Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is estimated computationally so as to obtain the activation at each node along each instant of time. In the transient case, the dynamics is implemented so as to conserve the total activation entering the system. In our equilibrium investigations, the internally stored activation is limited to the value of the respective threshold. The synchronization of the activation of the network is then quantified in terms of its normalized entropy. The equilibrium investigations involve the application of a number of complementary characterization methods, including spectra and Principal Component Analysis, as well as of an equivalent model capable of reproducing both the transient and equilibrium dynamics. The potential of such concepts and measurements is explored with respect to several theoretical models, as well as for the neuronal network of \emph{C. elegans}. A series of interesting results are obtained and discussed, including the fact that all models led to a transient period of synchronization, whose specific features depend on the topological structures of the networks. The investigations of the equilibrium dynamics revealed a series of remarkable insights, including the relationship between spiking oscillations and the hierarchical structure of the networks and the identification of twin correlation patterns between node degree and total activation, implying that hubs of connectivity are also hubs of integrate-and-fire activation.
We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating exci…
Several experiments and models have highlighted the importance of neuronal heterogeneity in brain dynamics and function. However, how such a cell-to-cell diversity can affect cortical computation, synchronization, and neuronal communication is still under debate. Previous studies have focused on the effect of neuronal heterogeneity in one neuronal population. Here we are specifically interested in the effect of neuronal variability on the phase relations between two populations, which can be related to different cortical communication hypotheses. It has been recently shown that two spiking neu…
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 …
Two dynamical systems unidirectionally coupled in a sender-receiver configuration can synchronize with a nonzero phase-lag. In particular, the system can exhibit anticipated synchronization (AS), which is characterized by a negative phase-lag, if the receiver (R) also receives a delayed negative self-feedback. Recently, AS was shown to occur between cortical-like neuronal populations in which the self-feedback is mediated by inhibitory synapses. In this biologically plausible scenario, a transition from the usual delayed synchronization (DS, with positive phase-lag) to AS can be mediated by th…
We show that the unavoidable increase in neuronal response latency to ongoing stimulation serves as a nonuniform gradual stretching of neuronal circuit delay loops and emerges as an essential mechanism in the formation of various types of neuronal timers. Synchronization emerges as a transient phenomenon without predefined precise matched synaptic delays. These findings are described in an experimental procedure where conditioned stimulations were enforced on a circuit of neurons embedded within a large-scale network of cortical cells in-vitro, and are corroborated by neuronal simulations. The…
Anticipated synchronization (AS) is a counter intuitive behavior that has been observed in several systems. When AS establishes in a sender-receiver configuration, the latter can predict the future dynamics of the former for certain parameter values. In particular, in neuroscience AS was proposed to explain the apparent discrepancy between information flow and time lag in the cortical activity recorded in monkeys. Despite its success, a clear understanding on the mechanisms yielding AS in neuronal circuits is still missing. Here we use the well-known phase-resetting-curve (PRC) approach to stu…
Two identical autonomous dynamical systems coupled in a master-slave configuration can exhibit anticipated synchronization (AS) if the slave also receives a delayed negative self-feedback. Recently, AS was shown to occur in systems of simplified neuron models, requiring the coupling of the neuronal membrane potential with its delayed value. However, this coupling has no obvious biological correlate. Here we propose a canonical neuronal microcircuit with standard chemical synapses, where the delayed inhibition is provided by an interneuron. In this biologically plausible scenario, a smooth tran…
In a generic neuron model, we present the linear response theory for the firing rate in response to both time dependent input currents and noise amplitudes. In both cases the signal transmission is strongly attenuated for frequencies above the stationary firing rate. For high frequencies both the mean input and the noise transmission function decay as ω^{-2}, independent of model details. Our results indicate that previously suggested mechanisms for near instantaneous transmission of information are not consistent with the spike generation mechanism of real neurons.
The role of synchronous firing in sensory coding and cognition remains controversial. While studies, focusing on its mechanistic consequences in attentional tasks, suggest that synchronization dynamically boosts sensory processing, others failed to find significant synchronization levels in such tasks. We attempt to understand both lines of evidence within a coherent theoretical framework. We conceptualize synchronization as an independent control parameter to study how the postsynaptic neuron transmits the average firing activity of a presynaptic population, in the presence of synchronization…
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 discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance-based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (elec…
We investigate the synchronization properties between two excitatory coupled neurons in the presence of an inhibitory loop mediated by an interneuron. Dynamical inhibition together with noise independently applied to each neuron provide phase diversity in the dynamics of the neuronal motif. We show that the interplay between the coupling strengths and external noise controls the phase relations between the neurons in a counter-intuitive way. For a master-slave configuration (unidirectional coupling) we find that the slave can anticipate the master, on average, if the slave is subject to the in…
We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect c…
We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barabási-Albert scale-free network (SFN) composed of inhibitory bursting Hindmarsh-Rose neurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without considering iSTDP, BS was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. In contrast, in our present work, we take into consideration iSTDP and investigate its effect o…
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled and interact with each other. The excitatory population is uncoupled, while the inhibitory population is tightly coupled. A geometric singular perturbation analysis yields existence and stability conditions for synchronization states under different firing patterns between the two populations, along with formulas for the periods…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon that can be seen in the brain. The network topology has a remarkable impact on both the function and the dynamics of neural networks. In this research, synchronization of neural networks is scrutinized through creating various topologies. These networks include both excitatory and inhibitory neurons. We investigate the dynamics of different networks by random…
For studying how dynamical responses to external stimuli depend on the synaptic-coupling type, we consider two types of excitatory and inhibitory synchronization (i.e., synchronization via synaptic excitation and inhibition) in complex small-world networks of excitatory regular spiking (RS) pyramidal neurons and inhibitory fast spiking (FS) interneurons. For both cases of excitatory and inhibitory synchronization, effects of synaptic couplings on dynamical responses to external time-periodic stimuli $S(t)$ (applied to a fraction of neurons) are investigated by varying the driving amplitude $A$…
The effect of the excitatory feedback in anticipated synchronization and phase bistability regimes in neuronal populations
Universidade Federal de Alagoas（阿拉戈阿斯联邦大学）；Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Universitat de les Illes Balears（巴利阿里群岛大学）；Florida Atlantic University（佛罗里达大西洋大学）
We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In the absence of STDP, stochastic burst synchronization (SBS) between noise-induced burstings of subthreshold neurons was previously found to occur over a large range of intermediate noise intensities. Here, we study the effect of additive STDP on the SBS by v…
We investigate temporal coherence and spatial synchronization on small-world networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence on two types of time-delayed coupling: $\{x_j(t-τ)-x_i (t)\}$ and $\{x_j(t-τ)-x_i(t-τ)\}$. For the former case, we show that time delay in the coupling can dramatically enhance temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time $τ$ is tuned to nearly match the intrinsic spike period of the neuronal network, the system dynamics reaches a most ordered state, which is both periodic in time…
An important idea in neural information processing is the communication-through-coherence hypothesis, according to which communication between two brain regions is effective only if they are phase-locked. Also of importance is neuronal variability, a phenomenon in which a single neuron's inter-firing times may be highly variable. In this work, we aim to connect these two ideas by studying the effects of that variability on the capability of neurons to reach phase synchronization. We simulate a network of modified-Hodgkin-Huxley-bursting neurons possessing a small-world topology. First, variabi…
Activity Regeneration from Silent States in Neuronal Networks with Transient Synaptic Memory
Pasargad Institute for Advanced Innovative Solutions (PIAIS)（帕萨加德先进创新解决方案研究所）；Zapata Briceño Institute for Human Intelligence Research（萨帕塔·布里塞尼奥人类智能研究所）；Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）
This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as wel…
Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the synchronization transition is affected when the time delays in the interactions between pairs of interacting neurons are non-uniform. We find that the presence of distributed time-delays does not change the behavior of the synchronization transition significantly, vis-a-vis networks with constant time-delay, where the value of the constant time-delay is the mean of the d…
The current-voltage (I-V) conversion characterizes the physiology of cellular microdomains and reflects cellular communication, excitability, and electrical transduction. Yet deriving such I-V laws remains a major challenge in most cellular microdomains due to their small sizes and the difficulty of accessing voltage with a high nanometer precision. We present here novel analytical relations derived for different numbers of ionic species inside a neuronal micro/nano-domains, such as dendritic spines. When a steady-state current is injected, we find a large deviation from the classical Ohm's la…
We consider clustered small-world networks with both inhibitory (I) and excitatory (E) populations. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensity $D$ for static synaptic strengths. By varying $D$, we investigate the effect of interpopulation STDPs on diverse population and individual properties of fast sparsely sy…
Epileptic seizures are considered as abnormally hypersynchronous neuronal activities of the brain. Do hypersynchronous neuronal activities in a brain region lead to seizure or the hypersynchronous activities take place due to the progression of the seizure? We have examined the ECoG signals of 21 epileptic patients consisting of 87 focal-onset seizures by three different measures namely, phase synchronization, amplitude correlation and simultaneous occurrence of peaks and troughs. Each of the measures indicates that for a majority of the focal-onset seizures, synchronization or correlation or …
Occurrence of strong or mass synchronization of a large number of neuronal populations in the brain characterizes its pathological states. In order to establish an understanding of the mechanism underlying such pathological synchronization we present a model of coupled populations of phase oscillators representing the interacting neuronal populations. Through numerical analysis, we discuss the occurrence of mass synchronization in the model, where a source population which gets strongly synchronized drives the target populations onto mass synchronization. We hypothesize and identify a possible…
Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons and synapses with superconducting Josephson junctions. The circuit models two mutually coupled excitatory neurons. In some regions of parameter space the neurons are desynchronized. In others, the Josephson neurons synchronize in one of two states, in-phase or anti-phase. An experimental alteration of the delay and strength of the connecting synapses can toggle the system back and forth in a phase-fl…
Recent experiments suggest that inhibitory networks of interneurons can synchronize the neuronal discharge in in vitro hippocampal slices. Subsequent theoretical work has shown that strong synchronization by mutual inhibition is only moderately robust against neuronal heterogeneities in the current drive, provided by activation of metabotropic glutamate receptors. In vivo neurons display greater variability in the interspike intervals due to the presence of synaptic noise. Noise and heterogeneity affect synchronization properties differently. In this paper we study using model simulations how …
In this paper, we propose a dynamic delayed feedback control approach for desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two…
Stochastic dynamics and synchronization in motif-based neuronal networks
Toronto Metropolitan University（多伦多都会大学）；University of Toronto（多伦多大学）；Florida State University（佛罗里达州立大学）；Institute of Molecular Biophysics, Florida State University（佛罗里达州立大学分子生物物理研究所）；St. Michael’s Hospital, Unity Health Toronto（圣迈克尔医院（联合健康多伦多））
Spatial awareness in mammals is based on an internalized representation of the environment, encoded by large networks of spiking neurons. While such representations can last for a long time, the underlying neuronal network is transient: neuronal cells die every day, synaptic connections appear and disappear, the networks constantly change their architecture due to various forms of synaptic and structural plasticity. How can a network with a dynamic architecture encode a stable map of space? We address this question using a physiological model of a "flickering" neuronal network and demonstrate …
Synchronization in neural networks is strongly tied to the implementation of cognitive processes, but abnormal neuronal synchronization has been linked to a number of brain disorders such as epilepsy and schizophrenia. Here we examine the effects of channel noise on the synchronization of small Hodgkin-Huxley neuronal networks. The principal feature of a Hodgkin-Huxley neuron is the existence of protein channels that transition between open and closed states with voltage dependent rate constants. The Hodgkin-Huxley model assumes infinitely many channels, so fluctuations in the number of open c…
The mammalian hippocampus plays a principal role in producing a cognitive map of space---an internalized representation of the animal's environment. The neuronal mechanisms producing this map depend primarily on the temporal structure of the hippocampal neurons' spiking activity, which is modulated by the oscillatory extracellular electrical field potential. In this paper, we discuss the integrative effect of the gamma rhythm, one of the principal components of these oscillations, on the ability of the place cell ensembles to encode a spatial map. Using methods of algebraic topology and statis…
Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains explosive transition or a continuous transition is an important feature of the neuronal network which can depend on network structure as well as synaptic types. In this study we consider the effect of synaptic interaction (electrical and chemical) as well as structural connectivity on synchronization transition in network models of Izhikevich neurons which spike reg…
While there is still a lot to learn about astrocytes and their neuromodulatory role in the spatial and temporal integration of neuronal activity, their introduction to neuromorphic hardware is timely, facilitating their computational exploration in basic science questions as well as their exploitation in real-world applications. Here, we present an astrocytic module that enables the development of a spiking Neuronal-Astrocytic Network (SNAN) into Intel's Loihi neuromorphic chip. The basis of the Loihi module is an end-to-end biophysically plausible compartmental model of an astrocyte that simu…
Synchronization phenomena are pervasive in biology. In neuronal networks, the mechanisms of synchronization have been extensively studied from both physiological and computational viewpoints. The functional role of synchronization has also attracted much interest and debate. In particular, synchronization may allow distant sites in the brain to communicate and cooperate with each other, and therefore it may play a role in temporal binding and in attention and sensory-motor integration mechanisms. In this article, we study another role for synchronization: the so-called "collective enhancement …
The scaling of transient times to zero-lag synchronization in networks composed of excitable units is shown to be governed by three features of the graph representing the network: the longest path between pairs of neurons (diameter), the largest loop (circumference) and the loop with the maximal average out degree. The upper bound of transient times can vary between O(1) and O(N2), where N is the size of the network, and its scaling can be predicted in many scenarios from finite time accumulated information of the transient. Results challenge the assumption that functionality of neural network…
Author summary: Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many cortical neurons is spike frequency adaptation, which is caused by slow transmembrane currents. We investigated how these adaptation currents affect the synchronization tendency of coupled model neurons. Using the efficient adaptive exponential integrate-and-fire (aEIF) model and a biophys…
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…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states. This transition cannot be explained only through the analysis of the spectral density of the connectivity matr…
We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different spatiotemporal patterns, corresponding to either non-synchronized or phase-synchronized states. Particularly interesting is what we call synchronization malleability, in which the system depicts significantly different phase synchronization degrees for the same parameters as a consequence of a different ordering of neural inputs. We analyze the functional connectivity…
We find that sensory noise delivered together with a weak periodic signal not only enhances nonlinear response of neuronal networks, but also improves the synchronization of the response to the signal. We reveal this phenomenon in neuronal networks that are in a dynamical state near a saddle-node bifurcation corresponding to appearance of sustained network oscillations. In this state, even a weak periodic signal can evoke sharp nonlinear oscillations of neuronal activity. These sharp network oscillations have a deterministic form and amplitude determined by nonlinear dynamical equations. The s…
The spiking activity of principal cells in mammalian hippocampus encodes an internalized neuronal representation of the ambient space---a cognitive map. Once learned, such a map enables the animal to navigate a given environment for a long period. However, the neuronal substrate that produces this map remains transient: the synaptic connections in the hippocampus and in the downstream neuronal networks never cease to form and to deteriorate at a rapid rate. How can the brain maintain a robust, reliable representation of space using a network that constantly changes its architecture? Here, we d…
Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, whilst adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems -- resonance pairs -- promote st…
Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of an exact model of the macroscopic dynamics, valid in the thermodynamic limit. The collective chaotic state is reproduced numerically with a finite population, and persists in the presence of weak heterogeneities. Finally, the relationship of the model's dynamics with fast neuronal oscillations is discussed.
We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity $D$.…
We use a biophysical model of a local neuronal circuit to study the implications of synaptic plasticity for the detection of weak sensory stimuli. Networks with fast plastic coupling show behavior consistent with stochastic resonance. Addition of an additional slow coupling that accounts for the asynchronous release of neurotransmitter results in qualitatively different properties of signal detection, and also leads to the appearance of transient post-stimulus bistability. Our results suggest testable hypothesis with regard to the self-organization and dynamics of local neuronal circuits.
We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal c…
The synchronization of different $γ$-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of PING (pyramidal-interneuronal network gamma) and ING (interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determined the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC), using numerical simulation of all-to-all coupled networks of integ…
The detection of neuronal communities is addressed with basis on two important concepts from neuroscience: facilitation of neuronal firing and nearly simultaneous beginning of activation of sets of neurons. More specifically, integrate-and-fire complex neuronal networks are activated at each of their nodes, and the dissemination of activation is monitored. As the activation received by each neuron accumulates, its firing gets facilitated. The time it takes for each neuron, other than the source, to receive the first non-zero input (beginning activation time) and the time for it to produce the …
Neuronal excitability is known to be affected by transcranial electrical stimulation. However, due to the existence of both excitatory and inhibitory neurons in the cortex, the mechanism of neuronal excitability shift is still not clear. Here, we study electrical stimulation disturbance on neuronal excitability in the neuromuscular system on an acute rat model. We design a special stimulation waveform of enveloped high frequency stimulation (EHFS). With modeling and in vivo measurements, EHFS is confirmed to synchronize the neuronal recruitment at the positive and negative electrode. This uniq…
