Multi-neuronal activity and functional connectivity in cell assemblies

Adaptive modeling and inference of higher-order coordination in neuronal assemblies: A dynamic greedy estimation approach

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Time-varying generalized linear models: characterizing and decoding neuronal dynamics in higher visual areas

To create a behaviorally relevant representation of the visual world, neurons in higher visual areas exhibit dynamic response changes to account for the time-varying interactions between external (e.g., visual input) and internal (e.g., reward value) factors. The resulting high-dimensional representational space poses challenges for precisely quantifying individual factors' contributions to the representation and readout of sensory information during a behavior. The widely used point process generalized linear model (GLM) approach provides a powerful framework for a quantitative description of neuronal processing as a function of various sensory and non-sensory inputs (encoding) as well as linking particular response components to particular behaviors (decoding), at the level of single trials and individual neurons. However, most existing variations of GLMs assume the neural systems to be time-invariant, making them inadequate for modeling nonstationary characteristics of neuronal sensitivity in higher visual areas. In this review, we summarize some of the existing GLM variations, with a focus on time-varying extensions. We highlight their applications to understanding neural representations in higher visual areas and decoding transient neuronal sensitivity as well as linking physiology to behavior through manipulation of model components. This time-varying class of statistical models provide valuable insights into the neural basis of various visual behaviors in higher visual areas and hold significant potential for uncovering the fundamental computational principles that govern neuronal processing underlying various behaviors in different regions of the brain.

Machine learning at the mesoscale: A computation-dissipation bottleneck

The cost of information processing in physical systems calls for a trade-off between performance and energetic expenditure. Here we formulate and study a computation-dissipation bottleneck in mesoscopic systems used as input-output devices. Using both real data sets and synthetic tasks, we show how nonequilibrium leads to enhanced performance. Our framework sheds light on a crucial compromise between information compression, input-output computation and dynamic irreversibility induced by nonreciprocal interactions.

Adaptive modeling and inference of higher-order coordination in neuronal assemblies: a dynamic greedy estimation approach

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model

Most natural systems operate far from equilibrium, displaying time-asymmetric, irreversible dynamics characterized by a positive entropy production while exchanging energy and matter with the environment. Although stochastic thermodynamics underpins the irreversible dynamics of small systems, the nonequilibrium thermodynamics of larger, more complex systems remains unexplored. Here, we investigate the asymmetric Sherrington-Kirkpatrick model with synchronous and asynchronous updates as a prototypical example of large-scale nonequilibrium processes. Using a path integral method, we calculate a generating functional over trajectories, obtaining exact solutions of the order parameters, path entropy, and steady-state entropy production of infinitely large networks. Entropy production peaks at critical order-disorder phase transitions, but is significantly larger for quasi-deterministic disordered dynamics. Consequently, entropy production can increase under distinct scenarios, requiring multiple thermodynamic quantities to describe the system accurately. These results contribute to developing an exact analytical theory of the nonequilibrium thermodynamics of large-scale physical and biological systems and their phase transitions.

The mechanics of correlated variability in segregated cortical excitatory subnetworks

Understanding the genesis of shared trial-to-trial variability in neural activity within sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since this variability likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells.

Simulations approaching data: cortical slow waves in inferred models of the whole hemisphere of mouse

The development of novel techniques to record wide-field brain activity enables estimation of data-driven models from thousands of recording channels and hence across large regions of cortex. These in turn improve our understanding of the modulation of brain states and the richness of traveling waves dynamics. Here, we infer data-driven models from high-resolution in-vivo recordings of mouse brain obtained from wide-field calcium imaging. We then assimilate experimental and simulated data through the characterization of the spatio-temporal features of cortical waves in experimental recordings. Inference is built in two steps: an inner loop that optimizes a mean-field model by likelihood maximization, and an outer loop that optimizes a periodic neuro-modulation via direct comparison of observables that characterize cortical slow waves. The model reproduces most of the features of the non-stationary and non-linear dynamics present in the high-resolution in-vivo recordings of the mouse brain. The proposed approach offers new methods of characterizing and understanding cortical waves for experimental and computational neuroscientists.

Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes

BACKGROUND

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron.

NEW METHOD

We provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. To the best of our knowledge, this is the first time that a Hawkes-diffusion model is investigated on such complex data. The first step of the proposed procedure is to select a subnetwork of neurons impacting the central neuron using a multivariate Hawkes process. Then we infer a jump-diffusion dynamic in which jumps are driven from a Hawkes process, the occurrences of which correspond to the spike trains of the aforementioned subset of neurons that interact with the central neuron.

RESULTS

From the Hawkes estimation step we recover a small connectivity graph which contains the central neuron, and we show that taking into account this information improves the inference of membrane potential through the proposed jump-diffusion model. A goodness of fit test is applied to validate the relevance of the Hawkes model in such context.

COMPARISON WITH EXISTING METHODS

We compare an empirical inference method and two sparse estimation procedures based on the Hawkes assumption for the reconstruction of the connectivity graph using the spike-trains. Then, the Hawkes-diffusion model is competed with the simple diffusion in terms of best fit to describe the behavior of the membrane potential of a central neuron surrounded by a network.

CONCLUSIONS

The present method takes advantage of both spike trains and membrane potential to understand the behavior of a fixed neuron. The entire code has been developed and is freely available on GitHub.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

Super-Selective Reconstruction of Causal and Direct Connectivity With Application to in vitro iPSC Neuronal Networks

Despite advancements in the development of cell-based in-vitro neuronal network models, the lack of appropriate computational tools limits their analyses. Methods aimed at deciphering the effective connections between neurons from extracellular spike recordings would increase utility of in vitro local neural circuits, especially for studies of human neural development and disease based on induced pluripotent stem cells (hiPSC). Current techniques allow statistical inference of functional couplings in the network but are fundamentally unable to correctly identify indirect and apparent connections between neurons, generating redundant maps with limited ability to model the causal dynamics of the network. In this paper, we describe a novel mathematically rigorous, model-free method to map effective-direct and causal-connectivity of neuronal networks from multi-electrode array data. The inference algorithm uses a combination of statistical and deterministic indicators which, first, enables identification of all existing functional links in the network and then reconstructs the directed and causal connection diagram via a super-selective rule enabling highly accurate classification of direct, indirect, and apparent links. Our method can be generally applied to the functional characterization of any in vitro neuronal networks. Here, we show that, given its accuracy, it can offer important insights into the functional development of in vitro hiPSC-derived neuronal cultures.

A unifying framework for mean-field theories of asymmetric kinetic Ising systems

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique assumptions about the system’s temporal evolution. This disparity of approaches makes it challenging to systematically advance mean-field methods beyond previous contributions. Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems from an information geometry perspective. The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions. This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional approaches, preserve the system’s correlations. We show that these new methods can outperform previous ones in predicting and assessing network properties near maximally fluctuating regimes.

Many mean-field theories are proposed for studying the non-equilibrium dynamics of complex systems, each based on specific assumptions about the system’s temporal evolution. Here, Aguilera et al. propose a unified framework for mean-field theories of asymmetric kinetic Ising systems to study non-equilibrium dynamics.

Model-based detection of putative synaptic connections from spike recordings with latency and type constraints

Detecting synaptic connections using large-scale extracellular spike recordings is a difficult statistical problem. Here, we develop an extension of a generalized linear model that explicitly separates fast synaptic effects and slow background fluctuations in cross-correlograms between pairs of neurons while incorporating circuit properties learned from the whole network. This model outperforms two previously developed synapse detection methods in the simulated networks and recovers plausible connections from hundreds of neurons in in vitro multielectrode array data.

Inferring Neuronal Couplings From Spiking Data Using a Systematic Procedure With a Statistical Criterion

Recent remarkable advances in experimental techniques have provided a background for inferring neuronal couplings from point process data that include a great number of neurons. Here, we propose a systematic procedure for pre- and postprocessing generic point process data in an objective manner to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch-Pitts model. The procedure has two steps: (1) determining time bin size for transforming the point process data into discrete-time binary data and (2) screening relevant couplings from the estimated couplings. For the first step, we decide the optimal time bin size by introducing the null hypothesis that all neurons would fire independently, then choosing a time bin size so that the null hypothesis is rejected with the strict criteria. The likelihood associated with the null hypothesis is analytically evaluated and used for the rejection process. For the second postprocessing step, after a certain estimator of coupling is obtained based on the preprocessed data set (any estimator can be used with the proposed procedure), the estimate is compared with many other estimates derived from data sets obtained by randomizing the original data set in the time direction. We accept the original estimate as relevant only if its absolute value is sufficiently larger than those of randomized data sets. These manipulations suppress false positive couplings induced by statistical noise. We apply this inference procedure to spiking data from synthetic and in vitro neuronal networks. The results show that the proposed procedure identifies the presence or absence of synaptic couplings fairly well, including their signs, for the synthetic and experimental data. In particular, the results support that we can infer the physical connections of underlying systems in favorable situations, even when using a simple statistical model.

On the Complexity of Logistic Regression Models

We investigate the complexity of logistic regression models, which is defined by counting the number of indistinguishable distributions that the model can represent (Balasubramanian, 1997). We find that the complexity of logistic models with binary inputs depends not only on the number of parameters but also on the distribution of inputs in a nontrivial way that standard treatments of complexity do not address. In particular, we observe that correlations among inputs induce effective dependencies among parameters, thus constraining the model and, consequently, reducing its complexity. We derive simple relations for the upper and lower bounds of the complexity. Furthermore, we show analytically that defining the model parameters on a finite support rather than the entire axis decreases the complexity in a manner that critically depends on the size of the domain. Based on our findings, we propose a novel model selection criterion that takes into account the entropy of the input distribution. We test our proposal on the problem of selecting the input variables of a logistic regression model in a Bayesian model selection framework. In our numerical tests, we find that while the reconstruction errors of standard model selection approaches (AIC, BIC, ℓ1 regularization) strongly depend on the sparsity of the ground truth, the reconstruction error of our method is always close to the minimum in all conditions of sparsity, data size, and strength of input correlations. Finally, we observe that when considering categorical instead of binary inputs, in a simple and mathematically tractable case, the contribution of the alphabet size to the complexity is very small compared to that of parameter space dimension. We further explore the issue by analyzing the data set of the "13 keys to the White House," a method for forecasting the outcomes of US presidential elections.

Dynamics of memory engrams

In this update article, we focus on "memory engrams", which are traces of long-term memory in the brain, and emphasizes that they are not static but dynamic. We first introduce the major findings in neuroscience and psychology reporting that memory engrams are sometimes diffuse and unstable, indicating that they are dynamically modified processes of consolidation and reconsolidation. Second, we introduce and discuss the concepts of cell assembly and engram cell, the former has been investigated by psychological experiments and behavioral electrophysiology and the latter is defined by recent combination of activity-dependent cell labelling with optogenetics to show causal relationships between cell population activity and behavioral changes. Third, we discuss the similarities and differences between the cell assembly and engram cell concepts to reveal the dynamics of memory engrams. We also discuss the advantages and problems of live-cell imaging, which has recently been developed to visualize multineuronal activities. The last section suggests the experimental strategy and background assumptions for future research of memory engrams. The former encourages recording of cell assemblies from different brain regions during memory consolidation-reconsolidation processes, while the latter emphasizes the multipotentiality of neurons and regions that contribute to dynamics of memory engrams in the working brain.

Spontaneous activity emerging from an inferred network model captures complex spatio-temporal dynamics of spike data

Inference methods are widely used to recover effective models from observed data. However, few studies attempted to investigate the dynamics of inferred models in neuroscience, and none, to our knowledge, at the network level. We introduce a principled modification of a widely used generalized linear model (GLM), and learn its structural and dynamic parameters from in-vitro spike data. The spontaneous activity of the new model captures prominent features of the non-stationary and non-linear dynamics displayed by the biological network, where the reference GLM largely fails, and also reflects fine-grained spatio-temporal dynamical features. Two ingredients were key for success. The first is a saturating transfer function: beyond its biological plausibility, it limits the neuron's information transfer, improving robustness against endogenous and external noise. The second is a super-Poisson spikes generative mechanism; it accounts for the undersampling of the network, and allows the model neuron to flexibly incorporate the observed activity fluctuations.

Multiple Approaches to the Investigation of Cell Assembly in Memory Research-Present and Future

In this review article we focus on research methodologies for detecting the actual activity of cell assemblies, which are populations of functionally connected neurons that encode information in the brain. We introduce and discuss traditional and novel experimental methods and those currently in development and briefly discuss their advantages and disadvantages for the detection of cell-assembly activity. First, we introduce the electrophysiological method, i.e., multineuronal recording, and review former and recent examples of studies showing models of dynamic coding by cell assemblies in behaving rodents and monkeys. We also discuss how the firing correlation of two neurons reflects the firing synchrony among the numerous surrounding neurons that constitute cell assemblies. Second, we review the recent outstanding studies that used the novel method of optogenetics to show causal relationships between cell-assembly activity and behavioral change. Third, we review the most recently developed method of live-cell imaging, which facilitates the simultaneous observation of firings of a large number of neurons in behaving rodents. Currently, all these available methods have both advantages and disadvantages, and no single measurement method can directly and precisely detect the actual activity of cell assemblies. The best strategy is to combine the available methods and utilize each of their advantages with the technique of operant conditioning of multiple-task behaviors in animals and, if necessary, with brain-machine interface technology to verify the accuracy of neural information detected as cell-assembly activity.

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions.

Reconstructing the functional connectivity of multiple spike trains using Hawkes models

BACKGROUND

Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods are in the general statistical framework of the multivariate Hawkes processes. However, they usually require a huge amount of data, some prior knowledge about the recorded network, and/or may produce an increasing number of spikes along time during simulation.

NEW METHOD

Here, we present a method, based on least-square estimators and LASSO penalty criteria, for a particular class of Hawkes processes that can be used for simulation.

RESULTS

Testing our method on small networks modeled with Leaky Integrate and Fire demonstrated that it efficiently detects both excitatory and inhibitory connections. The few errors that occasionally occur with complex networks including common inputs, weak and chained connections, can be discarded based on objective criteria.

COMPARISON WITH EXISTING METHODS

With respect to other existing methods, the present one allows to reconstruct functional connectivity of small networks without prior knowledge of their properties or architecture, using an experimentally realistic amount of data.

CONCLUSIONS

The present method is robust, stable, and can be used on a personal computer as a routine procedure to infer connectivity graphs and generate simulation models from simultaneous spike train recordings.

MEA Viewer: A high-performance interactive application for visualizing electrophysiological data

Action potentials can be recorded extracellularly from hundreds of neurons simultaneously with multi-electrode arrays. These can typically have as many as 120 or more electrodes. The brief duration of action potentials requires a high sampling frequency to reliably capture each waveform. The resulting raw data files are therefore large and difficult to visualize with traditional plotting tools. Common approaches to deal with the difficulties of data display, such as extracting spike times and performing spike train analysis, are useful in many contexts but they also significantly reduce data dimensionality. The use of tools which minimize data processing enable the development of heuristic perspective of experimental results. Here we introduce MEA Viewer, a high-performance open source application for the direct visualization of multi-channel electrophysiological data. MEA Viewer includes several high-performance visualizations, including an easily navigable overview of recorded extracellular action potentials from all data channels overlaid with spike timestamp data and an interactive raster plot. MEA Viewer can also display the two dimensional extent of action potential propagation in single neurons by signal averaging extracellular action potentials (eAPs) from single neurons detected on multiple electrodes. This view extracts and displays eAP timing information and eAP waveforms that are otherwise below the spike detection threshold. This entirely new method of using MEAs opens up novel research applications for medium density arrays. MEA Viewer is licensed under the General Public License version 3, GPLv3, and is available at http://github.com/dbridges/mea-tools.

Laminar Organization of Encoding and Memory Reactivation in the Parietal Cortex

Egocentric neural coding has been observed in parietal cortex (PC), but its topographical and laminar organization is not well characterized. We used multi-site recording to look for evidence of local clustering and laminar consistency of linear and angular velocity encoding in multi-neuronal spiking activity (MUA) and in the high-frequency (300-900 Hz) component of the local field potential (HF-LFP), believed to reflect local spiking activity. Rats were trained to run many trials on a large circular platform, either to LED-cued goal locations or as a spatial sequence from memory. Tuning to specific self-motion states was observed and exhibited distinct cortical depth-invariant coding properties. These patterns of collective local and laminar activation during behavior were reactivated in compressed form during post-experience sleep and temporally coupled to cortical delta waves and hippocampal sharp-wave ripples. Thus, PC neuron motion encoding is consistent across cortical laminae, and this consistency is maintained during memory reactivation.

Differential Covariance: A New Class of Methods to Estimate Sparse Connectivity from Neural Recordings

With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship of multiple neural signals. Correlation-based methods are a set of currently well-used techniques for functional connectivity estimation. However, due to explaining away and unobserved common inputs (Stevenson, Rebesco, Miller, & Körding, 2008 ), they produce spurious connections. The general linear model (GLM), which models spike trains as Poisson processes (Okatan, Wilson, & Brown, 2005 ; Truccolo, Eden, Fellows, Donoghue, & Brown, 2005 ; Pillow et al., 2008 ), avoids these confounds. We develop here a new class of methods by using differential signals based on simulated intracellular voltage recordings. It is equivalent to a regularized AR(2) model. We also expand the method to simulated local field potential recordings and calcium imaging. In all of our simulated data, the differential covariance-based methods achieved performance better than or similar to the GLM method and required fewer data samples. This new class of methods provides alternative ways to analyze neural signals.

Density-based clustering: A 'landscape view' of multi-channel neural data for inference and dynamic complexity analysis

Two, partially interwoven, hot topics in the analysis and statistical modeling of neural data, are the development of efficient and informative representations of the time series derived from multiple neural recordings, and the extraction of information about the connectivity structure of the underlying neural network from the recorded neural activities. In the present paper we show that state-space clustering can provide an easy and effective option for reducing the dimensionality of multiple neural time series, that it can improve inference of synaptic couplings from neural activities, and that it can also allow the construction of a compact representation of the multi-dimensional dynamics, that easily lends itself to complexity measures. We apply a variant of the ‘mean-shift’ algorithm to perform state-space clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are largely uncorrelated from memories embedded in the synaptic matrix. In this context, we show that the neural states identified as clusters’ centroids offer a parsimonious parametrization of the synaptic matrix, which allows a significant improvement in inferring the synaptic couplings from the neural activities. Moving to the more realistic case of a multi-modular spiking network, with spike-frequency adaptation inducing history-dependent effects, we propose a procedure inspired by Boltzmann learning, but extending its domain of application, to learn inter-module synaptic couplings so that the spiking network reproduces a prescribed pattern of spatial correlations; we then illustrate, in the spiking network, how clustering is effective in extracting relevant features of the network’s state-space landscape. Finally, we show that the knowledge of the cluster structure allows casting the multi-dimensional neural dynamics in the form of a symbolic dynamics of transitions between clusters; as an illustration of the potential of such reduction, we define and analyze a measure of complexity of the neural time series.

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.

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles.

GABAergic Interneurons are Required for Generation of Slow CA1 Oscillation in Rat Hippocampus

Neuronal oscillations are fundamental to hippocampal function. It has been shown that GABAergic interneurons make an important contribution to hippocampal oscillations, but the underlying mechanism is not well understood. Here, using whole-cell recording in the complete hippocampal formation isolated from rats at postnatal days 14-18, we showed that GABAA receptor-mediated activity enhanced the generation of slow CA1 oscillations. In vitro, slow oscillations (0.5-1.5 Hz) were generated in CA1 neurons, and they consisted primarily of excitatory rather than inhibitory membrane-potential changes. These oscillations were greatly reduced by blocking GABAA receptor-mediated activity with bicuculline and were enhanced by increasing such activity with midazolam, suggesting that interneurons are required for oscillation generation. Consistently, CA1 fast-spiking interneurons were found to generate action potentials usually preceding those in CA1 pyramidal cells. These findings indicate a GABAA receptor-based mechanism for the generation of the slow CA1 oscillation in the hippocampus.

Inferring synaptic structure in presence of neural interaction time scales

Biological networks display a variety of activity patterns reflecting a web of interactions that is complex both in space and time. Yet inference methods have mainly focused on reconstructing, from the network’s activity, the spatial structure, by assuming equilibrium conditions or, more recently, a probabilistic dynamics with a single arbitrary time-step. Here we show that, under this latter assumption, the inference procedure fails to reconstruct the synaptic matrix of a network of integrate-and-fire neurons when the chosen time scale of interaction does not closely match the synaptic delay or when no single time scale for the interaction can be identified; such failure, moreover, exposes a distinctive bias of the inference method that can lead to infer as inhibitory the excitatory synapses with interaction time scales longer than the model’s time-step. We therefore introduce a new two-step method, that first infers through cross-correlation profiles the delay-structure of the network and then reconstructs the synaptic matrix, and successfully test it on networks with different topologies and in different activity regimes. Although step one is able to accurately recover the delay-structure of the network, thus getting rid of any a priori guess about the time scales of the interaction, the inference method introduces nonetheless an arbitrary time scale, the time-bin dt used to binarize the spike trains. We therefore analytically and numerically study how the choice of dt affects the inference in our network model, finding that the relationship between the inferred couplings and the real synaptic efficacies, albeit being quadratic in both cases, depends critically on dt for the excitatory synapses only, whilst being basically independent of it for the inhibitory ones.