A Tutorial for Information Theory in Neuroscience

Multimodal perception links cellular state to decision making in single cells

Individual cells take decisions that are adapted to their internal state and surroundings, but how cells can reliably do this remains unclear. Using multiplexed quantification of signaling responses and markers of the cellular state, we find that signaling nodes in a network display adaptive information processing, which leads to heterogeneous growth factor responses and enables nodes to capture partially non-redundant information about the cellular state. Collectively, as a multimodal percept, this gives individual cells a large information processing capacity to accurately place growth factor concentration within the context of their cellular state and make cellular state-dependent decisions. We propose that heterogeneity and complexity in signaling networks have co-evolved to enable specific and context-aware cellular decision making in a multicellular setting.

Greater than the parts: a review of the information decomposition approach to causal emergence

Emergence is a profound subject that straddles many scientific disciplines, including the formation of galaxies and how consciousness arises from the collective activity of neurons. Despite the broad interest that exists on this concept, the study of emergence has suffered from a lack of formalisms that could be used to guide discussions and advance theories. Here, we summarize, elaborate on, and extend a recent formal theory of causal emergence based on information decomposition, which is quantifiable and amenable to empirical testing. This theory relates emergence with information about a system's temporal evolution that cannot be obtained from the parts of the system separately. This article provides an accessible but rigorous introduction to the framework, discussing the merits of the approach in various scenarios of interest. We also discuss several interpretation issues and potential misunderstandings, while highlighting the distinctive benefits of this formalism. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Compulsive alcohol drinking in rodents is associated with altered representations of behavioral control and seeking in dorsal medial prefrontal cortex

A key feature of compulsive alcohol drinking is continuing to drink despite negative consequences. To examine the changes in neural activity that underlie this behavior, compulsive alcohol drinking was assessed in a validated rodent model of heritable risk for excessive drinking (alcohol preferring (P) rats). Neural activity was measured in dorsal medial prefrontal cortex (dmPFC-a brain region involved in maladaptive decision-making) and assessed via change point analyses and novel principal component analyses. Neural population representations of specific decision-making variables were measured to determine how they were altered in animals that drink alcohol compulsively. Compulsive animals showed weakened representations of behavioral control signals, but strengthened representations of alcohol seeking-related signals. Finally, chemogenetic-based excitation of dmPFC prevented escalation of compulsive alcohol drinking. Collectively, these data indicate that compulsive alcohol drinking in rats is associated with alterations in dmPFC neural activity that underlie diminished behavioral control and enhanced seeking.

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.

Complexity-based Encoded Information Quantification in Neurophysiological Recordings

Brain activity differs vastly between sleep, cognitive tasks, and action. Information theory is an appropriate concept to analytically quantify these brain states. Based on neurophysiological recordings, this concept can handle complex data sets, is free of any requirements about the data structure, and can infer the present underlying brain mechanisms. Specifically, by utilizing algorithmic information theory, it is possible to estimate the absolute information contained in brain responses. While current approaches that apply this theory to neurophysiological recordings can discriminate between different brain states, they are limited in directly quantifying the degree of similarity or encoded information between brain responses. Here, we propose a method grounded in algorithmic information theory that affords direct statements about responses' similarity by estimating the encoded information through a compression-based scheme. We validated this method by applying it to both synthetic and real neurophysiological data and compared its efficiency to the mutual information measure. This proposed procedure is especially suited for task paradigms contrasting different event types because it can precisely quantify the similarity of neuronal responses.

Information content of brain states is explained by structural constraints on state energetics

Signal propagation along the structural connectome of the brain induces changes in the patterns of activity. These activity patterns define global brain states and contain information in accordance with their expected probability of occurrence. Being the physical substrate upon which information propagates, the structural connectome, in conjunction with the dynamics, determines the set of possible brain states and constrains the transition between accessible states. Yet, precisely how these structural constraints on state transitions relate to their information content remains unexplored. To address this gap in knowledge, we defined the information content as a function of the activation distribution, where statistically rare values of activation correspond to high information content. With this numerical definition in hand, we studied the spatiotemporal distribution of information content in functional magnetic resonance imaging (fMRI) data from the Human Connectome Project during different tasks, and report four key findings. First, information content strongly depends on cognitive context; its absolute level and spatial distribution depend on the cognitive task. Second, while information content shows similarities to other measures of brain activity, it is distinct from both Neurosynth maps and task contrast maps generated by a general linear model applied to the fMRI data. Third, the brain's structural wiring constrains the cost to control its state, where the cost to transition into high information content states is larger than that to transition into low information content states. Finally, all state transitions-especially those to high information content states-are less costly than expected from random network null models, thereby indicating the brains marked efficiency. Taken together, our findings establish an explanatory link between the information contained in a brain state and the energetic cost of attaining that state, thereby laying important groundwork for our understanding of large-scale cognitive computations.

A structural and functional subdivision in central orbitofrontal cortex

Economic choice requires many cognitive subprocesses, including stimulus detection, valuation, motor output, and outcome monitoring; many of these subprocesses are associated with the central orbitofrontal cortex (cOFC). Prior work has largely assumed that the cOFC is a single region with a single function. Here, we challenge that unified view with convergent anatomical and physiological results from rhesus macaques. Anatomically, we show that the cOFC can be subdivided according to its much stronger (medial) or weaker (lateral) bidirectional anatomical connectivity with the posterior cingulate cortex (PCC). We call these subregions cOFCm and cOFCl, respectively. These two subregions have notable functional differences. Specifically, cOFCm shows enhanced functional connectivity with PCC, as indicated by both spike-field coherence and mutual information. The cOFCm-PCC circuit, but not the cOFCl-PCC circuit, shows signatures of relaying choice signals from a non-spatial comparison framework to a spatially framed organization and shows a putative bidirectional mutually excitatory pattern.

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 R -Submodules

In the last few decades, the algebraic coding theory found widespread applications in various disciplines due to its rich fascinating mathematical structure. Linear codes, the basic codes in coding theory, are significant in data transmission. In this article, the authors' aim is to enlighten the reader about the role of linear codes in a fuzzy environment. Thus, the reader will be aware of linear codes over lattice valued intuitionistic fuzzy type-3 (LIF-3) R-submodule and α-intuitionistic fuzzy (α-IF) submodule. The proof that the level set of LIF-3 is contained in the level set of α-IF is given, and it is exclusively employed to define linear codes over α-IF submodule. Further, α-IF cyclic codes are presented along with their fundamental properties. Finally, an application based on genetic code is presented, and it is found that the technique of defining codes over α-IF submodule is entirely applicable in this scenario. More specifically, a mapping from the ℤ₆₄ module to a lattice L (comprising 64 codons) is considered, and α-IF codes are defined along with the respective degrees.

Artificial Visual Information Produced by Retinal Prostheses

Numerous retinal prosthetic systems have demonstrated somewhat useful vision can be restored to individuals who had lost their sight due to outer retinal degenerative diseases. Earlier prosthetic studies have mostly focused on the confinement of electrical stimulation for improved spatial resolution and/or the biased stimulation of specific retinal ganglion cell (RGC) types for selective activation of retinal ON/OFF pathway for enhanced visual percepts. To better replicate normal vision, it would be also crucial to consider information transmission by spiking activities arising in the RGC population since an incredible amount of visual information is transferred from the eye to the brain. In previous studies, however, it has not been well explored how much artificial visual information is created in response to electrical stimuli delivered by microelectrodes. In the present work, we discuss the importance of the neural information for high-quality artificial vision. First, we summarize the previous literatures which have computed information transmission rates from spiking activities of RGCs in response to visual stimuli. Second, we exemplify a couple of studies which computed the neural information from electrically evoked responses. Third, we briefly introduce how information rates can be computed in the representative two ways - direct method and reconstruction method. Fourth, we introduce in silico approaches modeling artificial retinal neural networks to explore the relationship between amount of information and the spiking patterns. Lastly, we conclude our review with clinical implications to emphasize the necessity of considering visual information transmission for further improvement of retinal prosthetics.

Group-level inference of information-based measures for the analyses of cognitive brain networks from neurophysiological data

The reproducibility crisis in neuroimaging and in particular in the case of underpowered studies has introduced doubts on our ability to reproduce, replicate and generalize findings. As a response, we have seen the emergence of suggested guidelines and principles for neuroscientists known as Good Scientific Practice for conducting more reliable research. Still, every study remains almost unique in its combination of analytical and statistical approaches. While it is understandable considering the diversity of designs and brain data recording, it also represents a striking point against reproducibility. Here, we propose a non-parametric permutation-based statistical framework, primarily designed for neurophysiological data, in order to perform group-level inferences on non-negative measures of information encompassing metrics from information-theory, machine-learning or measures of distances. The framework supports both fixed- and random-effect models to adapt to inter-individuals and inter-sessions variability. Using numerical simulations, we compared the accuracy in ground-truth retrieving of both group models, such as test- and cluster-wise corrections for multiple comparisons. We then reproduced and extended existing results using both spatially uniform MEG and non-uniform intracranial neurophysiological data. We showed how the framework can be used to extract stereotypical task- and behavior-related effects across the population covering scales from the local level of brain regions, inter-areal functional connectivity to measures summarizing network properties. We also present an open-source Python toolbox called Frites¹ that includes the proposed statistical pipeline using information-theoretic metrics such as single-trial functional connectivity estimations for the extraction of cognitive brain networks. Taken together, we believe that this framework deserves careful attention as its robustness and flexibility could be the starting point toward the uniformization of statistical approaches.

Brain-wide interactions during hippocampal sharp wave ripples

During periods of disengagement from the environment, transient population bursts, known as sharp wave ripples (SPW-Rs), occur sporadically. While numerous experiments have characterized the bidirectional relationship between SPW-Rs and activity in chosen brain areas, the topographic relationship between different segments of the hippocampus and brain-wide target areas has not been studied at high temporal and spatial resolution. Yet, such knowledge is necessary to infer the direction of communication. We analyzed two publicly available datasets with simultaneous high-density silicon probe recordings from across the mouse forebrain. We found that SPW-Rs coincide with a transient brain-wide increase in functional connectivity. In addition, we show that the diversity in SPW-R features, such as their incidence, magnitude, and intrahippocampal topography in the septotemporal axis, are correlated with slower excitability fluctuations in cortical and subcortical areas. Further, variations in SPW-R features correlated with the timing, sign, and magnitude of downstream responses with large-amplitude SPW-Rs followed by transient silence in extrahippocampal structures. Our findings expand on previous results and demonstrate that the activity patterns in extrahippocampal structures depend both on the intrahippocampal topographic origin and magnitude of hippocampal SPW-Rs.

Distinct neural codes in primate hippocampus and lateral prefrontal cortex during associative learning in virtual environments

The hippocampus (HPC) and the lateral prefrontal cortex (LPFC) are two cortical areas of the primate brain deemed essential to cognition. Here, we hypothesized that the codes mediating neuronal communication in the HPC and LPFC microcircuits have distinctively evolved to serve plasticity and memory function at different spatiotemporal scales. We used a virtual reality task in which animals selected one of the two targets in the arms of the maze, according to a learned context-color rule. Our results show that during associative learning, HPC principal cells concentrate spikes in bursts, enabling temporal summation and fast synaptic plasticity in small populations of neurons and ultimately facilitating rapid encoding of associative memories. On the other hand, layer II/III LPFC pyramidal cells fire spikes more sparsely distributed over time. The latter would facilitate broadcasting of signals loaded in short-term memory across neuronal populations without necessarily triggering fast synaptic plasticity.

Computational Modeling of Therapy with the NMDA Antagonist in Neurodegenerative Disease: Information Theory in the Mechanism of Action of Memantine

(1) Background: in patients with neurodegenerative diseases, noncompetitive N-methyl-D-aspartate (NMDA) receptor antagonists provide neuroprotective advantages. We performed memantine therapy and proved mathematical and computer modeling of neurodegenerative disease in this study. (2) Methods: a computer simulation environment of the N-methyl-D-aspartate receptor incorporating biological mechanisms of channel activation by high extracellular glutamic acid concentration. In comparison to controls, pathological models were essentially treated with doses of memantine 3−30 µM. (3) Results: the mean values and 95% CI for Shannon entropy in Alzheimer’s disease (AD) and memantine treatment models were 1.760 (95% CI, 1.704−1.818) vs. 2.385 (95% CI, 2.280−2.490). The Shannon entropy was significantly higher in the memantine treatment model relative to AD model (p = 0.0162). The mean values and 95% CI for the positive Lyapunov exponent in AD and memantine treatment models were 0.125 (95% CI, NE−NE) vs. 0.058 (95% CI, 0.044−0.073). The positive Lyapunov exponent was significantly higher in the AD model relative to the memantine treatment model (p = 0.0091). The mean values and 95% CI for transfer entropy in AD and memantine treatment models were 0.081 (95% CI, 0.048−0.114) vs. 0.040 (95% CI, 0.019−0.062). The transfer entropy was significantly higher in the AD model relative to the memantine treatment model (p = 0.0146). A correlation analysis showed positive and statistically significant correlations of the memantine concentrations and the positive Lyapunov exponent (correlation coefficient R = 0.87, p = 0.0023) and transfer entropy (TE) (correlation coefficient R = 0.99, p < 0.000001). (4) Conclusions: information theory results of simulation studies show that the NMDA antagonist, memantine, causes neuroprotective benefits in patients with AD. Our simulation study opens up remarkable new scenarios in which a medical product, drug, or device, can be developed and tested for efficacy based on parameters of information theory.

The Effects of Electroencephalogram Feature-Based Transcranial Alternating Current Stimulation on Working Memory and Electrophysiology

Transcranial alternating current stimulation (tACS) can influence cognitive functions by modulating brain oscillations. However, results regarding the effectiveness of tACS in regulating cognitive performance have been inconsistent. In the present study, we aimed to find electroencephalogram (EEG) characteristics associated with the improvements in working memory performance, to select tACS stimulus targets and frequency based on this feature, and to explore effects of selected stimulus on verbal working memory. To achieve this goal, we first investigated the EEG characteristics associated with improvements in working memory performance with the aid of EEG analyses and machine learning techniques. These analyses suggested that 8 Hz activity in the prefrontal region was related to accuracy in the verbal working memory task. The tACS stimulus target and pattern were then selected based on the EEG feature. Finally, the selected tACS frequency (8 Hz tACS in the prefrontal region) was applied to modulate working memory. Such modulation resulted significantly greater improvements, compared with 40 Hz and sham modulations (especially for participants with weak verbal working memory). In conclusion, using EEG features related to positive behavioral changes to select brain regions and stimulation patterns for tACS is an effective intervention for improving working memory. Our results contribute to the groundwork for future tACS closed-loop interventions for cognitive deterioration.

Cultural Evolution of Precise and Agreed-Upon Semantic Conventions in a Multiplayer Gaming App

The amount of information conveyed by linguistic conventions depends on their precision, yet the codes that humans and other animals use to communicate are quite ambiguous: they may map several vague meanings to the same symbol. How does semantic precision evolve, and what are the constraints that limit it? We address this question using a multiplayer gaming app, where individuals communicate with one another in a scaled-up referential game. Here, the goal is for a sender to use black and white symbols to communicate colors. We expected that the players' mappings between symbols and colors would grow more specific over time, through a selection process whereby precise mappings are preferentially copied. We found that players become increasingly more precise in their use of symbols over the course of their interactions. This trend did not, however, result from selective copying of precise mappings. We explore the implications of this result for the study of lexical ambiguity, Zipf's Law of Meaning, and disagreements over semantic conventions.

Functional connectivity inference from fMRI data using multivariate information measures

Shannon's entropy or an extension of Shannon's entropy can be used to quantify information transmission between or among variables. Mutual information is the pair-wise information that captures nonlinear relationships between variables. It is more robust than linear correlation methods. Beyond mutual information, two generalizations are defined for multivariate distributions: interaction information or co-information and total correlation or multi-mutual information. In comparison to mutual information, interaction information and total correlation are underutilized and poorly studied in applied neuroscience research. Quantifying information flow between brain regions is not explicitly explained in neuroscience by interaction information and total correlation. This article aims to clarify the distinctions between the neuroscience concepts of mutual information, interaction information, and total correlation. Additionally, we proposed a novel method for determining the interaction information between three variables using total correlation and conditional mutual information. On the other hand, how to apply it properly in practical situations. We supplied both simulation experiments and real neural studies to estimate functional connectivity in the brain with the above three higher-order information-theoretic approaches. In order to capture redundancy information for multivariate variables, we discovered that interaction information and total correlation were both robust, and it could be able to capture both well-known and yet-to-be-discovered functional brain connections.

Laminar microcircuitry of visual cortex producing attention-associated electric fields

Cognitive operations are widely studied by measuring electric fields through EEG and ECoG. However, despite their widespread use, the neural circuitry giving rise to these signals remains unknown because the functional architecture of cortical columns producing attention-associated electric fields has not been explored. Here, we detail the laminar cortical circuitry underlying an attention-associated electric field measured over posterior regions of the brain in humans and monkeys. First, we identified visual cortical area V4 as one plausible contributor to this attention-associated electric field through inverse modeling of cranial EEG in macaque monkeys performing a visual attention task. Next, we performed laminar neurophysiological recordings on the prelunate gyrus and identified the electric-field-producing dipoles as synaptic activity in distinct cortical layers of area V4. Specifically, activation in the extragranular layers of cortex resulted in the generation of the attention-associated dipole. Feature selectivity of a given cortical column determined the overall contribution to this electric field. Columns selective for the attended feature contributed more to the electric field than columns selective for a different feature. Last, the laminar profile of synaptic activity generated by V4 was sufficient to produce an attention-associated signal measurable outside of the column. These findings suggest that the top-down recipient cortical layers produce an attention-associated electric field that can be measured extracortically with the relative contribution of each column depending upon the underlying functional architecture.

Parametric Copula-GP model for analyzing multidimensional neuronal and behavioral relationships

One of the main goals of current systems neuroscience is to understand how neuronal populations integrate sensory information to inform behavior. However, estimating stimulus or behavioral information that is encoded in high-dimensional neuronal populations is challenging. We propose a method based on parametric copulas which allows modeling joint distributions of neuronal and behavioral variables characterized by different statistics and timescales. To account for temporal or spatial changes in dependencies between variables, we model varying copula parameters by means of Gaussian Processes (GP). We validate the resulting Copula-GP framework on synthetic data and on neuronal and behavioral recordings obtained in awake mice. We show that the use of a parametric description of the high-dimensional dependence structure in our method provides better accuracy in mutual information estimation in higher dimensions compared to other non-parametric methods. Moreover, by quantifying the redundancy between neuronal and behavioral variables, our model exposed the location of the reward zone in an unsupervised manner (i.e., without using any explicit cues about the task structure). These results demonstrate that the Copula-GP framework is particularly useful for the analysis of complex multidimensional relationships between neuronal, sensory and behavioral variables.

Understanding the relationship between a set of variables is a common problem in many fields, such as weather forecast or stock market data. In neuroscience, one of the main challenges is to characterize the dependencies between neuronal activity, sensory stimuli and behavioral outputs. A method of choice for modeling such statistical dependencies is based on copulas, which disentangle dependencies from single variable statistics. To account for changes in dependencies, we model changes in copula parameters by means of Gaussian Processes, conditioned on a task-related variable. The novelty of our approach includes 1) explicit modeling of the dependencies; and 2) combining different copulas to describe experimentally observed variability. We validate the goodness-of-fit as well as information estimates on synthetic data and on recordings from the visual cortex of mice performing a behavioral task. Our parametric model demonstrates significantly better performance in describing high dimensional dependencies compared to other commonly used techniques. We demonstrate that our model can estimate information and predict behaviorally-relevant parameters of the task without providing any explicit cues to the model. Our results indicate that our model is interpretable in the context of neuroscience applications, scalable to large datasets and suitable for accurate statistical modeling and information estimation.

CA2 inhibition reduces the precision of hippocampal assembly reactivation

The structured reactivation of hippocampal neuronal ensembles during fast synchronous oscillatory events, termed sharp-wave ripples (SWRs), has been suggested to play a crucial role in the storage and use of memory. Activity in both the CA2 and CA3 subregions can precede this population activity in CA1, and chronic inhibition of either region alters SWR oscillations. However, the precise contribution of CA2 to the oscillation, as well as to the reactivation of CA1 neurons within it, remains unclear. Here, we employ chemogenetics to transiently silence CA2 pyramidal cells in mice, and we observe that although SWRs still occur, the reactivation of CA1 pyramidal cell ensembles within the events lose both temporal and informational precision. These observations suggest that CA2 activity contributes to the fidelity of experience-dependent hippocampal replay.

Functional alterations in cortical processing of speech in glioma-infiltrated cortex

Recent developments in the biology of malignant gliomas have demonstrated that glioma cells interact with neurons through both paracrine signaling and electrochemical synapses. Glioma-neuron interactions consequently modulate the excitability of local neuronal circuits, and it is unclear the extent to which glioma-infiltrated cortex can meaningfully participate in neural computations. For example, gliomas may result in a local disorganization of activity that impedes the transient synchronization of neural oscillations. Alternatively, glioma-infiltrated cortex may retain the ability to engage in synchronized activity in a manner similar to normal-appearing cortex but exhibit other altered spatiotemporal patterns of activity with subsequent impact on cognitive processing. Here, we use subdural electrocorticography to sample both normal-appearing and glioma-infiltrated cortex during speech. We find that glioma-infiltrated cortex engages in synchronous activity during task performance in a manner similar to normal-appearing cortex but recruits a diffuse spatial network. On a temporal scale, we show that signals from glioma-infiltrated cortex have decreased entropy, which may affect its ability to encode information during nuanced tasks such as production of monosyllabic versus polysyllabic words. Furthermore, we show that temporal decoding strategies for distinguishing monosyllabic from polysyllabic words were feasible for signals arising from normal-appearing cortex but not from glioma-infiltrated cortex. These findings inform our understanding of cognitive processing in chronic disease states and have implications for neuromodulation and prosthetics in patients with malignant gliomas.

Cortical representation of group social communication in bats

Social interactions occur in group settings and are mediated by communication signals that are exchanged between individuals, often using vocalizations. The neural representation of group social communication remains largely unexplored. We conducted simultaneous wireless electrophysiological recordings from the frontal cortices of groups of Egyptian fruit bats engaged in both spontaneous and task-induced vocal interactions. We found that the activity of single neurons distinguished between vocalizations produced by self and by others, as well as among specific individuals. Coordinated neural activity among group members exhibited stable bidirectional interbrain correlation patterns specific to spontaneous communicative interactions. Tracking social and spatial arrangements within a group revealed a relationship between social preferences and intra- and interbrain activity patterns. Combined, these findings reveal a dedicated neural repertoire for group social communication within and across the brains of freely communicating groups of bats.

Narrow and Broad γ Bands Process Complementary Visual Information in Mouse Primary Visual Cortex

γ Band plays a key role in the encoding of visual features in the primary visual cortex (V1). In rodents V1 two ranges within the γ band are sensitive to contrast: a broad γ band (BB) increasing with contrast, and a narrow γ band (NB), peaking at ∼60 Hz, decreasing with contrast. The functional roles of the two bands and the neural circuits originating them are not completely clear yet. Here, we show, combining experimental and simulated data, that in mice V1 (1) BB carries information about high contrast and NB about low contrast; (2) BB modulation depends on excitatory-inhibitory interplay in the cortex, while NB modulation is because of entrainment to the thalamic drive. In awake mice presented with alternating gratings, NB power progressively decreased from low to intermediate levels of contrast where it reached a plateau. Conversely, BB power was constant across low levels of contrast, but it progressively increased from intermediate to high levels of contrast. Furthermore, BB response was stronger immediately after contrast reversal, while the opposite held for NB. These complementary modulations were reproduced by a recurrent excitatory-inhibitory leaky integrate-and-fire network provided that the thalamic inputs were composed of a sustained and a periodic component having complementary sensitivity ranges. These results show that in rodents the thalamic-driven NB plays a specific key role in encoding visual contrast. Moreover, we propose a simple and effective network model of response to visual stimuli in rodents that might help in investigating network dysfunctions of pathologic visual information processing.

GABA B Receptor-Mediated Regulation of Dendro-Somatic Synergy in Layer 5 Pyramidal Neurons

Synergistic interactions between independent synaptic input streams may fundamentally change the action potential (AP) output. Using partial information decomposition, we demonstrate here a substantial contribution of synergy between somatic and apical dendritic inputs to the information in the AP output of L5b pyramidal neurons. Activation of dendritic GABA_B receptors (GABA_BRs), known to decrease APs in vivo, potently decreased synergy and increased somatic control of AP output. Synergy was the result of the voltage-dependence of the transfer resistance between dendrite and soma, which showed a two-fold increase per 28.7 mV dendritic depolarization. GIRK channels activated by dendritic GABA_BRs decreased voltage-dependent transfer resistances and AP output. In contrast, inhibition of dendritic L-type Ca²⁺ channels prevented high-frequency bursts of APs, but did not affect dendro-somatic synergy. Finally, we show that NDNF-positive neurogliaform cells effectively control somatic AP via synaptic activation of dendritic GIRK channels. These results uncover a novel inhibitory mechanism that powerfully gates cellular information flow in the cortex.

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.

Information Theoretic Approaches to Deciphering the Neural Code with Functional Fluorescence Imaging

Information theoretic metrics have proven useful in quantifying the relationship between behaviorally relevant parameters and neuronal activity with relatively few assumptions. However, these metrics are typically applied to action potential (AP) recordings and were not designed for the slow timescales and variable amplitudes typical of functional fluorescence recordings (e.g., calcium imaging). The lack of research guidelines on how to apply and interpret these metrics with fluorescence traces means the neuroscience community has yet to realize the power of information theoretic metrics. Here, we used computational methods to create mock AP traces with known amounts of information. From these, we generated fluorescence traces and examined the ability of different information metrics to recover the known information values. We provide guidelines for how to use information metrics when applying them to functional fluorescence and demonstrate their appropriate application to GCaMP6f population recordings from mouse hippocampal neurons imaged during virtual navigation.

Toward an information theoretical description of communication in brain networks

Modeling communication dynamics in the brain is a key challenge in network neuroscience. We present here a framework that combines two measurements for any system where different communication processes are taking place on top of a fixed structural topology: path processing score (PPS) estimates how much the brain signal has changed or has been transformed between any two brain regions (source and target); path broadcasting strength (PBS) estimates the propagation of the signal through edges adjacent to the path being assessed. We use PPS and PBS to explore communication dynamics in large-scale brain networks. We show that brain communication dynamics can be divided into three main "communication regimes" of information transfer: absent communication (no communication happening); relay communication (information is being transferred almost intact); and transducted communication (the information is being transformed). We use PBS to categorize brain regions based on the way they broadcast information. Subcortical regions are mainly direct broadcasters to multiple receivers; Temporal and frontal nodes mainly operate as broadcast relay brain stations; visual and somatomotor cortices act as multichannel transducted broadcasters. This work paves the way toward the field of brain network information theory by providing a principled methodology to explore communication dynamics in large-scale brain networks.

Sensory Coding of Limb Kinematics in Motor Cortex across a Key Developmental Transition

Primary motor cortex (M1) undergoes protracted development in mammals, functioning initially as a sensory structure. Throughout the first postnatal week in rats, M1 is strongly activated by self-generated forelimb movements-especially by the twitches that occur during active sleep. Here, we quantify the kinematic features of forelimb movements to reveal receptive-field properties of individual units within the forelimb region of M1. At postnatal day 8 (P8), nearly all units were strongly modulated by movement amplitude, especially during active sleep. By P12, only a minority of units continued to exhibit amplitude tuning, regardless of behavioral state. At both ages, movement direction also modulated M1 activity, though to a lesser extent. Finally, at P12, M1 population-level activity became more sparse and decorrelated, along with a substantial alteration in the statistical distribution of M1 responses to limb movements. These findings reveal a transition toward a more complex and informationally rich representation of movement long before M1 develops its motor functionality.SIGNIFICANCE STATEMENT Primary motor cortex (M1) plays a fundamental role in the generation of voluntary movements and motor learning in adults. In early development, however, M1 functions as a prototypical sensory structure. Here, we demonstrate in infant rats that M1 codes for the kinematics of self-generated limb movements long before M1 develops its capacity to drive movements themselves. Moreover, we identify a key transition during the second postnatal week in which M1 activity becomes more informationally complex. Together, these findings further delineate the complex developmental path by which M1 develops its sensory functions in support of its later-emerging motor capacities.

Non-linear dimensionality reduction on extracellular waveforms reveals cell type diversity in premotor cortex

Cortical circuits are thought to contain a large number of cell types that coordinate to produce behavior. Current in vivo methods rely on clustering of specified features of extracellular waveforms to identify putative cell types, but these capture only a small amount of variation. Here, we develop a new method (WaveMAP) that combines non-linear dimensionality reduction with graph clustering to identify putative cell types. We apply WaveMAP to extracellular waveforms recorded from dorsal premotor cortex of macaque monkeys performing a decision-making task. Using WaveMAP, we robustly establish eight waveform clusters and show that these clusters recapitulate previously identified narrow- and broad-spiking types while revealing previously unknown diversity within these subtypes. The eight clusters exhibited distinct laminar distributions, characteristic firing rate patterns, and decision-related dynamics. Such insights were weaker when using feature-based approaches. WaveMAP therefore provides a more nuanced understanding of the dynamics of cell types in cortical circuits.

Aperiodic sleep networks promote memory consolidation

Hierarchical synchronization of sleep oscillations establishes communication pathways to support memory reactivation, transfer, and consolidation. From an information-theoretical perspective, oscillations constitute highly structured network states that provide limited information-coding capacity. Recent findings indicate that sleep oscillations occur in transient bursts that are interleaved with aperiodic network states, which were previously considered to be random noise. We argue that aperiodic activity exhibits unique and variable spatiotemporal patterns, providing an ideal information-rich neurophysiological substrate for imprinting new mnemonic patterns onto existing circuits. We discuss novel avenues in conceptualizing and quantifying aperiodic network states during sleep to further understand their relevance and interplay with sleep oscillations in support of memory consolidation.

A Quick and Easy Way to Estimate Entropy and Mutual Information for Neuroscience

Calculations of entropy of a signal or mutual information between two variables are valuable analytical tools in the field of neuroscience. They can be applied to all types of data, capture non-linear interactions and are model independent. Yet the limited size and number of recordings one can collect in a series of experiments makes their calculation highly prone to sampling bias. Mathematical methods to overcome this so-called "sampling disaster" exist, but require significant expertise, great time and computational costs. As such, there is a need for a simple, unbiased and computationally efficient tool for estimating the level of entropy and mutual information. In this article, we propose that application of entropy-encoding compression algorithms widely used in text and image compression fulfill these requirements. By simply saving the signal in PNG picture format and measuring the size of the file on the hard drive, we can estimate entropy changes through different conditions. Furthermore, with some simple modifications of the PNG file, we can also estimate the evolution of mutual information between a stimulus and the observed responses through different conditions. We first demonstrate the applicability of this method using white-noise-like signals. Then, while this method can be used in all kind of experimental conditions, we provide examples of its application in patch-clamp recordings, detection of place cells and histological data. Although this method does not give an absolute value of entropy or mutual information, it is mathematically correct, and its simplicity and broad use make it a powerful tool for their estimation through experiments.

High-frequency burst spiking in layer 5 thick-tufted pyramids of rat primary somatosensory cortex encodes exploratory touch

Diversity of cell-types that collectively shape the cortical microcircuit ensures the necessary computational richness to orchestrate a wide variety of behaviors. The information content embedded in spiking activity of identified cell-types remain unclear to a large extent. Here, we recorded spike responses upon whisker touch of anatomically identified excitatory cell-types in primary somatosensory cortex in naive, untrained rats. We find major differences across layers and cell-types. The temporal structure of spontaneous spiking contains high-frequency bursts (≥100 Hz) in all morphological cell-types but a significant increase upon whisker touch is restricted to layer L5 thick-tufted pyramids (L5tts) and thus provides a distinct neurophysiological signature. We find that whisker touch can also be decoded from L5tt bursting, but not from other cell-types. We observed high-frequency bursts in L5tts projecting to different subcortical regions, including thalamus, midbrain and brainstem. We conclude that bursts in L5tts allow accurate coding and decoding of exploratory whisker touch.

In order to investigate the information encoded by spiking activity in different neuronal cell types in the primary somatosensory cortex, de Kock et al performed electrophysiological recordings in untrained rats. They demonstrated that an increase in high-frequency burst spiking in thick tufted pyramids in layer 5 of the cortex allow accurate encoding of exploratory whisker touch.

Quantification of the Direct Solar Impact on Some Components of the Hydro-Climatic System

This study addresses the causal links between external factors and the main hydro-climatic variables by using a chain of methods to unravel the complexity of the direct sun–climate link. There is a gap in the literature on the description of a complete chain in addressing the structures of direct causal links of solar activity on terrestrial variables. This is why the present study uses the extensive facilities of the application of information theory in view of recent advances in different fields. Additionally, by other methods (e.g., neural networks) we first tested the existent non-linear links of solar–terrestrial influences on the hydro-climate system. The results related to the solar impact on terrestrial phenomena are promising, which is discriminant in the space-time domain. The implications prove robust for determining the causal measure of climate variables under direct solar impact, which makes it easier to consider solar activity in climate models by appropriate parametrizations. This study found that hydro-climatic variables are sensitive to solar impact only for certain frequencies (periods) and have a coherence with the Solar Flux only for some lags of the Solar Flux (in advance).

Assessing the solar variability signature in climate variables by information theory and wavelet coherence

The present study aims to investigate the possible influence of solar/geomagnetic forcing on climate variables, such as the drought index, Danube discharge and large-scale atmospheric indices. Our analysis was performed separately for each season for two time periods, 1901-2000 and 1948-2000. The relationship between terrestrial variables and external indices was established based on the application of (1) information theory elements, namely, synergy, redundancy, total correlation, transfer entropy and (2) wavelet coherence analysis. Bandpass filtering has also been applied. The most significant signature of the solar/geomagnetic forcing in the climate variables was obtained for the data smoothed by the bandpass filter. According to our results, significant solar/geomagnetic forcing appears in the terrestrial variables with a delay of 2-3 years.

Simultaneous CMOS-Based Imaging of Calcium Signaling of the Central Amygdala and the Dorsal Raphe Nucleus During Nociception in Freely Moving Mice

Fluorescence imaging devices have been indispensable in elucidating the workings of the brain in living animals, including unrestrained, active ones. Various devices are available, each with their own strengths and weaknesses in terms of many factors. We have developed CMOS-based needle-type imaging devices that are small and lightweight enough to be doubly implanted in freely moving mice. The design also allowed angled implantations to avoid critical areas. We demonstrated the utility of the devices by using them on GCaMP6 mice in a formalin test experiment. Simultaneous implantations to the capsular-lateral central amygdala (CeLC) and dorsal raphe nucleus (DRN) were proven to be safe and did not hinder the execution of the study. Analysis of the collected calcium signaling data, supported by behavior data, showed increased activity in both regions as a result of pain stimulation. Thus, we have successfully demonstrated the various advantages of the device in its application in the pain experiment.

Robotic hand augmentation drives changes in neural body representation

Humans have long been fascinated by the opportunities afforded through augmentation. This vision not only depends on technological innovations but also critically relies on our brain's ability to learn, adapt, and interface with augmentation devices. Here, we investigated whether successful motor augmentation with an extra robotic thumb can be achieved and what its implications are on the neural representation and function of the biological hand. Able-bodied participants were trained to use an extra robotic thumb (called the Third Thumb) over 5 days, including both lab-based and unstructured daily use. We challenged participants to complete normally bimanual tasks using only the augmented hand and examined their ability to develop hand-robot interactions. Participants were tested on a variety of behavioral and brain imaging tests, designed to interrogate the augmented hand's representation before and after the training. Training improved Third Thumb motor control, dexterity, and hand-robot coordination, even when cognitive load was increased or when vision was occluded. It also resulted in increased sense of embodiment over the Third Thumb. Consequently, augmentation influenced key aspects of hand representation and motor control. Third Thumb usage weakened natural kinematic synergies of the biological hand. Furthermore, brain decoding revealed a mild collapse of the augmented hand's motor representation after training, even while the Third Thumb was not worn. Together, our findings demonstrate that motor augmentation can be readily achieved, with potential for flexible use, reduced cognitive reliance, and increased sense of embodiment. Yet, augmentation may incur changes to the biological hand representation. Such neurocognitive consequences are crucial for successful implementation of future augmentation technologies.

Selecting an Effective Entropy Estimator for Short Sequences of Bits and Bytes with Maximum Entropy

Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon's entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.

Estimating Transfer Entropy in Continuous Time Between Neural Spike Trains or Other Event-Based Data

Transfer entropy (TE) is a widely used measure of directed information flows in a number of domains including neuroscience. Many real-world time series for which we are interested in information flows come in the form of (near) instantaneous events occurring over time. Examples include the spiking of biological neurons, trades on stock markets and posts to social media, amongst myriad other systems involving events in continuous time throughout the natural and social sciences. However, there exist severe limitations to the current approach to TE estimation on such event-based data via discretising the time series into time bins: it is not consistent, has high bias, converges slowly and cannot simultaneously capture relationships that occur with very fine time precision as well as those that occur over long time intervals. Building on recent work which derived a theoretical framework for TE in continuous time, we present an estimation framework for TE on event-based data and develop a k-nearest-neighbours estimator within this framework. This estimator is provably consistent, has favourable bias properties and converges orders of magnitude more quickly than the current state-of-the-art in discrete-time estimation on synthetic examples. We demonstrate failures of the traditionally-used source-time-shift method for null surrogate generation. In order to overcome these failures, we develop a local permutation scheme for generating surrogate time series conforming to the appropriate null hypothesis in order to test for the statistical significance of the TE and, as such, test for the conditional independence between the history of one point process and the updates of another. Our approach is shown to be capable of correctly rejecting or accepting the null hypothesis of conditional independence even in the presence of strong pairwise time-directed correlations. This capacity to accurately test for conditional independence is further demonstrated on models of a spiking neural circuit inspired by the pyloric circuit of the crustacean stomatogastric ganglion, succeeding where previous related estimators have failed.

Comparative Effects of Event Detection Methods on the Analysis and Interpretation of Ca2+ Imaging Data

Calcium imaging has gained substantial popularity as a tool to profile the activity of multiple simultaneously active cells at high spatiotemporal resolution. Among the diverse approaches to processing of Ca²⁺ imaging data is an often subjective decision of how to quantify baseline fluorescence or F ₀. We examine the effect of popular F ₀ determination methods on the interpretation of neuronal and astrocyte activity in a single dataset of rats trained to self-administer intravenous infusions of cocaine and compare them with an F ₀-independent wavelet ridgewalking event detection approach. We find that the choice of the processing method has a profound impact on the interpretation of widefield imaging results. All of the dF/F ₀ thresholding methods tended to introduce spurious events and fragment individual transients, leading to smaller calculated event durations and larger event frequencies. Analysis of simulated datasets confirmed these observations and indicated substantial intermethod variability as to the events classified as significant. Additionally, most dF/F ₀ methods on their own were unable to adequately account for bleaching of fluorescence, although the F ₀ smooth approach and the wavelet ridgewalking algorithm both did so. In general, the choice of the processing method led to dramatically different quantitative and sometimes opposing qualitative interpretations of the effects of cocaine self-administration both at the level of individual cells and at the level of cell networks. Significantly different distributions of event duration, amplitude, frequency, and network measures were found across the majority of dF/F ₀ approaches. The wavelet ridgewalking algorithm broadly outperformed dF/F ₀-based methods for both neuron and astrocyte recordings. These results indicate the need for heightened awareness of the limitations and tendencies associated with decisions to use particular Ca²⁺ image processing pipelines. Both quantification and interpretation of the effects of experimental manipulations are strongly sensitive to such decisions.

Devil in the details: Mechanistic variations impact information transfer across models of transcriptional cascades

The transcriptional network determines a cell’s internal state by regulating protein expression in response to changes in the local environment. Due to the interconnected nature of this network, information encoded in the abundance of various proteins will often propagate across chains of noisy intermediate signaling events. The data-processing inequality (DPI) leads us to expect that this intracellular game of “telephone” should degrade this type of signal, with longer chains losing successively more information to noise. However, a previous modeling effort predicted that because the steps of these signaling cascades do not truly represent independent stages of data processing, the limits of the DPI could seemingly be surpassed, and the amount of transmitted information could actually increase with chain length. What that work did not examine was whether this regime of growing information transmission was attainable by a signaling system constrained by the mechanistic details of more complex protein-binding kinetics. Here we address this knowledge gap through the lens of information theory by examining a model that explicitly accounts for the binding of each transcription factor to DNA. We analyze this model by comparing stochastic simulations of the fully nonlinear kinetics to simulations constrained by the linear response approximations that displayed a regime of growing information. Our simulations show that even when molecular binding is considered, there remains a regime wherein the transmitted information can grow with cascade length, but ends after a critical number of links determined by the kinetic parameter values. This inflection point marks where correlations decay in response to an oversaturation of binding sites, screening informative transcription factor fluctuations from further propagation down the chain where they eventually become indistinguishable from the surrounding levels of noise.

Mutual Information of Multiple Rhythms for EEG Signals

Electroencephalograms (EEG) are one of the most commonly used measures to study brain functioning at a macroscopic level. The structure of the EEG time series is composed of many neural rhythms interacting at different spatiotemporal scales. This interaction is often named as cross frequency coupling, and consists of transient couplings between various parameters of different rhythms. This coupling has been hypothesized to be a basic mechanism involved in cognitive functions. There are several methods to measure cross frequency coupling between two rhythms but no single method has been selected as the gold standard. Current methods only serve to explore two rhythms at a time, are computationally demanding, and impose assumptions about the nature of the signal. Here we present a new approach based on Information Theory in which we can characterize the interaction of more than two rhythms in a given EEG time series. It estimates the mutual information of multiple rhythms (MIMR) extracted from the original signal. We tested this measure using simulated and real empirical data. We simulated signals composed of three frequencies and background noise. When the coupling between each frequency component was manipulated, we found a significant variation in the MIMR. In addition, we found that MIMR was sensitive to real EEG time series collected with open vs. closed eyes, and intra-cortical recordings from epileptic and non-epileptic signals registered at different regions of the brain. MIMR is presented as a tool to explore multiple rhythms, easy to compute and without a priori assumptions.

Enhanced representation of natural sound sequences in the ventral auditory midbrain

The auditory midbrain (inferior colliculus, IC) plays an important role in sound processing, acting as hub for acoustic information extraction and for the implementation of fast audio-motor behaviors. IC neurons are topographically organized according to their sound frequency preference: dorsal IC regions encode low frequencies while ventral areas respond best to high frequencies, a type of sensory map defined as tonotopy. Tonotopic maps have been studied extensively using artificial stimuli (pure tones) but our knowledge of how these maps represent information about sequences of natural, spectro-temporally rich sounds is sparse. We studied this question by conducting simultaneous extracellular recordings across IC depths in awake bats (Carollia perspicillata) that listened to sequences of natural communication and echolocation sounds. The hypothesis was that information about these two types of sound streams is represented at different IC depths since they exhibit large differences in spectral composition, i.e., echolocation covers the high-frequency portion of the bat soundscape (> 45 kHz), while communication sounds are broadband and carry most power at low frequencies (20–25 kHz). Our results showed that mutual information between neuronal responses and acoustic stimuli, as well as response redundancy in pairs of neurons recorded simultaneously, increase exponentially with IC depth. The latter occurs regardless of the sound type presented to the bats (echolocation or communication). Taken together, our results indicate the existence of mutual information and redundancy maps at the midbrain level whose response cannot be predicted based on the frequency composition of natural sounds and classic neuronal tuning curves.

The amygdala instructs insular feedback for affective learning

Affective responses depend on assigning value to environmental predictors of threat or reward. Neuroanatomically, this affective value is encoded at both cortical and subcortical levels. However, the purpose of this distributed representation across functional hierarchies remains unclear. Using fMRI in mice, we mapped a discrete cortico-limbic loop between insular cortex (IC), central amygdala (CE), and nucleus basalis of Meynert (NBM), which decomposes the affective value of a conditioned stimulus (CS) into its salience and valence components. In IC, learning integrated unconditioned stimulus (US)-evoked bodily states into CS valence. In turn, CS salience in the CE recruited these CS representations bottom-up via the cholinergic NBM. This way, the CE incorporated interoceptive feedback from IC to improve discrimination of CS valence. Consequently, opto-/chemogenetic uncoupling of hierarchical information flow disrupted affective learning and conditioned responding. Dysfunctional interactions in the IC↔CE/NBM network may underlie intolerance to uncertainty, observed in autism and related psychiatric conditions.

Bidirectional control of fear memories by cerebellar neurons projecting to the ventrolateral periaqueductal grey

Fear conditioning is a form of associative learning that is known to involve different brain areas, notably the amygdala, the prefrontal cortex and the periaqueductal grey (PAG). Here, we describe the functional role of pathways that link the cerebellum with the fear network. We found that the cerebellar fastigial nucleus (FN) sends glutamatergic projections to vlPAG that synapse onto glutamatergic and GABAergic vlPAG neurons. Chemogenetic and optogenetic manipulations revealed that the FN-vlPAG pathway controls bi-directionally the strength of the fear memories, indicating an important role in the association of the conditioned and unconditioned stimuli, a function consistent with vlPAG encoding of fear prediction error. Moreover, FN-vlPAG projections also modulate extinction learning. We also found a FN-parafascicular thalamus pathway, which may relay cerebellar influence to the amygdala and modulates anxiety behaviors. Overall, our results reveal multiple contributions of the cerebellum to the emotional system.

The cerebellum has a role in motor control, but may also contribute to other functions. Here the authors demonstrate a role for the cerebellar fastigial nucleus projection onto ventrolateral periaqueductal grey neurons during fear acquisition.

Entropy and the Brain: An Overview

Entropy is a powerful tool for quantification of the brain function and its information processing capacity. This is evident in its broad domain of applications that range from functional interactivity between the brain regions to quantification of the state of consciousness. A number of previous reviews summarized the use of entropic measures in neuroscience. However, these studies either focused on the overall use of nonlinear analytical methodologies for quantification of the brain activity or their contents pertained to a particular area of neuroscientific research. The present study aims at complementing these previous reviews in two ways. First, by covering the literature that specifically makes use of entropy for studying the brain function. Second, by highlighting the three fields of research in which the use of entropy has yielded highly promising results: the (altered) state of consciousness, the ageing brain, and the quantification of the brain networks' information processing. In so doing, the present overview identifies that the use of entropic measures for the study of consciousness and its (altered) states led the field to substantially advance the previous findings. Moreover, it realizes that the use of these measures for the study of the ageing brain resulted in significant insights on various ways that the process of ageing may affect the dynamics and information processing capacity of the brain. It further reveals that their utilization for analysis of the brain regional interactivity formed a bridge between the previous two research areas, thereby providing further evidence in support of their results. It concludes by highlighting some potential considerations that may help future research to refine the use of entropic measures for the study of brain complexity and its function. The present study helps realize that (despite their seemingly differing lines of inquiry) the study of consciousness, the ageing brain, and the brain networks' information processing are highly interrelated. Specifically, it identifies that the complexity, as quantified by entropy, is a fundamental property of conscious experience, which also plays a vital role in the brain's capacity for adaptation and therefore whose loss by ageing constitutes a basis for diseases and disorders. Interestingly, these two perspectives neatly come together through the association of entropy and the brain capacity for information processing.

A Time-Varying Information Measure for Tracking Dynamics of Neural Codes in a Neural Ensemble

The amount of information that differentially correlated spikes in a neural ensemble carry is not the same; the information of different types of spikes is associated with different features of the stimulus. By calculating a neural ensemble’s information in response to a mixed stimulus comprising slow and fast signals, we show that the entropy of synchronous and asynchronous spikes are different, and their probability distributions are distinctively separable. We further show that these spikes carry a different amount of information. We propose a time-varying entropy (TVE) measure to track the dynamics of a neural code in an ensemble of neurons at each time bin. By applying the TVE to a multiplexed code, we show that synchronous and asynchronous spikes carry information in different time scales. Finally, a decoder based on the Kalman filtering approach is developed to reconstruct the stimulus from the spikes. We demonstrate that slow and fast features of the stimulus can be entirely reconstructed when this decoder is applied to asynchronous and synchronous spikes, respectively. The significance of this work is that the TVE can identify different types of information (for example, corresponding to synchronous and asynchronous spikes) that might simultaneously exist in a neural code.

Necessary Conditions for Reliable Propagation of Slowly Time-Varying Firing Rate

Reliable propagation of slow-modulations of the firing rate across multiple layers of a feedforward network (FFN) has proven difficult to capture in spiking neural models. In this paper, we explore necessary conditions for reliable and stable propagation of time-varying asynchronous spikes whose instantaneous rate of changes-in fairly short time windows [20-100] msec-represents information of slow fluctuations of the stimulus. Specifically, we study the effect of network size, level of background synaptic noise, and the variability of synaptic delays in an FFN with all-to-all connectivity. We show that network size and the level of background synaptic noise, together with the strength of synapses, are substantial factors enabling the propagation of asynchronous spikes in deep layers of an FFN. In contrast, the variability of synaptic delays has a minor effect on signal propagation.

Estimation of global and local complexities of brain networks: A random walks approach

The complexity of brain activity has been observed at many spatial scales and has been proposed to differentiate between mental states and disorders. Here we introduced a new measure of (global) network complexity, constructed as the sum of the complexities of its nodes (i.e., local complexity). The complexity of each node is obtained by comparing the sample entropy of the time series generated by the movement of a random walker on the network resulting from removing the node and its connections, with the sample entropy of the time series obtained from a regular lattice (ordered state) and a random network (disordered state). We studied the complexity of fMRI-based resting-state networks. We found that positively correlated (pos) networks comprising only the positive functional connections have higher complexity than anticorrelation (neg) networks (comprising the negative connections) and the network consisting of the absolute value of all connections (abs). We also observed a significant correlation between complexity and the strength of functional connectivity in the pos network. Our results suggest that the pos network is related to the information processing in the brain and that functional connectivity studies should analyze pos and neg networks separately instead of the abs network, as is commonly done.

Transfer Entropy as a Measure of Brain Connectivity: A Critical Analysis With the Help of Neural Mass Models

Objective: Assessing brain connectivity from electrophysiological signals is of great relevance in neuroscience, but results are still debated and depend crucially on how connectivity is defined and on mathematical instruments utilized. Aim of this work is to assess the capacity of bivariate Transfer Entropy (TE) to evaluate connectivity, using data generated from simple neural mass models of connected Regions of Interest (ROIs). Approach: Signals simulating mean field potentials were generated assuming two, three or four ROIs, connected via excitatory or by-synaptic inhibitory links. We investigated whether the presence of a statistically significant connection can be detected and if connection strength can be quantified. Main Results: Results suggest that TE can reliably estimate the strength of connectivity if neural populations work in their linear regions, and if the epoch lengths are longer than 10 s. In case of multivariate networks, some spurious connections can emerge (i.e., a statistically significant TE even in the absence of a true connection); however, quite a good correlation between TE and synaptic strength is still preserved. Moreover, TE appears more robust for distal regions (longer delays) compared with proximal regions (smaller delays): an approximate a priori knowledge on this delay can improve the procedure. Finally, non-linear phenomena affect the assessment of connectivity, since they may significantly reduce TE estimation: information transmission between two ROIs may be weak, due to non-linear phenomena, even if a strong causal connection is present. Significance: Changes in functional connectivity during different tasks or brain conditions, might not always reflect a true change in the connecting network, but rather a change in information transmission. A limitation of the work is the use of bivariate TE. In perspective, the use of multivariate TE can improve estimation and reduce some of the problems encountered in the present study.

Hierarchical Representations of Aggression in a Hypothalamic-Midbrain Circuit

Although the ventromedial hypothalamus ventrolateral area (VMHvl) is now well established as a critical locus for the generation of conspecific aggression, its role is complex, with neurons responding during multiple phases of social interactions with both males and females. It has been previously unclear how the brain uses this complex multidimensional signal and coordinates a discrete action: the attack. Here, we find a hypothalamic-midbrain circuit that represents hierarchically organized social signals during aggression. Optogenetic-assisted circuit mapping reveals a preferential projection from VMHvlvGlut2 to lPAGvGlut2 cells, and inactivation of downstream lPAGvGlut2 populations results in aggression-specific deficits. lPAG neurons are selective for attack action and exhibit short-latency, time-locked spiking relative to the activity of jaw muscles during biting. Last, we find that this projection conveys male-biased signals from the VMHvl to downstream lPAGvGlut2 neurons that are sensitive to features of ongoing activity, suggesting that action selectivity is generated by a combination of pre- and postsynaptic mechanisms.

Upper Limit on the Thermodynamic Information Content of an Action Potential

In computational neuroscience, spiking neurons are often analyzed as computing devices that register bits of information, with each action potential carrying at most one bit of Shannon entropy. Here, I question this interpretation by using Landauer's principle to estimate an upper limit for the quantity of thermodynamic information that can be processed within a single action potential in a typical mammalian neuron. A straightforward calculation shows that an action potential in a typical mammalian cortical pyramidal cell can process up to approximately 3.4 · 1011 bits of thermodynamic information, or about 4.9 · 1011 bits of Shannon entropy. This result suggests that an action potential can, in principle, carry much more than a single bit of Shannon entropy.