Cortical reliability amid noise and chaos

The Determining Role of Covariances in Large Networks of Stochastic Neurons

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network's populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity.

Neurobiological Causal Models of Language Processing

The language faculty is physically realized in the neurobiological infrastructure of the human brain. Despite significant efforts, an integrated understanding of this system remains a formidable challenge. What is missing from most theoretical accounts is a specification of the neural mechanisms that implement language function. Computational models that have been put forward generally lack an explicit neurobiological foundation. We propose a neurobiologically informed causal modeling approach which offers a framework for how to bridge this gap. A neurobiological causal model is a mechanistic description of language processing that is grounded in, and constrained by, the characteristics of the neurobiological substrate. It intends to model the generators of language behavior at the level of implementational causality. We describe key features and neurobiological component parts from which causal models can be built and provide guidelines on how to implement them in model simulations. Then we outline how this approach can shed new light on the core computational machinery for language, the long-term storage of words in the mental lexicon and combinatorial processing in sentence comprehension. In contrast to cognitive theories of behavior, causal models are formulated in the "machine language" of neurobiology which is universal to human cognition. We argue that neurobiological causal modeling should be pursued in addition to existing approaches. Eventually, this approach will allow us to develop an explicit computational neurobiology of language.

Striatal Neurons Are Recruited Dynamically into Collective Representations of Self-Initiated and Learned Actions in Freely Moving Mice

Striatal spiny projection neurons are hyperpolarized-at-rest (HaR) and driven to action potential threshold by a small number of powerful inputs-an input-output configuration that is detrimental to response reliability. Because the striatum is important for habitual behaviors and goal-directed learning, we conducted a microendoscopic imaging in freely moving mice that express a genetically encoded Ca2+ indicator sparsely in striatal HaR neurons to evaluate their response reliability during self-initiated movements and operant conditioning. The sparse expression was critical for longitudinal studies of response reliability, and for studying correlations among HaR neurons while minimizing spurious correlations arising from contamination by the background signal. We found that HaR neurons are recruited dynamically into action representation, with distinct neuronal subsets being engaged in a moment-by-moment fashion. While individual neurons respond with little reliability, the population response remained stable across days. Moreover, we found evidence for the temporal coupling between neuronal subsets during conditioned (but not innate) behaviors.

Mutual generation in neuronal activity across the brain via deep neural approach, and its network interpretation

In the brain, many regions work in a network-like association, yet it is not known how durable these associations are in terms of activity and could survive without structural connections. To assess the association or similarity between brain regions with a generating approach, this study evaluated the similarity of activities of neurons within each region after disconnecting between regions. The "generation" approach here refers to using a multi-layer LSTM (Long Short-Term Memory) model to learn the rules of activity generation in one region and then apply that knowledge to generate activity in other regions. Surprisingly, the results revealed that activity generation from one region to disconnected regions was possible with similar accuracy to generation between the same regions in many cases. Notably, firing rates and synchronization of firing between neuron pairs, often used as neuronal representations, could be reproduced with precision. Additionally, accuracies were associated with the relative angle between brain regions and the strength of the structural connections that initially connected them. This outcome enables us to look into trends governing non-uniformity of the cortex based on the potential to generate informative data and reduces the need for animal experiments.

Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms

This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and sufficient properties that its substrate must satisfy (postulates), and expresses them in mathematical terms. In principle, the postulates can be applied to any system of units in a state to determine whether it is conscious, to what degree, and in what way. IIT offers a parsimonious explanation of empirical evidence, makes testable predictions concerning both the presence and the quality of experience, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate formulation of the axioms as postulates and mathematical expressions, the introduction of a unique measure of intrinsic information that is consistent with the postulates, and an explicit assessment of causal relations. By fully unfolding a system's irreducible cause-effect power, the distinctions and relations specified by a substrate can account for the quality of experience.

Transcriptomic cell type structures in vivo neuronal activity across multiple timescales

Cell type is hypothesized to be a key determinant of a neuron's role within a circuit. Here, we examine whether a neuron's transcriptomic type influences the timing of its activity. We develop a deep-learning architecture that learns features of interevent intervals across timescales (ms to >30 min). We show that transcriptomic cell-class information is embedded in the timing of single neuron activity in the intact brain of behaving animals (calcium imaging and extracellular electrophysiology) as well as in a bio-realistic model of the visual cortex. Further, a subset of excitatory cell types are distinguishable but can be classified with higher accuracy when considering cortical layer and projection class. Finally, we show that computational fingerprints of cell types may be universalizable across structured stimuli and naturalistic movies. Our results indicate that transcriptomic class and type may be imprinted in the timing of single neuron activity across diverse stimuli.

Model simulations unveil the structure-function-dynamics relationship of the cerebellar cortical microcircuit

The cerebellar network is renowned for its regular architecture that has inspired foundational computational theories. However, the relationship between circuit structure, function and dynamics remains elusive. To tackle the issue, we developed an advanced computational modeling framework that allows us to reconstruct and simulate the structure and function of the mouse cerebellar cortex using morphologically realistic multi-compartmental neuron models. The cerebellar connectome is generated through appropriate connection rules, unifying a collection of scattered experimental data into a coherent construct and providing a new model-based ground-truth about circuit organization. Naturalistic background and sensory-burst stimulation are used for functional validation against recordings in vivo, monitoring the impact of cellular mechanisms on signal propagation, inhibitory control, and long-term synaptic plasticity. Our simulations show how mossy fibers entrain the local neuronal microcircuit, boosting the formation of columns of activity travelling from the granular to the molecular layer providing a new resource for the investigation of local microcircuit computation and of the neural correlates of behavior.

Increased Reliability of Visually-Evoked Activity in Area V1 of the MECP2-Duplication Mouse Model of Autism

Atypical sensory processing is now thought to be a core feature of the autism spectrum. Influential theories have proposed that both increased and decreased neural response reliability within sensory systems could underlie altered sensory processing in autism. Here, we report evidence for abnormally increased reliability of visual-evoked responses in layer 2/3 neurons of adult male and female primary visual cortex in the MECP2-duplication syndrome animal model of autism. Increased response reliability was due in part to decreased response amplitude, decreased fluctuations in endogenous activity, and an abnormal decoupling of visual-evoked activity from endogenous activity. Similar to what was observed neuronally, the optokinetic reflex occurred more reliably at low contrasts in mutant mice compared with controls. Retinal responses did not explain our observations. These data suggest that the circuit mechanisms for combining sensory-evoked and endogenous signal and noise processes may be altered in this form of syndromic autism.SIGNIFICANCE STATEMENT Atypical sensory processing is now thought to be a core feature of the autism spectrum. Influential theories have proposed that both increased and decreased neural response reliability within sensory systems could underlie altered sensory processing in autism. Here, we report evidence for abnormally increased reliability of visual-evoked responses in primary visual cortex of the animal model for MECP2-duplication syndrome, a high-penetrance single-gene cause of autism. Visual-evoked activity was abnormally decoupled from endogenous activity in mutant mice, suggesting in line with the influential "hypo-priors" theory of autism that sensory priors embedded in endogenous activity may have less influence on perception in autism.

Computational Concepts for Reconstructing and Simulating Brain Tissue

It has previously been shown that it is possible to derive a new class of biophysically detailed brain tissue models when one computationally analyzes and exploits the interdependencies or the multi-modal and multi-scale organization of the brain. These reconstructions, sometimes referred to as digital twins, enable a spectrum of scientific investigations. Building such models has become possible because of increase in quantitative data but also advances in computational capabilities, algorithmic and methodological innovations. This chapter presents the computational science concepts that provide the foundation to the data-driven approach to reconstructing and simulating brain tissue as developed by the EPFL Blue Brain Project, which was originally applied to neocortical microcircuitry and extended to other brain regions. Accordingly, the chapter covers aspects such as a knowledge graph-based data organization and the importance of the concept of a dataset release. We illustrate algorithmic advances in finding suitable parameters for electrical models of neurons or how spatial constraints can be exploited for predicting synaptic connections. Furthermore, we explain how in silico experimentation with such models necessitates specific addressing schemes or requires strategies for an efficient simulation. The entire data-driven approach relies on the systematic validation of the model. We conclude by discussing complementary strategies that not only enable judging the fidelity of the model but also form the basis for its systematic refinements.

Consciousness is supported by near-critical slow cortical electrodynamics

Mounting evidence suggests that during conscious states, the electrodynamics of the cortex are poised near a critical point or phase transition and that this near-critical behavior supports the vast flow of information through cortical networks during conscious states. Here, we empirically identify a mathematically specific critical point near which waking cortical oscillatory dynamics operate, which is known as the edge-of-chaos critical point, or the boundary between stability and chaos. We do so by applying the recently developed modified 0-1 chaos test to electrocorticography (ECoG) and magnetoencephalography (MEG) recordings from the cortices of humans and macaques across normal waking, generalized seizure, anesthesia, and psychedelic states. Our evidence suggests that cortical information processing is disrupted during unconscious states because of a transition of low-frequency cortical electric oscillations away from this critical point; conversely, we show that psychedelics may increase the information richness of cortical activity by tuning low-frequency cortical oscillations closer to this critical point. Finally, we analyze clinical electroencephalography (EEG) recordings from patients with disorders of consciousness (DOC) and show that assessing the proximity of slow cortical oscillatory electrodynamics to the edge-of-chaos critical point may be useful as an index of consciousness in the clinical setting.

Non-additive activity modulation during a decision making task involving tactic selection

Human brain imaging has revealed that stimulus-induced activity does generally not simply add to the pre-stimulus activity, but rather builds in a non-additive way on this activity. Here we investigate this subject at the single neuron level and address the question whether and to what extent a strong form of non-additivity where activity drops post-cue is present in different areas of monkey cortex, including prefrontal and agranular frontal areas, during a perceptual decision making task involving action and tactic selection. Specifically we analyze spike train data recorded in vivo from the posterior dorsomedial prefrontal cortex (pmPFC), the supplementary motor area (SMA) and the presupplementary motor area (pre-SMA). For each neuron, we compute the ratio of the trial-averaged pre-stimulus spike count to the trial-averaged post-stimulus count. We also perform the ratio and averaging procedures in reverse order. We find that the statistics of these quantities behave differently across areas. pmPFC involved in tactic selection shows stronger non-additivity compared to the two other areas which more generically just increase their firing rate pos-stimulus. pmPFC behaved more similarly to pre-SMA, a likely consequence of the reciprocal connections between these areas. The trial-averaged ratio statistic was reproduced by a surrogate inhomogeneous Poisson process in which the measured trial-averaged firing rate for a given neuron is used as its time-dependent rate. Principal component analysis (PCA) of the trial-averaged firing rates of neuronal ensembles further reveals area-specific time courses of response to the stimulus, including latency to peak neural response, for the typical population activity. Our work demonstrates subtle forms of area-specific non-additivity based on the fine variability structure of pre- and post-stimulus spiking activity on the single neuron level. It also reveals significant differences between areas for PCA and surrogate analysis, complementing previous observations of regional differences based solely on post-stimulus responses. Moreover, we observe regional differences in non-additivity which are related to the monkey's successful tactic selection and decision making.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-021-09702-0.

Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies

In motor-related brain regions, movement intention has been successfully decoded from in-vivo spike train by isolating a lower-dimension manifold that the high-dimensional spiking activity is constrained to. The mechanism enforcing this constraint remains unclear, although it has been hypothesized to be implemented by the connectivity of the sampled neurons. We test this idea and explore the interactions between local synaptic connectivity and its ability to encode information in a lower dimensional manifold through simulations of a detailed microcircuit model with realistic sources of noise. We confirm that even in isolation such a model can encode the identity of different stimuli in a lower-dimensional space. We then demonstrate that the reliability of the encoding depends on the connectivity between the sampled neurons by specifically sampling populations whose connectivity maximizes certain topological metrics. Finally, we developed an alternative method for determining stimulus identity from the activity of neurons by combining their spike trains with their recurrent connectivity. We found that this method performs better for sampled groups of neurons that perform worse under the classical approach, predicting the possibility of two separate encoding strategies in a single microcircuit.

The Role of Hub Neurons in Modulating Cortical Dynamics

Many neurodegenerative diseases are associated with the death of specific neuron types in particular brain regions. What makes the death of specific neuron types particularly harmful for the integrity and dynamics of the respective network is not well understood. To start addressing this question we used the most up-to-date biologically realistic dense neocortical microcircuit (NMC) of the rodent, which has reconstructed a volume of 0.3 mm³ and containing 31,000 neurons, ∼37 million synapses, and 55 morphological cell types arranged in six cortical layers. Using modern network science tools, we identified hub neurons in the NMC, that are connected synaptically to a large number of their neighbors and systematically examined the impact of abolishing these cells. In general, the structural integrity of the network is robust to cells’ attack; yet, attacking hub neurons strongly impacted the small-world topology of the network, whereas similar attacks on random neurons have a negligible effect. Such hub-specific attacks are also impactful on the network dynamics, both when the network is at its spontaneous synchronous state and when it was presented with synchronized thalamo-cortical visual-like input. We found that attacking layer 5 hub neurons is most harmful to the structural and functional integrity of the NMC. The significance of our results for understanding the role of specific neuron types and cortical layers for disease manifestation is discussed.

Measuring Synchronization between Spikes and Local Field Potential Based on the Kullback-Leibler Divergence

Neurophysiological studies have shown that there is a close relationship between spikes and local field potential (LFP), which reflects crucial neural coding information. In this paper, we used a new method to evaluate the synchronization between spikes and LFP. All possible phases of LFP from −π to π were first binned into a freely chosen number of bins; then, the probability of spikes falling in each bin was calculated, and the deviation degree from the uniform distribution based on the Kullback–Leibler divergence was calculated to define the synchronization between spikes and LFP. The simulation results demonstrate that the method is rapid, basically unaffected by the total number of spikes, and can adequately resist the noise of spike trains. We applied this method to the experimental data of patients with intractable epilepsy, and we observed the synchronization between spikes and LFP in the formation of memory. These results show that our proposed method is a powerful tool that can quantitatively measure the synchronization between spikes and LFP.

In silico voltage-sensitive dye imaging reveals the emergent dynamics of cortical populations

Voltage-sensitive dye imaging (VSDI) is a powerful technique for interrogating membrane potential dynamics in assemblies of cortical neurons, but with effective resolution limits that confound interpretation. To address this limitation, we developed an in silico model of VSDI in a biologically faithful digital reconstruction of rodent neocortical microcircuitry. Using this model, we extend previous experimental observations regarding the cellular origins of VSDI, finding that the signal is driven primarily by neurons in layers 2/3 and 5, and that VSDI measurements do not capture individual spikes. Furthermore, we test the capacity of VSD image sequences to discriminate between afferent thalamic inputs at various spatial locations to estimate a lower bound on the functional resolution of VSDI. Our approach underscores the power of a bottom-up computational approach for relating scales of cortical processing.

A Cerebellar Computational Mechanism for Delay Conditioning at Precise Time Intervals

The cerebellum is known to have an important role in sensing and execution of precise time intervals, but the mechanism by which arbitrary time intervals can be recognized and replicated with high precision is unknown. We propose a computational model in which precise time intervals can be identified from the pattern of individual spike activity in a population of parallel fibers in the cerebellar cortex. The model depends on the presence of repeatable sequences of spikes in response to conditioned stimulus input. We emulate granule cells using a population of Izhikevich neuron approximations driven by random but repeatable mossy fiber input. We emulate long-term depression (LTD) and long-term potentiation (LTP) synaptic plasticity at the parallel fiber to Purkinje cell synapse. We simulate a delay conditioning paradigm with a conditioned stimulus (CS) presented to the mossy fibers and an unconditioned stimulus (US) some time later issued to the Purkinje cells as a teaching signal. We show that Purkinje cells rapidly adapt to decrease firing probability following onset of the CS only at the interval for which the US had occurred. We suggest that detection of replicable spike patterns provides an accurate and easily learned timing structure that could be an important mechanism for behaviors that require identification and production of precise time intervals.

Interstitial ions: A key regulator of state-dependent neural activity?

Throughout the nervous system, ion gradients drive fundamental processes. Yet, the roles of interstitial ions in brain functioning is largely forgotten. Emerging literature is now revitalizing this area of neuroscience by showing that interstitial cations (K+, Ca2+ and Mg2+) are not static quantities but change dynamically across states such as sleep and locomotion. In turn, these state-dependent changes are capable of sculpting neuronal activity; for example, changing the local interstitial ion composition in the cortex is sufficient for modulating the prevalence of slow-frequency neuronal oscillations, or potentiating the gain of visually evoked responses. Disturbances in interstitial ionic homeostasis may also play a central role in the pathogenesis of central nervous system diseases. For example, impairments in K+ buffering occur in a number of neurodegenerative diseases, and abnormalities in neuronal activity in disease models disappear when interstitial K+ is normalized. Here we provide an overview of the roles of interstitial ions in physiology and pathology. We propose the brain uses interstitial ion signaling as a global mechanism to coordinate its complex activity patterns, and ion homeostasis failure contributes to central nervous system diseases affecting cognitive functions and behavior.

Bring the Noise: Reconceptualizing Spontaneous Neural Activity

Definitions of what constitutes the 'signal of interest' in neuroscience can be controversial, due in part to continuously evolving notions regarding the significance of spontaneous neural activity. This review highlights how the challenge of separating brain signal from noise has led to new conceptualizations of brain functional organization at both the micro- and macroscopic level. Recent debates in the functional neuroimaging community surrounding artifact removal processes have revived earlier discussions surrounding how to appropriately isolate and measure neuronal signals against a background of noise from various sources. Insights from electrophysiological studies and computational modeling can inform current theory and data analytic practices in human functional neuroimaging, given that signal and noise may be inextricably linked in the brain.

Understanding Computational Costs of Cellular-Level Brain Tissue Simulations Through Analytical Performance Models

Computational modeling and simulation have become essential tools in the quest to better understand the brain's makeup and to decipher the causal interrelations of its components. The breadth of biochemical and biophysical processes and structures in the brain has led to the development of a large variety of model abstractions and specialized tools, often times requiring high performance computing resources for their timely execution. What has been missing so far was an in-depth analysis of the complexity of the computational kernels, hindering a systematic approach to identifying bottlenecks of algorithms and hardware. If whole brain models are to be achieved on emerging computer generations, models and simulation engines will have to be carefully co-designed for the intrinsic hardware tradeoffs. For the first time, we present a systematic exploration based on analytic performance modeling. We base our analysis on three in silico models, chosen as representative examples of the most widely employed modeling abstractions: current-based point neurons, conductance-based point neurons and conductance-based detailed neurons. We identify that the synaptic modeling formalism, i.e. current or conductance-based representation, and not the level of morphological detail, is the most significant factor in determining the properties of memory bandwidth saturation and shared-memory scaling of in silico models. Even though general purpose computing has, until now, largely been able to deliver high performance, we find that for all types of abstractions, network latency and memory bandwidth will become severe bottlenecks as the number of neurons to be simulated grows. By adapting and extending a performance modeling approach, we deliver a first characterization of the performance landscape of brain tissue simulations, allowing us to pinpoint current bottlenecks for state-of-the-art in silico models, and make projections for future hardware and software requirements.

Impact of higher order network structure on emergent cortical activity

Synaptic connectivity between neocortical neurons is highly structured. The network structure of synaptic connectivity includes first-order properties that can be described by pairwise statistics, such as strengths of connections between different neuron types and distance-dependent connectivity, and higher order properties, such as an abundance of cliques of all-to-all connected neurons. The relative impact of first- and higher order structure on emergent cortical network activity is unknown. Here, we compare network structure and emergent activity in two neocortical microcircuit models with different synaptic connectivity. Both models have a similar first-order structure, but only one model includes higher order structure arising from morphological diversity within neuronal types. We find that such morphological diversity leads to more heterogeneous degree distributions, increases the number of cliques, and contributes to a small-world topology. The increase in higher order network structure is accompanied by more nuanced changes in neuronal firing patterns, such as an increased dependence of pairwise correlations on the positions of neurons in cliques. Our study shows that circuit models with very similar first-order structure of synaptic connectivity can have a drastically different higher order network structure, and suggests that the higher order structure imposed by morphological diversity within neuronal types has an impact on emergent cortical activity.