.

Spike train statistics and dynamics with synaptic input from any renewal process: a population density approach

In the probability density function (PDF) approach to neural network modeling, a common simplifying assumption is that the arrival times of elementary postsynaptic events are governed by a Poisson process. This assumption ignores temporal correlations in the input that sometimes have important physiological consequences. We extend PDF methods to models with synaptic event times governed by any modulated renewal process. We focus on the integrate-and-fire neuron with instantaneous synaptic kinetics and a random elementary excitatory postsynaptic potential (EPSP), A. Between presynaptic events, the membrane voltage, v, decays exponentially toward rest, while s, the time since the last synaptic input event, evolves with unit velocity. When a synaptic event arrives, v jumps by A, and s is reset to zero. If v crosses the threshold voltage, an action potential occurs, and v is reset to v(reset). The probability per unit time of a synaptic event at time t, given the elapsed time s since the last event, h(s, t), depends on specifics of the renewal process. We study how regularity of the train of synaptic input events affects output spike rate, PDF and coefficient of variation (CV) of the interspike interval, and the autocorrelation function of the output spike train. In the limit of a deterministic, clocklike train of input events, the PDF of the interspike interval converges to a sum of delta functions, with coefficients determined by the PDF for A. The limiting autocorrelation function of the output spike train is a sum of delta functions whose coefficients fall under a damped oscillatory envelope. When the EPSP CV, sigma A/mu A, is equal to 0.45, a CV for the intersynaptic event interval, sigma T/mu T = 0.35, is functionally equivalent to a deterministic periodic train of synaptic input events (CV = 0) with respect to spike statistics. We discuss the relevance to neural network simulations.

Data-driven significance estimation for precise spike correlation

The mechanisms underlying neuronal coding and, in particular, the role of temporal spike coordination are hotly debated. However, this debate is often confounded by an implicit discussion about the use of appropriate analysis methods. To avoid incorrect interpretation of data, the analysis of simultaneous spike trains for precise spike correlation needs to be properly adjusted to the features of the experimental spike trains. In particular, nonstationarity of the firing of individual neurons in time or across trials, a spike train structure deviating from Poisson, or a co-occurrence of such features in parallel spike trains are potent generators of false positives. Problems can be avoided by including these features in the null hypothesis of the significance test. In this context, the use of surrogate data becomes increasingly important, because the complexity of the data typically prevents analytical solutions. This review provides an overview of the potential obstacles in the correlation analysis of parallel spike data and possible routes to overcome them. The discussion is illustrated at every stage of the argument by referring to a specific analysis tool (the Unitary Events method). The conclusions, however, are of a general nature and hold for other analysis techniques. Thorough testing and calibration of analysis tools and the impact of potentially erroneous preprocessing stages are emphasized.

Cortical mechanisms of smooth eye movements revealed by dynamic covariations of neural and behavioral responses

Neural activity in the frontal eye fields controls smooth pursuit eye movements, but the relationship between single neuron responses, cortical population responses, and eye movements is not well understood. We describe an approach to dynamically link trial-to-trial fluctuations in neural responses to parallel variations in pursuit and demonstrate that individual neurons predict eye velocity fluctuations at particular moments during the course of behavior, while the population of neurons collectively tiles the entire duration of the movement. The analysis also reveals the strength of correlations in the eye movement predictions derived from pairs of simultaneously recorded neurons and suggests a simple model of cortical processing. These findings constrain the primate cortical code for movement, suggesting that either a few neurons are sufficient to drive pursuit at any given time or that many neurons operate collectively at each moment with remarkably little variation added to motor command signals downstream from the cortex.

Deconstruction of spatial integrity in visual stimulus detected by modulation of synchronized activity in cat visual cortex

Spatiotemporal relationships among contour segments can influence synchronization of neural responses in the primary visual cortex. We performed a systematic study to dissociate the impact of spatial and temporal factors in the signaling of contour integration via synchrony. In addition, we characterized the temporal evolution of this process to clarify potential underlying mechanisms. With a 10 x 10 microelectrode array, we recorded the simultaneous activity of multiple cells in the cat primary visual cortex while stimulating with drifting sine-wave gratings. We preserved temporal integrity and systematically degraded spatial integrity of the sine-wave gratings by adding spatial noise. Neural synchronization was analyzed in the time and frequency domains by conducting cross-correlation and coherence analyses. The general association between neural spike trains depends strongly on spatial integrity, with coherence in the gamma band (35-70 Hz) showing greater sensitivity to the change of spatial structure than other frequency bands. Analysis of the temporal dynamics of synchronization in both time and frequency domains suggests that spike timing synchronization is triggered nearly instantaneously by coherent structure in the stimuli, whereas frequency-specific oscillatory components develop more slowly, presumably through network interactions. Our results suggest that, whereas temporal integrity is required for the generation of synchrony, spatial integrity is critical in triggering subsequent gamma band synchronization.

MI neuronal responses to peripheral whisker stimulation: relationship to neuronal activity in si barrels and septa

The whisker region in the rodent primary motor (MI) cortex receives dense projections from neurons aligned with the layer IV septa in the whisker region of the primary somatosensory (SI) cortex. To compare whisker-induced responses in MI with respect to the SI responses in the septa and adjoining barrel regions, we used several experimental approaches in anesthetized rats. Reversible inactivation of SI and the surrounding cortex suppressed the magnitude of whisker-induced responses in the MI whisker region by 80%. Subsequent laminar analysis of MI responses to electrical or mechanical stimulation of the whisker pad revealed that the most responsive MI neurons were located >or=1.0 mm below the pia. When layer IV neurons in SI were recorded simultaneously with deep MI neurons during low-frequency (2-Hz) deflections of the whiskers, the neurons in the SI barrels responded 2-6 ms earlier than those in MI. Barrel neurons displayed similar response latencies at all stimulus frequencies, but the response latencies in MI and the SI septa increased significantly when the whiskers were deflected at frequencies of 8 Hz. Finally, cross-correlation analysis of neuronal activity in SI and MI revealed greater amounts of time-locked coordination among septa-MI neuron pairs than among barrel-MI neuron pairs. These results suggest that the somatosensory corticocortical inputs to MI cortex convey information processed by the SI septal circuits.

NeuroXidence: reliable and efficient analysis of an excess or deficiency of joint-spike events

We present a non-parametric and computationally efficient method named NeuroXidence that detects coordinated firing of two or more neurons and tests whether the observed level of coordinated firing is significantly different from that expected by chance. The method considers the full auto-structure of the data, including the changes in the rate responses and the history dependencies in the spiking activity. Also, the method accounts for trial-by-trial variability in the dataset, such as the variability of the rate responses and their latencies. NeuroXidence can be applied to short data windows lasting only tens of milliseconds, which enables the tracking of transient neuronal states correlated to information processing. We demonstrate, on both simulated data and single-unit activity recorded in cat visual cortex, that NeuroXidence discriminates reliably between significant and spurious events that occur by chance.

Computational properties of networks of synchronous groups of spiking neurons

We demonstrate a model in which synchronously firing ensembles of neurons are networked to produce computational results. Each ensemble is a group of biological integrate-and-fire spiking neurons, with probabilistic interconnections between groups. An analogy is drawn in which each individual processing unit of an artificial neural network corresponds to a neuronal group in a biological model. The activation value of a unit in the artificial neural network corresponds to the fraction of active neurons, synchronously firing, in a biological neuronal group. Weights of the artificial neural network correspond to the product of the interconnection density between groups, the group size of the presynaptic group, and the postsynaptic potential heights in the synchronous group model. All three of these parameters can modulate connection strengths between neuronal groups in the synchronous group models. We give an example of nonlinear classification (XOR) and a function approximation example in which the capability of the artificial neural network can be captured by a neural network model with biological integrate-and-fire neurons configured as a network of synchronously firing ensembles of such neurons. We point out that the general function approximation capability proven for feedforward artificial neural networks appears to be approximated by networks of neuronal groups that fire in synchrony, where the groups comprise integrate-and-fire neurons. We discuss the advantages of this type of model for biological systems, its possible learning mechanisms, and the associated timing relationships.