Inferring network properties from time series using transfer entropy and mutual information: Validation of multivariate versus bivariate approaches

Response inhibition in premotor cortex corresponds to a complex reshuffle of the mesoscopic information network

Recent studies have explored functional and effective neural networks in animal models; however, the dynamics of information propagation among functional modules under cognitive control remain largely unknown. Here, we addressed the issue using transfer entropy and graph theory methods on mesoscopic neural activities recorded in the dorsal premotor cortex of rhesus monkeys. We focused our study on the decision time of a Stop-signal task, looking for patterns in the network configuration that could influence motor plan maturation when the Stop signal is provided. When comparing trials with successful inhibition to those with generated movement, the nodes of the network resulted organized into four clusters, hierarchically arranged, and distinctly involved in information transfer. Interestingly, the hierarchies and the strength of information transmission between clusters varied throughout the task, distinguishing between generated movements and canceled ones and corresponding to measurable levels of network complexity. Our results suggest a putative mechanism for motor inhibition in premotor cortex: a topological reshuffle of the information exchanged among ensembles of neurons.

Systematic evaluation of fMRI data-processing pipelines for consistent functional connectomics

Functional interactions between brain regions can be viewed as a network, enabling neuroscientists to investigate brain function through network science. Here, we systematically evaluate 768 data-processing pipelines for network reconstruction from resting-state functional MRI, evaluating the effect of brain parcellation, connectivity definition, and global signal regression. Our criteria seek pipelines that minimise motion confounds and spurious test-retest discrepancies of network topology, while being sensitive to both inter-subject differences and experimental effects of interest. We reveal vast and systematic variability across pipelines' suitability for functional connectomics. Inappropriate choice of data-processing pipeline can produce results that are not only misleading, but systematically so, with the majority of pipelines failing at least one criterion. However, a set of optimal pipelines consistently satisfy all criteria across different datasets, spanning minutes, weeks, and months. We provide a full breakdown of each pipeline's performance across criteria and datasets, to inform future best practices in functional connectomics.

Computational Insights into Prostaglandin E2 Ligand Binding and Activation of G-Protein-Coupled Receptors

G-protein coupled receptors (GPCRs) are eukaryotic integral membrane proteins that regulate signal transduction cascade pathways implicated in a variety of human diseases and are consequently of interest as drug targets. For this reason, it is of interest to investigate the way in which specific ligands bind and trigger conformational changes in the receptor during activation and how this in turn modulates intracellular signaling. In the present study, we investigate the way in which the ligand Prostaglandin E2 interacts with three GPCRs in the E-prostanoid family: EP1, EP2, and EP3. We examine information transfer pathways based on long-time scale molecular dynamics simulations using transfer entropy and betweenness centrality to measure the physical transfer of information among residues in the system. We monitor specific residues involved in binding to the ligand and investigate how the information transfer behavior of these residues changes upon ligand binding. Our results provide key insights that enable a deeper understanding of EP activation and signal transduction functioning pathways at the molecular level, as well as enabling us to make some predictions about the activation pathway for the EP1 receptor, for which little structural information is currently available. Our results should advance ongoing efforts in the development of potential therapeutics targeting these receptors.

Static and dynamic fMRI-derived functional connectomes represent largely similar information

Functional connectivity (FC) of blood oxygen level-dependent (BOLD) fMRI time series can be estimated using methods that differ in sensitivity to the temporal order of time points (static vs. dynamic) and the number of regions considered in estimating a single edge (bivariate vs. multivariate). Previous research suggests that dynamic FC explains variability in FC fluctuations and behavior beyond static FC. Our aim was to systematically compare methods on both dimensions. We compared five FC methods: Pearson's/full correlation (static, bivariate), lagged correlation (dynamic, bivariate), partial correlation (static, multivariate), and multivariate AR model with and without self-connections (dynamic, multivariate). We compared these methods by (i) assessing similarities between FC matrices, (ii) by comparing node centrality measures, and (iii) by comparing the patterns of brain-behavior associations. Although FC estimates did not differ as a function of sensitivity to temporal order, we observed differences between the multivariate and bivariate FC methods. The dynamic FC estimates were highly correlated with the static FC estimates, especially when comparing group-level FC matrices. Similarly, there were high correlations between the patterns of brain-behavior associations obtained using the dynamic and static FC methods. We conclude that the dynamic FC estimates represent information largely similar to that of the static FC.

Evidence for increased parallel information transmission in human brain networks compared to macaques and male mice

Brain communication, defined as information transmission through white-matter connections, is at the foundation of the brain's computational capacities that subtend almost all aspects of behavior: from sensory perception shared across mammalian species, to complex cognitive functions in humans. How did communication strategies in macroscale brain networks adapt across evolution to accomplish increasingly complex functions? By applying a graph- and information-theory approach to assess information-related pathways in male mouse, macaque and human brains, we show a brain communication gap between selective information transmission in non-human mammals, where brain regions share information through single polysynaptic pathways, and parallel information transmission in humans, where regions share information through multiple parallel pathways. In humans, parallel transmission acts as a major connector between unimodal and transmodal systems. The layout of information-related pathways is unique to individuals across different mammalian species, pointing at the individual-level specificity of information routing architecture. Our work provides evidence that different communication patterns are tied to the evolution of mammalian brain networks.

Static and dynamic functional connectomes represent largely similar information

Functional connectivity (FC) of blood-oxygen-level-dependent (BOLD) fMRI time series can be estimated using methods that differ in sensitivity to the temporal order of time points (static vs. dynamic) and the number of regions considered in estimating a single edge (bivariate vs. multivariate). Previous research suggests that dynamic FC explains variability in FC fluctuations and behavior beyond static FC. Our aim was to systematically compare methods on both dimensions. We compared five FC methods: Pearson's/full correlation (static, bivariate), lagged correlation (dynamic, bivariate), partial correlation (static, multivariate) and multivariate AR model with and without self-connections (dynamic, multivariate). We compared these methods by (i) assessing similarities between FC matrices, (ii) by comparing node centrality measures, and (iii) by comparing the patterns of brain-behavior associations. Although FC estimates did not differ as a function of sensitivity to temporal order, we observed differences between the multivariate and bivariate FC methods. The dynamic FC estimates were highly correlated with the static FC estimates, especially when comparing group-level FC matrices. Similarly, there were high correlations between the patterns of brain-behavior associations obtained using the dynamic and static FC methods. We conclude that the dynamic FC estimates represent information largely similar to that of the static FC.

Information-processing dynamics in neural networks of macaque cerebral cortex reflect cognitive state and behavior

One of the essential functions of biological neural networks is the processing of information. This includes everything from processing sensory information to perceive the environment, up to processing motor information to interact with the environment. Due to methodological limitations, it has been historically unclear how information processing changes during different cognitive or behavioral states and to what extent information is processed within or between the network of neurons in different brain areas. In this study, we leverage recent advances in the calculation of information dynamics to explore neural-level processing within and between the frontoparietal areas AIP, F5, and M1 during a delayed grasping task performed by three macaque monkeys. While information processing was high within all areas during all cognitive and behavioral states of the task, interareal processing varied widely: During visuomotor transformation, AIP and F5 formed a reciprocally connected processing unit, while no processing was present between areas during the memory period. Movement execution was processed globally across all areas with predominance of processing in the feedback direction. Furthermore, the fine-scale network structure reconfigured at the neuron level in response to different grasping conditions, despite no differences in the overall amount of information present. These results suggest that areas dynamically form higher-order processing units according to the cognitive or behavioral demand and that the information-processing network is hierarchically organized at the neuron level, with the coarse network structure determining the behavioral state and finer changes reflecting different conditions.

Arousal system stimulation and anesthetic state alter visuoparietal connectivity

Cortical information processing is under the precise control of the ascending arousal system (AAS). Anesthesia suppresses cortical arousal that can be mitigated by exogenous stimulation of the AAS. The question remains to what extent cortical information processing is regained by AAS stimulation. We investigate the effect of electrical stimulation of the nucleus Pontis Oralis (PnO), a distinct source of ascending AAS projections, on cortical functional connectivity (FC) and information storage at mild, moderate, and deep anesthesia. Local field potentials (LFPs) recorded previously in the secondary visual cortex (V2) and the adjacent parietal association cortex (PtA) in chronically instrumented unrestrained rats. We hypothesized that PnO stimulation would induce electrocortical arousal accompanied by enhanced FC and active information storage (AIS) implying improved information processing. In fact, stimulation reduced FC in slow oscillations (0.3-2.5 Hz) at low anesthetic level and increased FC at high anesthetic level. These effects were augmented following stimulation suggesting stimulus-induced plasticity. The observed opposite stimulation-anesthetic impact was less clear in the γ-band activity (30-70 Hz). In addition, FC in slow oscillations was more sensitive to stimulation and anesthetic level than FC in γ-band activity which exhibited a rather constant spatial FC structure that was symmetric between specific, topographically related sites in V2 and PtA. Invariant networks were defined as a set of strongly connected electrode channels, which were invariant to experimental conditions. In invariant networks, stimulation decreased AIS and increasing anesthetic level increased AIS. Conversely, in non-invariant (complement) networks, stimulation did not affect AIS at low anesthetic level but increased it at high anesthetic level. The results suggest that arousal stimulation alters cortical FC and information storage as a function of anesthetic level with a prolonged effect beyond the duration of stimulation. The findings help better understand how the arousal system may influence information processing in cortical networks at different levels of anesthesia.

Revealing the Dynamics of Neural Information Processing with Multivariate Information Decomposition

The varied cognitive abilities and rich adaptive behaviors enabled by the animal nervous system are often described in terms of information processing. This framing raises the issue of how biological neural circuits actually process information, and some of the most fundamental outstanding questions in neuroscience center on understanding the mechanisms of neural information processing. Classical information theory has long been understood to be a natural framework within which information processing can be understood, and recent advances in the field of multivariate information theory offer new insights into the structure of computation in complex systems. In this review, we provide an introduction to the conceptual and practical issues associated with using multivariate information theory to analyze information processing in neural circuits, as well as discussing recent empirical work in this vein. Specifically, we provide an accessible introduction to the partial information decomposition (PID) framework. PID reveals redundant, unique, and synergistic modes by which neurons integrate information from multiple sources. We focus particularly on the synergistic mode, which quantifies the “higher-order” information carried in the patterns of multiple inputs and is not reducible to input from any single source. Recent work in a variety of model systems has revealed that synergistic dynamics are ubiquitous in neural circuitry and show reliable structure–function relationships, emerging disproportionately in neuronal rich clubs, downstream of recurrent connectivity, and in the convergence of correlated activity. We draw on the existing literature on higher-order information dynamics in neuronal networks to illustrate the insights that have been gained by taking an information decomposition perspective on neural activity. Finally, we briefly discuss future promising directions for information decomposition approaches to neuroscience, such as work on behaving animals, multi-target generalizations of PID, and time-resolved local analyses.

Early lock-in of structured and specialised information flows during neural development

The brains of many organisms are capable of complicated distributed computation underpinned by a highly advanced information processing capacity. Although substantial progress has been made towards characterising the information flow component of this capacity in mature brains, there is a distinct lack of work characterising its emergence during neural development. This lack of progress has been largely driven by the lack of effective estimators of information processing operations for spiking data. Here, we leverage recent advances in this estimation task in order to quantify the changes in transfer entropy during development. We do so by studying the changes in the intrinsic dynamics of the spontaneous activity of developing dissociated neural cell cultures. We find that the quantity of information flowing across these networks undergoes a dramatic increase across development. Moreover, the spatial structure of these flows exhibits a tendency to lock-in at the point when they arise. We also characterise the flow of information during the crucial periods of population bursts. We find that, during these bursts, nodes tend to undertake specialised computational roles as either transmitters, mediators, or receivers of information, with these roles tending to align with their average spike ordering. Further, we find that these roles are regularly locked-in when the information flows are established. Finally, we compare these results to information flows in a model network developing according to a spike-timing-dependent plasticity learning rule. Similar temporal patterns in the development of information flows were observed in these networks, hinting at the broader generality of these phenomena.

Directed functional and structural connectivity in a large-scale model for the mouse cortex

Inferring the structural connectivity from electrophysiological measurements is a fundamental challenge in systems neuroscience. Directed functional connectivity measures, such as the generalized partial directed coherence (GPDC), provide estimates of the causal influence between areas. However, the relation between causality estimates and structural connectivity is still not clear. We analyzed this problem by evaluating the effectiveness of GPDC to estimate the connectivity of a ground-truth, data-constrained computational model of a large-scale network model of the mouse cortex. The model contains 19 cortical areas composed of spiking neurons, with areas connected by long-range projections with weights obtained from a tract-tracing cortical connectome. We show that GPDC values provide a reasonable estimate of structural connectivity, with an average Pearson correlation over simulations of 0.74. Moreover, even in a typical electrophysiological recording scenario containing five areas, the mean correlation was above 0.6. These results suggest that it may be possible to empirically estimate structural connectivity from functional connectivity even when detailed whole-brain recordings are not achievable.

We analyzed the relationship between structural and directed functional connectivity by evaluating the effectiveness of generalized partial directed coherence (GPDC) to estimate the connectivity of a ground-truth, data-constrained computational model of a large-scale network model of the mouse cortex. We show that GPDC values provide a reasonable estimate of structural connectivity even in a typical electrophysiological recording scenario containing few areas. These results suggest that it may be possible to empirically estimate structural connectivity from functional connectivity even when detailed whole-brain recordings are not achievable.

Estimating the Unique Information of Continuous Variables

The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these mechanisms by identifying synergistic, redundant, and unique contributions to the mutual information between one and several variables. While many works have studied aspects of PID for Gaussian and discrete distributions, the case of general continuous distributions is still uncharted territory. In this work we present a method for estimating the unique information in continuous distributions, for the case of one versus two variables. Our method solves the associated optimization problem over the space of distributions with fixed bivariate marginals by combining copula decompositions and techniques developed to optimize variational autoencoders. We obtain excellent agreement with known analytic results for Gaussians, and illustrate the power of our new approach in several brain-inspired neural models. Our method is capable of recovering the effective connectivity of a chaotic network of rate neurons, and uncovers a complex trade-off between redundancy, synergy and unique information in recurrent networks trained to solve a generalized XOR task.

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.

An Information-Theoretic Framework to Measure the Dynamic Interaction Between Neural Spike Trains

OBJECTIVE

While understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience, existing methods either do not consider the inherent point-process nature of spike trains or are based on parametric assumptions. This work presents an information-theoretic framework for the model-free, continuous-time estimation of both undirected (symmetric) and directed (Granger-causal) interactions between spike trains.

METHODS

The framework computes the mutual information rate (MIR) and the transfer entropy rate (TER) for two point processes X and Y, showing that the MIR between X and Y can be decomposed as the sum of the TER along the directions X → Y and Y → X. We present theoretical expressions and introduce strategies to estimate efficiently the two measures through nearest neighbor statistics.

RESULTS

Using simulations of independent and coupled point processes, we show the accuracy of MIR and TER to assess interactions even for weakly coupled and short realizations, and demonstrate the superiority of continuous-time estimation over the standard discrete-time approach. We also apply the MIR and TER to real-world data, specifically, recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons. Using this dataset, we demonstrate the ability of MIR and TER to describe how the functional networks between recording units emerge over the course of the maturation of the neuronal cultures.

CONCLUSION AND SIGNIFICANCE

the proposed framework provides principled measures to assess undirected and directed spike train interactions with more efficiency and flexibility than previous discrete-time or parametric approaches, opening new perspectives for the analysis of point-process data in neuroscience and many other fields.