Data-driven significance estimation for precise spike correlation

Uncovering the organization of neural circuits with Generalized Phase Locking Analysis

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.

Third-order motifs are sufficient to fully and uniquely characterize spatiotemporal neural network activity

Neuroscientific analyses balance between capturing the brain's complexity and expressing that complexity in meaningful and understandable ways. Here we present a novel approach that fully characterizes neural network activity and does so by uniquely transforming raw signals into easily interpretable and biologically relevant metrics of network behavior. We first prove that third-order (triple) correlation describes network activity in its entirety using the triple correlation uniqueness theorem. Triple correlation quantifies the relationships among three events separated by spatial and temporal lags, which are triplet motifs. Classifying these motifs by their event sequencing leads to fourteen qualitatively distinct motif classes that embody well-studied network behaviors including synchrony, feedback, feedforward, convergence, and divergence. Within these motif classes, the summed triple correlations provide novel metrics of network behavior, as well as being inclusive of commonly used analyses. We demonstrate the power of this approach on a range of networks with increasingly obscured signals, from ideal noiseless simulations to noisy experimental data. This approach can be easily applied to any recording modality, so existing neural datasets are ripe for reanalysis. Triple correlation is an accessible signal processing tool with a solid theoretical foundation capable of revealing previously elusive information within recordings of neural networks.

Evaluating the statistical similarity of neural network activity and connectivity via eigenvector angles

Neural systems are networks, and strategic comparisons between multiple networks are a prevalent task in many research scenarios. In this study, we construct a statistical test for the comparison of matrices representing pairwise aspects of neural networks, in particular, the correlation between spiking activity and connectivity. The "eigenangle test" quantifies the similarity of two matrices by the angles between their ranked eigenvectors. We calibrate the behavior of the test for use with correlation matrices using stochastic models of correlated spiking activity and demonstrate how it compares to classical two-sample tests, such as the Kolmogorov-Smirnov distance, in the sense that it is able to evaluate also structural aspects of pairwise measures. Furthermore, the principle of the eigenangle test can be applied to compare the similarity of adjacency matrices of certain types of networks. Thus, the approach can be used to quantitatively explore the relationship between connectivity and activity with the same metric. By applying the eigenangle test to the comparison of connectivity matrices and correlation matrices of a random balanced network model before and after a specific synaptic rewiring intervention, we gauge the influence of connectivity features on the correlated activity. Potential applications of the eigenangle test include simulation experiments, model validation, and data analysis.

Estimating Permutation Entropy Variability via Surrogate Time Series

In the last decade permutation entropy (PE) has become a popular tool to analyze the degree of randomness within a time series. In typical applications, changes in the dynamics of a source are inferred by observing changes of PE computed on different time series generated by that source. However, most works neglect the crucial question related to the statistical significance of these changes. The main reason probably lies in the difficulty of assessing, out of a single time series, not only the PE value, but also its uncertainty. In this paper we propose a method to overcome this issue by using generation of surrogate time series. The analysis conducted on both synthetic and experimental time series shows the reliability of the approach, which can be promptly implemented by means of widely available numerical tools. The method is computationally affordable for a broad range of users.

Dynamical Characteristics of Recurrent Neuronal Networks Are Robust Against Low Synaptic Weight Resolution

The representation of the natural-density, heterogeneous connectivity of neuronal network models at relevant spatial scales remains a challenge for Computational Neuroscience and Neuromorphic Computing. In particular, the memory demands imposed by the vast number of synapses in brain-scale network simulations constitute a major obstacle. Limiting the number resolution of synaptic weights appears to be a natural strategy to reduce memory and compute load. In this study, we investigate the effects of a limited synaptic-weight resolution on the dynamics of recurrent spiking neuronal networks resembling local cortical circuits and develop strategies for minimizing deviations from the dynamics of networks with high-resolution synaptic weights. We mimic the effect of a limited synaptic weight resolution by replacing normally distributed synaptic weights with weights drawn from a discrete distribution, and compare the resulting statistics characterizing firing rates, spike-train irregularity, and correlation coefficients with the reference solution. We show that a naive discretization of synaptic weights generally leads to a distortion of the spike-train statistics. If the weights are discretized such that the mean and the variance of the total synaptic input currents are preserved, the firing statistics remain unaffected for the types of networks considered in this study. For networks with sufficiently heterogeneous in-degrees, the firing statistics can be preserved even if all synaptic weights are replaced by the mean of the weight distribution. We conclude that even for simple networks with non-plastic neurons and synapses, a discretization of synaptic weights can lead to substantial deviations in the firing statistics unless the discretization is performed with care and guided by a rigorous validation process. For the network model used in this study, the synaptic weights can be replaced by low-resolution weights without affecting its macroscopic dynamical characteristics, thereby saving substantial amounts of memory.

Inferring Excitatory and Inhibitory Connections in Neuronal Networks

The comprehension of neuronal network functioning, from most basic mechanisms of signal transmission to complex patterns of memory and decision making, is at the basis of the modern research in experimental and computational neurophysiology. While mechanistic knowledge of neurons and synapses structure increased, the study of functional and effective networks is more complex, involving emergent phenomena, nonlinear responses, collective waves, correlation and causal interactions. Refined data analysis may help in inferring functional/effective interactions and connectivity from neuronal activity. The Transfer Entropy (TE) technique is, among other things, well suited to predict structural interactions between neurons, and to infer both effective and structural connectivity in small- and large-scale networks. To efficiently disentangle the excitatory and inhibitory neural activities, in the article we present a revised version of TE, split in two contributions and characterized by a suited delay time. The method is tested on in silico small neuronal networks, built to simulate the calcium activity as measured via calcium imaging in two-dimensional neuronal cultures. The inhibitory connections are well characterized, still preserving a high accuracy for excitatory connections prediction. The method could be applied to study effective and structural interactions in systems of excitable cells, both in physiological and in pathological conditions.

From Univariate to Multivariate Coupling Between Continuous Signals and Point Processes: A Mathematical Framework

Time series data sets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the systems under study. To better extract this information, we investigate the asymptotic statistical properties of coupling measures between continuous signals and point processes. We first introduce martingale stochastic integration theory as a mathematical model for a family of statistical quantities that include the phase locking value, a classical coupling measure to characterize complex dynamics. Based on the martingale central limit theorem, we can then derive the asymptotic gaussian distribution of estimates of such coupling measure that can be exploited for statistical testing. Second, based on multivariate extensions of this result and random matrix theory, we establish a principled way to analyze the low-rank coupling between a large number of point processes and continuous signals. For a null hypothesis of no coupling, we establish sufficient conditions for the empirical distribution of squared singular values of the matrix to converge, as the number of measured signals increases, to the well-known Marchenko-Pastur (MP) law, and the largest squared singular value converges to the upper end of the MP support. This justifies a simple thresholding approach to assess the significance of multivariate coupling. Finally, we illustrate with simulations the relevance of our univariate and multivariate results in the context of neural time series, addressing how to reliably quantify the interplay between multichannel local field potential signals and the spiking activity of a large population of neurons.

Duplicate Detection of Spike Events: A Relevant Problem in Human Single-Unit Recordings

Single-unit recordings in the brain of behaving human subjects provide a unique opportunity to advance our understanding of neural mechanisms of cognition. These recordings are exclusively performed in medical centers during diagnostic or therapeutic procedures. The presence of medical instruments along with other aspects of the hospital environment limit the control of electrical noise compared to animal laboratory environments. Here, we highlight the problem of an increased occurrence of simultaneous spike events on different recording channels in human single-unit recordings. Most of these simultaneous events were detected in clusters previously labeled as artifacts and showed similar waveforms. These events may result from common external noise sources or from different micro-electrodes recording activity from the same neuron. To address the problem of duplicate recorded events, we introduce an open-source algorithm to identify these artificial spike events based on their synchronicity and waveform similarity. Applying our method to a comprehensive dataset of human single-unit recordings, we demonstrate that our algorithm can substantially increase the data quality of these recordings. Given our findings, we argue that future studies of single-unit activity recorded under noisy conditions should employ algorithms of this kind to improve data quality.

A convolutional neural network for estimating synaptic connectivity from spike trains

The recent increase in reliable, simultaneous high channel count extracellular recordings is exciting for physiologists and theoreticians because it offers the possibility of reconstructing the underlying neuronal circuits. We recently presented a method of inferring this circuit connectivity from neuronal spike trains by applying the generalized linear model to cross-correlograms. Although the algorithm can do a good job of circuit reconstruction, the parameters need to be carefully tuned for each individual dataset. Here we present another method using a Convolutional Neural Network for Estimating synaptic Connectivity from spike trains. After adaptation to huge amounts of simulated data, this method robustly captures the specific feature of monosynaptic impact in a noisy cross-correlogram. There are no user-adjustable parameters. With this new method, we have constructed diagrams of neuronal circuits recorded in several cortical areas of monkeys.

Arche-writing and data-production in theory-oriented scientific practice: the case of free-viewing as experimental system to test the temporal correlation hypothesis

Data production in experimental sciences depends on localised experimental systems, but the epistemic properties of data transcend the contingencies of the processes that produce them. Philosophers often believe that experimental systems instantiate but do not produce the epistemic properties of data. In this paper, we argue that experimental systems' local functioning entails intrinsic capacities to produce the epistemic properties of data. We develop this idea by applying Derrida's model of arche-writing to study a case of theory-oriented experimental practice. Derrida's model relativises or dissolves the conceptual distinction between the moment of data production and a subsequent moment of data dissemination. It thus has consequences for understanding both data production (despite being intrinsically local, data production a priori generates transferrable and modellable information) and data dissemination (when modelling information, researchers needs to refer this information to the context of its production). We study a case of data production in a non-exploratory experimental system designed to test a pre-existing hypothesis in visual neuroscience. A case of theory-oriented experimental practice should allow us to identify the autonomous functioning of experimental systems in data production more clearly, insofar as it allows us to study the limits of pre-existing theory in the activities of these systems. We suggest that pre-existing concepts, hypotheses and theories condition the relevance but not the production of experimental data.

Detecting prediction limit of marked point processes using constrained random shuffle surrogate data

Marked point processes refer to time series of discrete events with additional information about the events. Seismic activities, neural activities, and price movements in financial markets are typical examples of marked point process data. In this paper, we propose a method for investigating the prediction limits of marked point process data, where random shuffle surrogate data with time window constraints are proposed and utilized to estimate the prediction limits. We applied the proposed method to the marked point process data obtained from several dynamical systems and investigated the relationship between the largest Lyapunov exponent and the prediction limit estimated by the proposed method. The results revealed a positive correlation between the reciprocal of the estimated prediction limit and the largest Lyapunov exponent of the underlying dynamical systems in marked point processes.

Spiking Correlation Analysis of Synchronous Spikes Evoked by Acupuncture Mechanical Stimulus

Acupuncturing the ST36 acupoint can evoke the response of the sensory nervous system, which is translated into output electrical signals in the spinal dorsal root. Neural response activities, especially synchronous spike events, evoked by different acupuncture manipulations have remarkable differences. In order to identify these network collaborative activities, we analyze the underlying spike correlation in the synchronous spike event. In this paper, we adopt a log-linear model to describe network response activities evoked by different acupuncture manipulations. Then the state-space model and Bayesian theory are used to estimate network spike correlations. Two sets of simulation data are used to test the effectiveness of the estimation algorithm and the model goodness-of-fit. In addition, simulation data are also used to analyze the relationship between spike correlations and synchronous spike events. Finally, we use this method to identify network spike correlations evoked by four different acupuncture manipulations. Results show that reinforcing manipulations (twirling reinforcing and lifting-thrusting reinforcing) can evoke the third-order spike correlation but reducing manipulations (twirling reducing and lifting-thrusting reducing) does not. This is the main reason why synchronous spikes evoked by reinforcing manipulations are more abundant than reducing manipulations.

Free-viewing as experimental system to test the Temporal Correlation Hypothesis: A case of theory-generative experimental practice

Theory-free characterizations of experimental systems miss normative and conceptual components that sometimes are crucial to understanding their historical development. In the following paper, we show that these components may be part of the intrinsic capacities of experimental systems themselves. We study a case of non-exploratory and theory-oriented research in experimental neuroscience that concerns the construction of free-viewing as an experimental system to test one particular pre-existing hypothesis, the Temporal Correlation Hypothesis (TCH), at a laboratory in Santiago de Chile, during 2002-2008. We show that the system does not take well-formulated pre-existing predictions or hypotheses to test them directly, but re-creates them and re-signifies them in terms that are not implied by the theoretical background from which they originally derived. Therefore, we conclude that there is a sui generis way in which experimental systems produce proper theoretical knowledge.

SpiSeMe: A multi-language package for spike train surrogate generation

Many studies in nonlinear science heavily rely on surrogate-based hypothesis testing to provide significance estimations of analysis results. Among the complex data produced by nonlinear systems, spike trains are a class of sequences requiring algorithms for surrogate generation that are typically more sophisticated and computationally demanding than methods developed for continuous signals. Although algorithms to specifically generate surrogate spike trains exist, the availability of open-source, portable implementations is still incomplete. In this paper, we introduce the SpiSeMe (Spike Sequence Mime) software package that implements four algorithms for the generation of surrogate data out of spike trains and more generally out of any sequence of discrete events. The purpose of the package is to provide a unified and portable toolbox to carry out surrogate generation on point-process data. Code is provided in three languages, namely, C++, Matlab, and Python, thus allowing straightforward integration of package functions into most analysis pipelines.

Generation of surrogate event sequences via joint distribution of successive inter-event intervals

The study of many dynamical systems relies on the analysis of experimentally-recorded sequences of events for which information is encoded in the sequence of interevent intervals. A correct interpretation of the results of the application of analytical techniques to these sequences requires the assessment of statistical significance. In most cases, the corresponding null-hypothesis distribution is unknown, thus forbidding an evaluation of the significance. An alternative solution, which is efficient in the case of continuous signals, is provided by the generation of surrogate data that share statistical and spectral properties with the original dataset. However, in the case of event sequences, the available algorithms for the generation of surrogate data can become cumbersome and computationally demanding. In this work, we present a new method for the generation of surrogate event sequences that relies on the joint distribution of successive interevent intervals. Our method, which was tested on both synthetic and experimental sequences, performs equally well or even better than conventional methods in terms of interevent interval distribution and autocorrelation while abating the computational time by at least one order of magnitude.

Reconstructing neuronal circuitry from parallel spike trains

State-of-the-art techniques allow researchers to record large numbers of spike trains in parallel for many hours. With enough such data, we should be able to infer the connectivity among neurons. Here we develop a method for reconstructing neuronal circuitry by applying a generalized linear model (GLM) to spike cross-correlations. Our method estimates connections between neurons in units of postsynaptic potentials and the amount of spike recordings needed to verify connections. The performance of inference is optimized by counting the estimation errors using synthetic data. This method is superior to other established methods in correctly estimating connectivity. By applying our method to rat hippocampal data, we show that the types of estimated connections match the results inferred from other physiological cues. Thus our method provides the means to build a circuit diagram from recorded spike trains, thereby providing a basis for elucidating the differences in information processing in different brain regions.

Current techniques have enabled the simultaneous collection of spike train data from large numbers of neurons. Here, the authors report a method to infer the underlying neural circuit connectivity diagram based on a generalized linear model applied to spike cross-correlations between neurons.

Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits

Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical circuits. To integrate these properties from anatomy and physiology, and to elucidate the links between them, we develop a novel cortical circuit model that captures a range of realistic features of synaptic connectivity. We show that the model accounts for the emergence of higher-order connectivity structures, including highly connected hub neurons that form an interconnected rich-club. The circuit model exhibits a rich repertoire of dynamical activity states, ranging from asynchronous to localized and global propagating wave states. We find that around the transition between asynchronous and localized propagating wave states, our model quantitatively reproduces a variety of major empirical findings regarding neural spatiotemporal dynamics, which otherwise remain disjointed in existing studies. These dynamics include diverse coupling (correlation) between spiking activity of individual neurons and the population, dynamical wave patterns with variable speeds and precise temporal structures of neural spikes. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to the diverse population coupling. These findings establish an integrated account of structural connectivity and activity dynamics of local cortical circuits, and provide new insights into understanding their working mechanisms.

To integrate essential anatomical and physiological properties of local cortical circuits and to elucidate mechanistic links between them, we develop a novel circuit model capturing key synaptic connectivity features. We show that the model explains the emergence of a range of connectivity patterns such as rich-club connectivity, and gives rise to a rich repertoire of cortical states. We identify both the anatomical and physiological mechanisms underlying the transition of these cortical states, and show that our model reconciles an otherwise disparate set of key physiological findings on neural activity dynamics. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to diverse neural population correlations as observed recently. Our model thus provides a framework for integrating and explaining a variety of neural connectivity properties and spatiotemporal activity dynamics observed in experimental studies, and provides novel experimentally testable predictions.

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.

Surrogate Data Methods Based on a Shuffling of the Trials for Synchrony Detection: The Centering Issue

We investigate several distribution-free dependence detection procedures, all based on a shuffling of the trials, from a statistical point of view. The mathematical justification of such procedures lies in the bootstrap principle and its approximation properties. In particular, we show that such a shuffling has mainly to be done on centered quantities-that is, quantities with zero mean under independence-to construct correct p-values, meaning that the corresponding tests control their false positive (FP) rate. Thanks to this study, we introduce a method, named permutation UE, which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count. Each involved single test of this procedure achieves the prescribed level, so that the corresponding multiple testing procedure controls the false discovery rate (FDR), and this with as few assumptions as possible on the underneath distribution, except independence and identical distribution across trials. The mathematical meaning of this assumption is discussed, and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross-trials stationarity. Some simulations show, moreover, that permutation UE outperforms the trial-shuffling of Pipa and Grün ( 2003 ) and the MTGAUE method of Tuleau-Malot et al. ( 2014 ) in terms of single levels and FDR, for a comparable amount of false negatives. Application to real data is also provided.

A framework for computational modelling of interaural time difference discrimination of normal and hearing-impaired listeners

Different computational models have been developed to study the interaural time difference (ITD) perception. However, only few have used a physiologically inspired architecture to study ITD discrimination. Furthermore, they do not include aspects of hearing impairment. In this work, a framework was developed to predict ITD thresholds in listeners with normal and impaired hearing. It combines the physiologically inspired model of the auditory periphery proposed by Zilany, Bruce, Nelson, and Carney [(2009). J. Acoust. Soc. Am. 126(5), 2390-2412] as a front end with a coincidence detection stage and a neurometric decision device as a back end. It was validated by comparing its predictions against behavioral data for narrowband stimuli from literature. The framework is able to model ITD discrimination of normal-hearing and hearing-impaired listeners at a group level. Additionally, it was used to explore the effect of different proportions of outer- and inner-hair cell impairment on ITD discrimination.

Uncovering Neuronal Networks Defined by Consistent Between-Neuron Spike Timing from Neuronal Spike Recordings

It is widely assumed that distributed neuronal networks are fundamental to the functioning of the brain. Consistent spike timing between neurons is thought to be one of the key principles for the formation of these networks. This can involve synchronous spiking or spiking with time delays, forming spike sequences when the order of spiking is consistent. Finding networks defined by their sequence of time-shifted spikes, denoted here as spike timing networks, is a tremendous challenge. As neurons can participate in multiple spike sequences at multiple between-spike time delays, the possible complexity of networks is prohibitively large. We present a novel approach that is capable of (1) extracting spike timing networks regardless of their sequence complexity, and (2) that describes their spiking sequences with high temporal precision. We achieve this by decomposing frequency-transformed neuronal spiking into separate networks, characterizing each network’s spike sequence by a time delay per neuron, forming a spike sequence timeline. These networks provide a detailed template for an investigation of the experimental relevance of their spike sequences. Using simulated spike timing networks, we show network extraction is robust to spiking noise, spike timing jitter, and partial occurrences of the involved spike sequences. Using rat multineuron recordings, we demonstrate the approach is capable of revealing real spike timing networks with sub-millisecond temporal precision. By uncovering spike timing networks, the prevalence, structure, and function of complex spike sequences can be investigated in greater detail, allowing us to gain a better understanding of their role in neuronal functioning.

Massively parallel recordings in macaque motor cortex during an instructed delayed reach-to-grasp task

We publish two electrophysiological datasets recorded in motor cortex of two macaque monkeys during an instructed delayed reach-to-grasp task, using chronically implanted 10-by-10 Utah electrode arrays. We provide a) raw neural signals (sampled at 30 kHz), b) time stamps and spike waveforms of offline sorted single and multi units (93/49 and 156/19 SUA/MUA for the two monkeys, respectively), c) trial events and the monkey’s behavior, and d) extensive metadata hierarchically structured via the odML metadata framework (including quality assessment post-processing steps, such as trial rejections). The dataset of one monkey contains a simultaneously saved record of the local field potential (LFP) sampled at 1 kHz. To load the datasets in Python, we provide code based on the Neo data framework that produces a data structure which is annotated with relevant metadata. We complement this loading routine with an example code demonstrating how to access the data objects (e.g., raw signals) contained in such structures. For Matlab users, we provide the annotated data structures as mat files.

Methods for identification of spike patterns in massively parallel spike trains

Temporally, precise correlations between simultaneously recorded neurons have been interpreted as signatures of cell assemblies, i.e., groups of neurons that form processing units. Evidence for this hypothesis was found on the level of pairwise correlations in simultaneous recordings of few neurons. Increasing the number of simultaneously recorded neurons increases the chances to detect cell assembly activity due to the larger sample size. Recent technological advances have enabled the recording of 100 or more neurons in parallel. However, these massively parallel spike train data require novel statistical tools to be analyzed for correlations, because they raise considerable combinatorial and multiple testing issues. Recently, various of such methods have started to develop. First approaches were based on population or pairwise measures of synchronization, and later led to methods for the detection of various types of higher-order synchronization and of spatio-temporal patterns. The latest techniques combine data mining with analysis of statistical significance. Here, we give a comparative overview of these methods, of their assumptions and of the types of correlations they can detect.

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.

Computational Neuroscience: Mathematical and Statistical Perspectives

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm.

Neuronal Assemblies Evidence Distributed Interactions within a Tactile Discrimination Task in Rats

Accumulating evidence suggests that neural interactions are distributed and relate to animal behavior, but many open questions remain. The neural assembly hypothesis, formulated by Hebb, states that synchronously active single neurons may transiently organize into functional neural circuits-neuronal assemblies (NAs)-and that would constitute the fundamental unit of information processing in the brain. However, the formation, vanishing, and temporal evolution of NAs are not fully understood. In particular, characterizing NAs in multiple brain regions over the course of behavioral tasks is relevant to assess the highly distributed nature of brain processing. In the context of NA characterization, active tactile discrimination tasks with rats are elucidative because they engage several cortical areas in the processing of information that are otherwise masked in passive or anesthetized scenarios. In this work, we investigate the dynamic formation of NAs within and among four different cortical regions in long-range fronto-parieto-occipital networks (primary somatosensory, primary visual, prefrontal, and posterior parietal cortices), simultaneously recorded from seven rats engaged in an active tactile discrimination task. Our results first confirm that task-related neuronal firing rate dynamics in all four regions is significantly modulated. Notably, a support vector machine decoder reveals that neural populations contain more information about the tactile stimulus than the majority of single neurons alone. Then, over the course of the task, we identify the emergence and vanishing of NAs whose participating neurons are shown to contain more information about animal behavior than randomly chosen neurons. Taken together, our results further support the role of multiple and distributed neurons as the functional unit of information processing in the brain (NA hypothesis) and their link to active animal behavior.

Changes in neuronal activity of cortico-basal ganglia-thalamic networks induced by acute dopaminergic manipulations in rats

The basal ganglia are thought to be particularly sensitive to changes in dopaminergic tone, and the realization that reduced dopaminergic signaling causes pronounced motor dysfunction is the rationale behind dopamine replacement therapy in Parkinson's disease. It has, however, proven difficult to identify which neurophysiological changes that ultimately lead to motor dysfunctions. To clarify this, we have here recorded neuronal activity throughout the cortico-basal ganglia-thalamic circuits in freely behaving rats during periods of immobility following acute dopaminergic manipulations, involving both vesicular dopamine depletion and antagonism of D1 and D2 type dopamine receptors. Synchronized and rhythmic activities were detected in the form of betaband oscillations in local field potentials and as cortical entrainment of action potentials in several basal ganglia structures. Analyses of the temporal development of synchronized oscillations revealed a spread from cortex to gradually also include deeper structures. In addition, firing rate changes involving neurons in all parts of the network were observed. These changes were typically relatively balanced within each structure, resulting in negligible net rate changes. Animals treated with D1 receptor antagonist showed a rapid onset of hypokinesia that preceded most of the neurophysiological changes, with the exception of these balanced rate changes. Parallel rate changes in functionally coupled ensembles of neurons in different structures may therefore be the first step in a cascade of neurophysiological changes underlying motor symptoms in the parkinsonian state. We suggest that balanced rate changes in distributed networks are possible mechanism of disease that should be further investigated in conditions involving dopaminergic dysfunction.

Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models

Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.

Networks of interacting units are ubiquitous in various fields of biology; e.g. gene regulatory networks, neuronal networks, social structures. If a limited set of observables is accessible, maximum-entropy models provide a way to construct a statistical model for such networks, under particular assumptions. The pairwise maximum-entropy model only uses the first two moments among those observables, and can be interpreted as a network with only pairwise interactions. If correlations are on average positive, we here show that the maximum entropy distribution tends to become bimodal. In the application to neuronal activity this is a problem, because the bimodality is an artefact of the statistical model and not observed in real data. This problem could also affect other fields in biology. We here explain under which conditions bimodality arises and present a solution to the problem by introducing a collective negative feedback, corresponding to a modified maximum-entropy model. This result may point to the existence of a homeostatic mechanism active in the system that is not part of our set of observable units.

Distinct Temporal Coordination of Spontaneous Population Activity between Basal Forebrain and Auditory Cortex

The basal forebrain (BF) has long been implicated in attention, learning and memory, and recent studies have established a causal relationship between artificial BF activation and arousal. However, neural ensemble dynamics in the BF still remains unclear. Here, recording neural population activity in the BF and comparing it with simultaneously recorded cortical population under both anesthetized and unanesthetized conditions, we investigate the difference in the structure of spontaneous population activity between the BF and the auditory cortex (AC) in mice. The AC neuronal population show a skewed spike rate distribution, a higher proportion of short (≤80 ms) inter-spike intervals (ISIs) and a rich repertoire of rhythmic firing across frequencies. Although the distribution of spontaneous firing rate in the BF is also skewed, a proportion of short ISIs can be explained by a Poisson model at short time scales (≤20 ms) and spike count correlations are lower compared to AC cells, with optogenetically identified cholinergic cell pairs showing exceptionally higher correlations. Furthermore, a smaller fraction of BF neurons shows spike-field entrainment across frequencies: a subset of BF neurons fire rhythmically at slow (≤6 Hz) frequencies, with varied phase preferences to ongoing field potentials, in contrast to a consistent phase preference of AC populations. Firing of these slow rhythmic BF cells is correlated to a greater degree than other rhythmic BF cell pairs. Overall, the fundamental difference in the structure of population activity between the AC and BF is their temporal coordination, in particular their operational timescales. These results suggest that BF neurons slowly modulate downstream populations whereas cortical circuits transmit signals on multiple timescales. Thus, the characterization of the neural ensemble dynamics in the BF provides further insight into the neural mechanisms, by which brain states are regulated.

Emergent cortical circuit dynamics contain dense, interwoven ensembles of spike sequences

Temporal codes are theoretically powerful encoding schemes, but their precise form in the neocortex remains unknown in part because of the large number of possible codes and the difficulty in disambiguating informative spikes from statistical noise. A biologically plausible and computationally powerful temporal coding scheme is the Hebbian assembly phase sequence (APS), which predicts reliable propagation of spikes between functionally related assemblies of neurons. Here, we sought to measure the inherent capacity of neocortical networks to produce reliable sequences of spikes, as would be predicted by an APS code. To record microcircuit activity, the scale at which computation is implemented, we used two-photon calcium imaging to densely sample spontaneous activity in murine neocortical networks ex vivo. We show that the population spike histogram is sufficient to produce a spatiotemporal progression of activity across the population. To more comprehensively evaluate the capacity for sequential spiking that cannot be explained by the overall population spiking, we identify statistically significant spike sequences. We found a large repertoire of sequence spikes that collectively comprise the majority of spiking in the circuit. Sequences manifest probabilistically and share neuron membership, resulting in unique ensembles of interwoven sequences characterizing individual spatiotemporal progressions of activity. Distillation of population dynamics into its constituent sequences provides a way to capture trial-to-trial variability and may prove to be a powerful decoding substrate in vivo. Informed by these data, we suggest that the Hebbian APS be reformulated as interwoven sequences with flexible assembly membership due to shared overlapping neurons.NEW & NOTEWORTHY Neocortical computation occurs largely within microcircuits comprised of individual neurons and their connections within small volumes (<500 μm³). We found evidence for a long-postulated temporal code, the Hebbian assembly phase sequence, by identifying repeated and co-occurring sequences of spikes. Variance in population activity across trials was explained in part by the ensemble of active sequences. The presence of interwoven sequences suggests that neuronal assembly structure can be variable and is determined by previous activity.

Information reduction in a reverberatory neuronal network through convergence to complex oscillatory firing patterns

Dynamics of a reverberating neural net is studied by means of computer simulation. The net, which is composed of 9 leaky integrate-and-fire (LIF) neurons arranged in a square lattice, is fully connected with interneuronal communication delay proportional to the corresponding distance. The network is initially stimulated with different stimuli and then goes freely. For each stimulus, in the course of free evolution, activity either dies out completely or the network converges to a periodic trajectory, which may be different for different stimuli. The latter is observed for a set of 285290 initial stimuli which constitutes 83% of all stimuli applied. After applying each stimulus from the set, 102 different periodic end-states are found. The conclusion is made, after analyzing the trajectories, that neuronal firing is the necessary prerequisite for merging different trajectories into a single one, which eventually transforms into a periodic regime. Observed phenomena of self-organization in the time domain are discussed as a possible model for processes taking place during perception. The repetitive firing in the periodic regimes could underpin memory formation.

Robustness and versatility of a nonlinear interdependence method for directional coupling detection from spike trains

The detection of directional couplings between dynamics based on measured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons. One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure L. Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes. We also examine the influence of different parameters and spike train distances. Our results show that the measure L is versatile and robust to various types of noise, and thus suitable for application to experimental data.

Synchronous Spike Patterns in Macaque Motor Cortex during an Instructed-Delay Reach-to-Grasp Task

The computational role of spike time synchronization at millisecond precision among neurons in the cerebral cortex is hotly debated. Studies performed on data of limited size provided experimental evidence that low-order correlations occur in relation to behavior. Advances in electrophysiological technology to record from hundreds of neurons simultaneously provide the opportunity to observe coordinated spiking activity of larger populations of cells. We recently published a method that combines data mining and statistical evaluation to search for significant patterns of synchronous spikes in massively parallel spike trains (Torre et al., 2013). The method solves the computational and multiple testing problems raised by the high dimensionality of the data. In the current study, we used our method on simultaneous recordings from two macaque monkeys engaged in an instructed-delay reach-to-grasp task to determine the emergence of spike synchronization in relation to behavior. We found a multitude of synchronous spike patterns aligned in both monkeys along a preferential mediolateral orientation in brain space. The occurrence of the patterns is highly specific to behavior, indicating that different behaviors are associated with the synchronization of different groups of neurons ("cell assemblies"). However, pooled patterns that overlap in neuronal composition exhibit no specificity, suggesting that exclusive cell assemblies become active during different behaviors, but can recruit partly identical neurons. These findings are consistent across multiple recording sessions analyzed across the two monkeys.

SIGNIFICANCE STATEMENT

Neurons in the brain communicate via electrical impulses called spikes. How spikes are coordinated to process information is still largely unknown. Synchronous spikes are effective in triggering a spike emission in receiving neurons and have been shown to occur in relation to behavior in a number of studies on simultaneous recordings of few neurons. We recently published a method to extend this type of investigation to larger data. Here, we apply it to simultaneous recordings of hundreds of neurons from the motor cortex of macaque monkeys performing a motor task. Our analysis reveals groups of neurons selectively synchronizing their activity in relation to behavior, which sheds new light on the role of synchrony in information processing in the cerebral cortex.

Detection and Evaluation of Spatio-Temporal Spike Patterns in Massively Parallel Spike Train Data with SPADE

Repeated, precise sequences of spikes are largely considered a signature of activation of cell assemblies. These repeated sequences are commonly known under the name of spatio-temporal patterns (STPs). STPs are hypothesized to play a role in the communication of information in the computational process operated by the cerebral cortex. A variety of statistical methods for the detection of STPs have been developed and applied to electrophysiological recordings, but such methods scale poorly with the current size of available parallel spike train recordings (more than 100 neurons). In this work, we introduce a novel method capable of overcoming the computational and statistical limits of existing analysis techniques in detecting repeating STPs within massively parallel spike trains (MPST). We employ advanced data mining techniques to efficiently extract repeating sequences of spikes from the data. Then, we introduce and compare two alternative approaches to distinguish statistically significant patterns from chance sequences. The first approach uses a measure known as conceptual stability, of which we investigate a computationally cheap approximation for applications to such large data sets. The second approach is based on the evaluation of pattern statistical significance. In particular, we provide an extension to STPs of a method we recently introduced for the evaluation of statistical significance of synchronous spike patterns. The performance of the two approaches is evaluated in terms of computational load and statistical power on a variety of artificial data sets that replicate specific features of experimental data. Both methods provide an effective and robust procedure for detection of STPs in MPST data. The method based on significance evaluation shows the best overall performance, although at a higher computational cost. We name the novel procedure the spatio-temporal Spike PAttern Detection and Evaluation (SPADE) analysis.

Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.

Simultaneous analysis of large-scale neural populations is necessary to understand coding principles of neurons because they concertedly process information. Methods of thermodynamics and statistical mechanics are useful to understand collective phenomena of the interacting elements, and they have been successfully used to understand diverse activity of neurons. However, most analysis methods assume stationary data, in which activity rates of neurons and their correlations are constant over time. This assumption is easily violated in the data recorded from awake animals. Neural correlations likely organize dynamically during behavior and cognition, and this may be independent from the modulated activity rates of individual neurons. Recently several methods were proposed to simultaneously estimate dynamics of neural interactions. However, these methods are applicable to up to about 10 neurons. Here by combining multiple analytic approximation methods, we made it possible to estimate time-varying interactions of much larger neural populations. The method allows us to trace dynamic macroscopic properties of neural circuitries such as sparseness, entropy, and sensitivity. Using these statistics, researchers can now quantify to what extent neurons are correlated or de-correlated, and test if neural systems are susceptible within a specific behavioral period.

Spike-Centered Jitter Can Mistake Temporal Structure

Jitter-type spike resampling methods are routinely applied in neurophysiology for detecting temporal structure in spike trains (point processes). Several variations have been proposed. The concern has been raised, based on numerical experiments involving Poisson spike processes, that such procedures can be conservative. We study the issue and find it can be resolved by reemphasizing the distinction between spike-centered (basic) jitter and interval jitter. Focusing on spiking processes with no temporal structure, interval jitter generates an exact hypothesis test, guaranteeing valid conclusions. In contrast, such a guarantee is not available for spike-centered jitter. We construct explicit examples in which spike-centered jitter hallucinates temporal structure, in the sense of exaggerated false-positive rates. Finally, we illustrate numerically that Poisson approximations to jitter computations, while computationally efficient, can also result in inaccurate hypothesis tests. We highlight the value of classical statistical frameworks for guiding the design and interpretation of spike resampling methods.

Cell assemblies at multiple time scales with arbitrary lag constellations

Hebb's idea of a cell assembly as the fundamental unit of neural information processing has dominated neuroscience like no other theoretical concept within the past 60 years. A range of different physiological phenomena, from precisely synchronized spiking to broadly simultaneous rate increases, has been subsumed under this term. Yet progress in this area is hampered by the lack of statistical tools that would enable to extract assemblies with arbitrary constellations of time lags, and at multiple temporal scales, partly due to the severe computational burden. Here we present such a unifying methodological and conceptual framework which detects assembly structure at many different time scales, levels of precision, and with arbitrary internal organization. Applying this methodology to multiple single unit recordings from various cortical areas, we find that there is no universal cortical coding scheme, but that assembly structure and precision significantly depends on the brain area recorded and ongoing task demands.

DOI:http://dx.doi.org/10.7554/eLife.19428.001

Estimating Fast Neural Input Using Anatomical and Functional Connectivity

In the last 20 years there has been an increased interest in estimating signals that are sent between neurons and brain areas. During this time many new methods have appeared for measuring those signals. Here we review a wide range of methods for which connected neurons can be identified anatomically, by tracing axons that run between the cells, or functionally, by detecting if the activity of two neurons are correlated with a short lag. The signals that are sent between the neurons are represented by the activity in the neurons that are connected to the target population or by the activity at the corresponding synapses. The different methods not only differ in the accuracy of the signal measurement but they also differ in the type of signal being measured. For example, unselective recording of all neurons in the source population encompasses more indirect pathways to the target population than if one selectively record from the neurons that project to the target population. Infact, this degree of selectivity is similar to that of optogenetic perturbations; one can perturb selectively or unselectively. Thus it becomes possible to match a given signal measurement method with a signal perturbation method, something that allows for an exact input control to any neuronal population.

Repertoire of mesoscopic cortical activity is not reduced during anesthesia

Consciousness has been linked to the repertoire of brain states at various spatiotemporal scales. Anesthesia is thought to modify consciousness by altering information integration in cortical and thalamocortical circuits. At a mesoscopic scale, neuronal populations in the cortex form synchronized ensembles whose characteristics are presumably state-dependent but this has not been rigorously tested. In this study, spontaneous neuronal activity was recorded with 64-contact microelectrode arrays in primary visual cortex of chronically instrumented, unrestrained rats under stepwise decreasing levels of desflurane anesthesia (8%, 6%, 4%, and 2% inhaled concentrations) and wakefulness (0% concentration). Negative phases of the local field potentials formed compact, spatially contiguous activity patterns (CAPs) that were not due to chance. The number of CAPs was 120% higher in wakefulness and deep anesthesia associated with burst-suppression than at intermediate levels of consciousness. The frequency distribution of CAP sizes followed a power-law with slope -1.5 in relatively deep anesthesia (8-6%) but deviated from that at the lighter levels. Temporal variance and entropy of CAP sizes were lowest in wakefulness (76% and 24% lower at 0% than at 8% desflurane, respectively) but changed little during recovery of consciousness. CAPs categorized by K-means clustering were conserved at all anesthesia levels and wakefulness, although their proportion changed in a state-dependent manner. These observations yield new knowledge about the dynamic landscape of ongoing population activity in sensory cortex at graded levels of anesthesia. The repertoire of population activity and self-organized criticality at the mesoscopic scale do not appear to contribute to anesthetic suppression of consciousness, which may instead depend on large-scale effects, more subtle dynamic properties, or changes outside of primary sensory cortex.

ASSET: Analysis of Sequences of Synchronous Events in Massively Parallel Spike Trains

With the ability to observe the activity from large numbers of neurons simultaneously using modern recording technologies, the chance to identify sub-networks involved in coordinated processing increases. Sequences of synchronous spike events (SSEs) constitute one type of such coordinated spiking that propagates activity in a temporally precise manner. The synfire chain was proposed as one potential model for such network processing. Previous work introduced a method for visualization of SSEs in massively parallel spike trains, based on an intersection matrix that contains in each entry the degree of overlap of active neurons in two corresponding time bins. Repeated SSEs are reflected in the matrix as diagonal structures of high overlap values. The method as such, however, leaves the task of identifying these diagonal structures to visual inspection rather than to a quantitative analysis. Here we present ASSET (Analysis of Sequences of Synchronous EvenTs), an improved, fully automated method which determines diagonal structures in the intersection matrix by a robust mathematical procedure. The method consists of a sequence of steps that i) assess which entries in the matrix potentially belong to a diagonal structure, ii) cluster these entries into individual diagonal structures and iii) determine the neurons composing the associated SSEs. We employ parallel point processes generated by stochastic simulations as test data to demonstrate the performance of the method under a wide range of realistic scenarios, including different types of non-stationarity of the spiking activity and different correlation structures. Finally, the ability of the method to discover SSEs is demonstrated on complex data from large network simulations with embedded synfire chains. Thus, ASSET represents an effective and efficient tool to analyze massively parallel spike data for temporal sequences of synchronous activity.

Propagation of spontaneous slow-wave activity across columns and layers of the adult rat barrel cortex in vivo

During slow-wave sleep, neocortical networks exhibit self-organized activity switching between periods of concurrent spiking (up-states) and periods of network silence (down-states), a phenomenon also occurring under the effects of different anesthetics and in in vitro brain slice preparations. Although this type of ongoing activity has been implicated into important functions such as memory consolidation and learning, the manner in which it propagates across different cortical modules (i.e., columns and layers) has not been fully characterized. In the present study, we investigated this issue by measuring spontaneous activity at large scale in the adult rat barrel cortex under urethane anesthesia by means of voltage-sensitive dye imaging and 128-channel probe recordings. Up to 74 neurons located in all layers of up to four functionally identified barrel-related columns were recorded simultaneously. The spontaneous activity propagated isotropically across the cortical surface with a median speed of ~35 µm/ms. A concomitant radial spread of activation was present from deep to superficial cortical layers. Thus, spontaneous activity occurred rather globally in the barrel cortex, with ≥50 % of the up-states presenting spikes in ≥3 columns and layers. Temporally precise spike sequences, which occurred repeatedly (although sporadically) within the up-states, were typically led by putative excitatory neurons in the infragranular cortical layers. In summary, our data provide for the first time an overall view of the spontaneous slow-wave activity within the barrel cortex circuit, characterizing its propagation across columns and layers at high spatio-temporal resolution.

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or "spikes" nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons' fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron's firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.

Ambiguity and nonidentifiability in the statistical analysis of neural codes

Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, "Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?" For another example, "How much of a neuron's observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?" However, a neuron's theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.

Bootstrap testing for cross-correlation under low firing activity

A new cross-correlation synchrony index for neural activity is proposed. The index is based on the integration of the kernel estimation of the cross-correlation function. It is used to test for the dynamic synchronization levels of spontaneous neural activity under two induced brain states: sleep-like and awake-like. Two bootstrap resampling plans are proposed to approximate the distribution of the test statistics. The results of the first bootstrap method indicate that it is useful to discern significant differences in the synchronization dynamics of brain states characterized by a neural activity with low firing rate. The second bootstrap method is useful to unveil subtle differences in the synchronization levels of the awake-like state, depending on the activation pathway.

Signs of timing in motor cortex during movement preparation and cue anticipation

The capacity to accurately anticipate the timing of predictable events is essential for sensorimotor behavior. Motor cortex holds an established role in movement preparation and execution. In this chapter we review the different ways in which motor cortical activity is modulated by event timing in sensorimotor delay tasks. During movement preparation, both single neuron and population responses reflect the temporal constraints of the task. Anticipatory modulations prior to sensory cues are also observed in motor cortex when the cue timing is predictable. We propose that the motor cortical activity during cue anticipation and movement preparation is embedded in a timing network that facilitates sensorimotor processing. In this context, the pre-cue and post-cue activity may reflect a presetting mechanism, complementing processing during movement execution, while prohibiting premature responses in situations requiring delayed motor output.

SPIKY: a graphical user interface for monitoring spike train synchrony

Techniques for recording large-scale neuronal spiking activity are developing very fast. This leads to an increasing demand for algorithms capable of analyzing large amounts of experimental spike train data. One of the most crucial and demanding tasks is the identification of similarity patterns with a very high temporal resolution and across different spatial scales. To address this task, in recent years three time-resolved measures of spike train synchrony have been proposed, the ISI-distance, the SPIKE-distance, and event synchronization. The Matlab source codes for calculating and visualizing these measures have been made publicly available. However, due to the many different possible representations of the results the use of these codes is rather complicated and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and interactive interface. Here we address this need and present SPIKY, a graphical user interface that facilitates the application of time-resolved measures of spike train synchrony to both simulated and real data. SPIKY includes implementations of the ISI-distance, the SPIKE-distance, and the SPIKE-synchronization (an improved and simplified extension of event synchronization) that have been optimized with respect to computation speed and memory demand. It also comprises a spike train generator and an event detector that makes it capable of analyzing continuous data. Finally, the SPIKY package includes additional complementary programs aimed at the analysis of large numbers of datasets and the estimation of significance levels.

A statistical method of identifying interactions in neuron-glia systems based on functional multicell Ca2+ imaging

Crosstalk between neurons and glia may constitute a significant part of information processing in the brain. We present a novel method of statistically identifying interactions in a neuron-glia network. We attempted to identify neuron-glia interactions from neuronal and glial activities via maximum-a-posteriori (MAP)-based parameter estimation by developing a generalized linear model (GLM) of a neuron-glia network. The interactions in our interest included functional connectivity and response functions. We evaluated the cross-validated likelihood of GLMs that resulted from the addition or removal of connections to confirm the existence of specific neuron-to-glia or glia-to-neuron connections. We only accepted addition or removal when the modification improved the cross-validated likelihood. We applied the method to a high-throughput, multicellular in vitro Ca2+ imaging dataset obtained from the CA3 region of a rat hippocampus, and then evaluated the reliability of connectivity estimates using a statistical test based on a surrogate method. Our findings based on the estimated connectivity were in good agreement with currently available physiological knowledge, suggesting our method can elucidate undiscovered functions of neuron-glia systems.

Different fixational eye movements mediate the prevention and the reversal of visual fading

Fixational eye movements (FEMs; including microsaccades, drift and tremor) are thought to improve visibility during fixation by thwarting neural adaptation to unchanging stimuli, but how the different FEM types influence this process is a matter of debate. Attempts to answer this question have been hampered by the failure to distinguish between the prevention of fading (where fading is blocked before it happens in the first place) and the reversal of fading (where vision is restored after fading has already occurred). Because fading during fixation is a detriment to clear vision, the prevention of fading, which avoids visual degradation before it happens, is a more desirable scenario than improving visibility after fading has occurred. Yet previous studies have not examined the role of FEMs in the prevention of fading, but have focused on visual restoration instead. Here we set out to determine the differential contributions and efficacies of microsaccades and drift to preventing fading in human vision. Our results indicate that both microsaccades and drift mediate the prevention of visual fading. We also found that drift is a potentially larger contributor to preventing fading than microsaccades, although microsaccades are more effective than drift. Microsaccades moreover prevented foveal and peripheral fading in an equivalent fashion, and their efficacy was independent of their size, number, and direction. Our data also suggest that faster drift may prevent fading better than slower drift. These findings may help to reconcile the long-standing controversy concerning the comparative roles of microsaccades and drift in visibility during fixation.