43 pages, 2 figures, 1 table. Accepted for publication in the "Encyclopedia of Computational Neuroscience," D. Jaeger and R. Jung eds., Springer-Verlag New York, 2020 (2nd edition)
Although lagging behind classical computational neuroscience, theoretical and computational approaches are beginning to emerge to characterize different aspects of neuron-glial interactions. This chapter aims to provide essential knowledge on neuron-glial interactions in the mammalian brain, leveraging on computational studies that focus on structure (anatomy) and function (physiology) of such interactions in the healthy brain. Although our understanding of the need of neuron-glial interactions in the brain is still at its infancy, being mostly based on predictions that await for experimental validation, simple general modeling arguments borrowed from control theory are introduced to support the importance of including such interactions in traditional neuron-based modeling paradigms.
Despite the fact that the phenomenon of bursting activity is important for functioning of living neural networks, the mechanisms of its origin are still not clear. In this paper, we propose a new phenomenological model that can explain the mechanisms of the formation of bursting activity based on short-term synaptic plasticity, recurrent connections, and neuron-glial interactions. We show that neuron-glial interactions can induce bursting activity. The bifurcation scenarios of emergence of bursting activity are in the focus of the paper. Proposed study is important for understanding of the com…
In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network mo…
We investigate the theory of observers in the quantum mechanical world by using a novel model of the human brain which incorporates the glial network into the Hopfield model of the neural network. Our model is based on a microscopic construction of a quantum Hamiltonian of the synaptic junctions. Using the Eguchi-Kawai large N reduction, we show that, when the number of neurons and astrocytes is exponentially large, the degrees of freedom of the dynamics of the neural and glial networks can be completely removed and, consequently, that the retention time of the superposition of the wave functi…
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites, the axons and the synapses as well as the surrounding glial cells, as a collection of all kinds of oscillating modes arisen from the electric circuital environment of neuronal action potentials. By analyzing the dynamics of this neural model through the master equation approach of open quantum systems, we investigate the collective behavior of neurons. After…
Neuronal and glial cells release diverse proteoglycans and glycoproteins, which aggregate in the extracellular space and form the extracellular matrix (ECM) that may in turn regulate major cellular functions. Brain cells also release extracellular proteases that may degrade the ECM, and both synthesis and degradation of ECM are activity-dependent. In this study we introduce a mathematical model describing population dynamics of neurons interacting with ECM molecules over extended timescales. It is demonstrated that depending on the prevalent biophysical mechanism of ECM-neuronal interactions, …
Recent developments in the interfacing of neurons with silicon chips may pave the way for progress in constructing scalable neurocomputers. The assembly of synthetic neuronal networks with predefined synaptic connections and controlled geometric structure has been realized experimentally within the last decade. Furthermore, when such neuronal networks are interfaced with semiconductors, action potentials in neurons of the network can be elicited by capacitative stimulators, and voltage measurements can be made by transistors incorporated into the associated silicon chip. Despite the impressive…
Opioid peptides are well-known modulators of the central control of reproduction. Among them, dynorphin coexpressed in kisspeptin (KP) neurons of the arcuate nucleus (ARC) has been thoroughly studied for its autocrine effect on KP release through $κ$ opioid receptors. Other studies have suggested a role for $β$-endorphin (BEND), a peptide cleaved from the proopiomelanocortin (POMC) precursor, on food intake and central control of reproduction. Similarly to KP, BEND content in the ARC of sheep is modulated by day length and BEND modulates food intake in a dose-dependent manner. As KP levels in …
Synaptic plasticity and neuron cross-talk are some of the important key mechanisms underlying formation of dynamic clusters of active neurons. The essence of this study is to model and decipher the mechanism of emergence of a task-specific functional connectivity among a population of neurons. We have used our proposed neuron activity pattern (NAP) model to define an assorted range of interactions and simulated across a 2D lattice with two-state (firing/non-firing) neurons. We observed the emergence of scale-free, hierarchically organized ordered patterns of active neurons, that we call as fun…
The ongoing activity of neurons generates a spatially- and time-varying field of extracellular voltage ($V_e$). This $V_e$ field reflects population-level neural activity, but does it modulate neural dynamics and the function of neural circuits? We provide a cable theory framework to study how a bundle of model neurons generates $V_e$ and how this $V_e$ feeds back and influences membrane potential ($V_m$). We find that these "ephaptic interactions" are small but not negligible. The model neural population can generate $V_e$ with millivolt-scale amplitude and this $V_e$ perturbs the $V_m$ of "n…
Synaptic plasticity depends on the interaction between electrical activity in neurons and the synaptic proteome, the collection of over 1000 proteins in the post-synaptic density (PSD) of synapses. To construct models of synaptic plasticity with realistic numbers of proteins, we aim to combine rule-based models of molecular interactions in the synaptic proteome with compartmental models of the electrical activity of neurons. Rule-based models allow interactions between the combinatorially large number of protein complexes in the postsynaptic proteome to be expressed straightforwardly. Simulati…
The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations emerges in sparsely connected networks. We apply linear response theory to evaluate the influence of detailed network structure on neuron dynamics. It turns out that pairwise correlations induced by direct and indirect network connections can be related to the matrix of direct linear interactions. Furthermore, we study the influence of characteristics of th…
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the salamander retina responding to natural movies. We show that pairwise interactions between neurons account for observed higher-order correlations, and that for groups of 10 or more neurons pairwise interactions can no longer be regarded as small perturbations in an independent syst…
Epileptic seizures are characterised by abnormal brain dynamics at multiple scales, engaging single neurons, neuronal ensembles and coarse brain regions. Key to understanding the cause of such emergent population dynamics, is capturing the collective behaviour of neuronal activity at multiple brain scales. In this thesis I make use of the larval zebrafish to capture single cell neuronal activity across the whole brain during epileptic seizures. Firstly, I make use of statistical physics methods to quantify the collective behaviour of single neuron dynamics during epileptic seizures. Here, I de…
The connectome is a wiring diagram mapping all the neural connections in the brain. At the cellular level, it provides a map of the neurons and synapses within a part or all of the brain of an organism. In recent years, significant advances have been made in the study of the connectome via network science and graph theory. This analysis is fundamental to understand neurotransmission (fast synaptic transmission) networks. However, neurons use other forms of communication as neuromodulation that, instead of conveying excitation or inhibition, change neuronal and synaptic properties. This additio…
We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or different nuclei in the brain. The dynamical activity pattern that results from these interactions depends on the strength of synaptic coupling between them. Importantly, the overall dynamics of a brain region in the absence of external input, so called ongoing brain activity, has been attributed to the dynamics of such interactions. In our study, two different network scenarios are considered: a syst…
We investigated the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We found spike death phenomena, namely, the state of neurons transits from limit cycle to fixed point or transient state. The phenomena occur under the perturbation of excitatory synaptic interaction that has a high efficacy. We showed that the decrease of synaptic current results in spike death through depressing the feedback of sodium ionic current. In the networks with spike death property the degree of synchronization is lower and unsensitive to the heterogeneity of …
The neuronal paradigm of studying the brain has left us with limitations in both our understanding of how neurons process information to achieve biological intelligence and how such knowledge may be translated into artificial intelligence and its most brain-derived branch, neuromorphic computing. Overturning our fundamental assumptions of how the brain works, the recent exploration of astrocytes is revealing that these long-neglected brain cells dynamically regulate learning by interacting with neuronal activity at the synaptic level. Following recent experimental evidence, we designed an asso…
We present two Bayesian procedures to infer the interactions and external currents in an assembly of stochastic integrate-and-fire neurons from the recording of their spiking activity. The first procedure is based on the exact calculation of the most likely time courses of the neuron membrane potentials conditioned by the recorded spikes, and is exact for a vanishing noise variance and for an instantaneous synaptic integration. The second procedure takes into account the presence of fluctuations around the most likely time courses of the potentials, and can deal with moderate noise levels. The…
Correlations in sensory neural networks have both extrinsic and intrinsic origins. Extrinsic or stimulus correlations arise from shared inputs to the network, and thus depend strongly on the stimulus ensemble. Intrinsic or noise correlations reflect biophysical mechanisms of interactions between neurons, which are expected to be robust to changes of the stimulus ensemble. Despite the importance of this distinction for understanding how sensory networks encode information collectively, no method exists to reliably separate intrinsic interactions from extrinsic correlations in neural activity da…
Biological cortical networks are potentially fully recurrent networks without any distinct output layer, where recognition may instead rely on the distribution of activity across its neurons. Because such biological networks can have rich dynamics, they are well-designed to cope with dynamical interactions of the types that occur in nature, while traditional machine learning networks may struggle to make sense of such data. Here we connected a simple model neuronal network (based on the 'linear summation neuron model' featuring biologically realistic dynamics (LSM), consisting of 10 of excitat…
Spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle interplay between interaction delays, noise and the excitable character of a single neuron. Dependence of the cluster properties on the time-lag, noise intensity and the synaptic strength is investigated.
We study the effect that the heterogeneity present among the elements of an ensemble of coupled excitable neurons have on the collective response of the system to an external signal. We have considered two different interaction scenarios, one in which the neurons are diffusively coupled and another in which the neurons interact via pulse-like signals. We found that the type of interaction between the neurons has a crucial role in determining the response of the system to the external modulation. We develop a mean-field theory based on an order parameter expansion that quantitatively reproduces…
Maximum Entropy models can be inferred from large data-sets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multielectrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows to shed light upon differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, Maximum Entrop…
We study the ordering kinetics in $d=2$ ferromagnets which corresponds to populated neuron activities with long-ranged interactions, $V(r)\sim r^{-n}$ associated with short-ranged interaction. We present the results from comprehensive Monte Carlo (MC) simulations for the nonconserved Ising model with $n\ge 2$. Our results of long-ranged neuron kinetics are consistent with the same dynamical behavior of short-ranged case ($n > 4$). The calculated characteristic length scale in long-ranged interaction is found to be $n$ dependent ($L(t)\sim t^{1/(n-2)}$), whereas short-ranged interaction follows…
One of the main current issues in Neurobiology concerns the understanding of interrelated spiking activity among multineuronal ensembles and differences between stimulus-driven and spontaneous activity in neurophysiological experiments. Multi electrode array recordings that are now commonly used monitor neuronal activity in the form of spike trains from many well identified neurons. A basic question when analyzing such data is the identification of the directed graph describing "synaptic coupling" between neurons. In this article we deal with this matter working with a high quality multielectr…
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the retina, and show that pairwise interactions account for observed higher-order correlations. By first finding a representative ensemble for observed networks we can create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical…
In this study, we analyzed the activity of monkey V1 neurons responding to grating stimuli of different orientations using inference methods for a time-dependent Ising model. The method provides optimal estimation of time-dependent neural interactions with credible intervals according to the sequential Bayes estimation algorithm. Furthermore, it allows us to trace dynamics of macroscopic network properties such as entropy, sparseness, and fluctuation. Here we report that, in all examined stimulus conditions, pairwise interactions contribute to increasing sparseness and fluctuation. We then dem…
We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where travelling synchronization waves are observed out of a first-neighbours based coupling, to evaluate the changes induced when higher-order dynamical interactions are included. We observe that the travelling wave phenomenon gets enhanced by these interactions, allowing the information to travel further in the system without generating pathological full synchronization states. This scheme could be a step towards a simple modelization of neurogli…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its applicatio…
The mammalian brain could contain dense and sparse network connectivity structures, including both excitatory and inhibitory neurons, but is without any clearly defined output layer. The neurons have time constants, which mean that the integrated network structure has state memory. The network structure contains complex mutual interactions between the neurons under different conditions, which depend on the internal state of the network. The internal state can be defined as the distribution of activity across all individual neurons across the network. Therefore, the state of a neuron/network be…
The specific connectivity of a neuronal network is reflected in the dynamics of the signals recorded on its nodes. The analysis of how the activity in one node predicts the behaviour of another gives the directionality in their relationship. However, each node is composed of many different elements which define the properties of the links. For instance, excitatory and inhibitory neuronal subtypes determine the functionality of the connection. Classic indexes such as the Granger causality (GC) quantifies these interactions, but they do not infer into the mechanism behind them. Here, we introduc…
Introduction- Identifying the potential firing patterns following different brain regions under normal and abnormal conditions increases our understanding of events at the level of neural interactions in the brain. The Izhikevich model is one of the simplest biologically plausible models, i.e. capable of capturing the most recognized firing patterns of neurons. This property makes the model efficient in simulating the large-scale networks of neurons. Improving the Izhikevich model for adapting to the neuronal activity of the rat brain with great accuracy would make the model effective for futu…
Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global i…
Neural oscillations are electrical activities of the brain measurable at different frequencies. This paper studies the interaction between the fast and slow processes in the brain. We recorded signals intracranially from the simple Wistar rats, performed the signal processing, and computed the correlation between envelopes of the high-frequency gamma rhythm and a low-frequency ECoG signal. The analysis shows that the low-frequency signal (delta rhythm) modulates the gamma rhythm with a small time delay. Further, we used simple excitable neuron models, namely FitzHugh-Nagumo and Hindmarsh-Rose,…
We propose a novel discrete model of central pattern generators (CPG), neuronal ensembles generating rhythmic activity. The model emphasizes the role of nonsynaptic interactions and the diversity of electrical properties in nervous systems. Neurons in the model release different neurotransmitters into the shared extracellular space (ECS) so each neuron with the appropriate set of receptors can receive signals from other neurons. We consider neurons, differing in their electrical activity, represented as finite-state machines functioning in discrete time steps. Discrete modeling is aimed to pro…
The study of neuronal interactions is currently at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, the Brainome, etc.) which attempt to obtain a detailed map of the entire brain. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix. This work explores the application of free random variables to the study of large synaptic interaction matrices. Besides recovering in a straightforward way kno…
Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward networks, activity is exclusively driven by excitatory neurons and the wiring patterns between them, while inhibitory neurons play only a stabilizing role for the network dynamics. Motivated by recent experimental discoveries of hippocampal circuitry, cortical circuitry, and the diversity of inhibitory neurons throughout the brain, here we illustrate that o…
Predictive coding is a promising theoretical framework in neuroscience for understanding information transmission and perception. It posits that the brain perceives the external world through internal models and updates these models under the guidance of prediction errors. Previous studies on predictive coding emphasized top-down feedback interactions in hierarchical multi-layered networks but largely ignored lateral recurrent interactions. We perform analytical and numerical investigations in this work on the effects of single-layer lateral interactions. We consider a simple predictive respon…
How Long Is the Coast of a Neuron? Resolution-Dependent Interaction Order and Computational Capacity
Massachusetts Institute of Technology（麻省理工学院）；NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI)（美国国家科学基金会人工智能基础相互作用AI研究所）
The fundamental, powerful process of computation in the brain has been widely misunderstood. The paper [1] associates the general failure to build intelligent thinking machines with current reductionist principles of temporal coding and advocates for a change in paradigm regarding the brain analogy. Since fragments of information are stored in proteins which can shift between several structures to perform their function, the biological substrate is actively involved in physical computation. The intrinsic nonlinear dynamics of action potentials and synaptic activities maintain physical interact…
