Effects of neuronal variability on phase synchronization of neural networks
Kalel Luiz Rossi, Roberto Cesar Budzisnki, Joao Antonio Paludo Silveira, Bruno Rafael Reichert Boaretto, Thiago Lima Prado, Sergio Roberto Lopes, Ulrike Feudel
备注：
11 pages, 7 figures, to be submitted to Neural Networks journal
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, variability is shown to be correlated with the average degree of phase synchronization of the network. Next, restricting to spatial variability - which measures the deviation of firing times between all neurons in the network - we show that it is positively correlated to a behavior we call promiscuity, which is the tendency of neurons to to have their relative phases change with time. This relation is observed in all cases we tested, regardless of the degree of synchronization or the strength of the inter-neuronal coupling: high variability implies high promiscuity (low duration of phase-locking), even if the network as a whole is synchronized and the coupling is strong. We argue that spatial variability actually generates promiscuity. Therefore, we conclude that variability has a strong influence on both the degree and the manner in which neurons phase synchronize, which is another reason for its relevance in neural communication.
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…
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…
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…
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 …
We examine whether a single biophysical cortical circuit model can explain both spiking and perceptual variability. We consider perceptual rivalry, which provides a window into intrinsic neural processing since neural activity in some brain areas is correlated to the alternating perception rather than the constant ambiguous stimulus. The prevalent theory for spiking variability is a chaotic attractor called the balanced state; whereas, the source of perceptual variability is an open question. We present a dynamical model with a chaotic attractor that explains both spiking and perceptual variab…
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…
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…
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…
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…
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…
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…
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…
Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow $\mathrm{K}^+$-currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in-vivo like fluctuating synaptic input, spike rate output and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current which primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold. A spike-dependent adap…
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…
The threshold voltage for action potential generation is a key regulator of neuronal signal transduction, yet the mechanism of its dynamic variation is still not well described. In this paper, we propose that threshold phenomena can be classified as parameter thresholds and state thresholds. Voltage thresholds which belong to the state threshold are determined by the `general separatrix' in state space. We demonstrate that the separatrix generally exists in the state space of neuron models. The general form of separatrix was assumed as the function of both states and stimuli and the previously…
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 …
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 …
Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such a…
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…
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 act…
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…
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））
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…
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…
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…
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 $A$…
Inhibition is considered to shape neural activity, and broaden its pattern repertoire. In the sensory organs, where the anatomy of neural circuits is highly structured, lateral inhibition sharpens contrast among stimulus properties. The impact of inhibition on stimulus processing and the involvement of lateral inhibition is less clear when activity propagates to the less-structured relay stations. Here we take a synthetic approach to disentangle the impacts of inhibition from that of specialized anatomy on the repertoire of evoked activity patterns, and as a result, the network capacity to uni…
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…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly Gaussian -- which they tend to be in large networks -- we obtain deterministic equations for the temporal evolution of the mean firing rates and the noise covariance matrix that can be solved straightforwardly given the network connectivity. We also obtain spike count statistics such as Fano factors and pairwise correlations, assuming doubly-stochastic action po…
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…
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…
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…
Since the first recordings made of evoked action potentials it has become apparent that the responses of individual neurons to ongoing physiologically relevant input, are highly variable. This variability is manifested in non-stationary behavior of practically every observable neuronal response feature. Here we introduce the Neuronal Response Clamp, a closed-loop technique enabling full control over two important single neuron activity variables: response probability and stimulus-spike latency. The technique is applicable over extended durations (up to several hours), and is effective even on …
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…
Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for general non-renewal processes to calculate the interval and count statistics of superimposed processes governed by a slow adaptation variable. For an ensemble of spike-frequency adapting neurons this results in the regularization of the population activity and an enhanced post-synaptic signal decoding. We confirm our theoretical results in a population of cortical neurons.
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…
Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can potentially address a range of theoretical problems and provide a straightforward explanation for our cognition. However, this idea is merely a hypothesis with many questions unsolved. In this paper, I will bring up a new framework to defend the idea of neuronal representations. The strategy is from micro- to macro-level. Specifically, in the micro-level, I first p…
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…
Understanding the role of astrocytes in brain computation is a nascent challenge, promising immense rewards, in terms of new neurobiological knowledge that can be translated into artificial intelligence. In our ongoing effort to identify principles endow-ing the astrocyte with unique functions in brain computation, and translate them into neural-astrocytic networks (NANs), we propose a biophysically realistic model of an astrocyte that preserves the experimentally observed spatial allocation of its distinct subcellular compartments. We show how our model may encode, and modu-late, the extent o…
This work explores four nonlinear classical models of neural oscillators, the Hodgkin-Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Nonlinear contraction theory is used to develop observers and perform synchronization analysis on these systems. Neural oscillation and signaling models are based on the biological function of the neuron, with behavior mediated through the channeling of ions across the cell membrane. The variable assumed to be measured is the membrane potential, which may be obtained empirically through the use of a neuronal force-c…
We investigate different dynamical regimes of neuronal network in the CA3 area of the hippocampus. The proposed neuronal circuit includes two fast- and two slowly-spiking cells which are interconnected by means of dynamical synapses. On the individual level, each neuron is modeled by FitzHugh-Nagumo equations. Three basic rhythmic patterns are observed: gamma-rhythm in which the fast neurons are uniformly spiking, theta-rhythm in which the individual spikes are separated by quiet epochs, and theta/gamma rhythm with repeated patches of spikes. We analyze the influence of asymmetry of synaptic s…
We examine the response of type II excitable neurons to trains of synaptic pulses, as a function of the pulse frequency and amplitude. We show that the resonant behavior characteristic of type II excitability, already described for harmonic inputs, is also present for pulsed inputs. With this in mind, we study the response of neurons to pulsed input trains whose frequency varies continuously in time, and observe that the receiving neuron synchronizes episodically to the input pulses, whenever the pulse frequency lies within the neuron's locking range. We propose this behavior as a mechanism of…
Phase- and amplitude-dependent control of synchronization in excitatory-inhibitory networks via pulsed stimulation
Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran（巴斯研究学院物理系）；School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran（基础科学研究所生物科学学院）；Pasargad Institute for Advanced Innovative Solutions (PIAIS), Tehran, Iran（帕萨加德先进创新解决方案研究所）；The Zapata-Briceño Institute of Neuroscience, Madrid, Spain（萨帕塔-布里斯涅奥神经科学研究所）
Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of coupled neural oscillators. Coupled oscillator theory thus informs the synchronization of spiking neuronal networks. A crucial aspect of coupled oscillator theory is the phase response curve (PRC), which describes the impact of a perturbation to the phase of an oscillator. In neural terms, the perturbation represents an incoming synaptic potential which may e…
