Excitatory Synaptic Coupling Research Articles

Emergent Dynamics and Spatio Temporal Patterns on Multiplex Neuronal Networks.

We present a study on the emergence of a variety of spatio temporal patterns among neurons that are connected in a multiplex framework, with neurons on two layers with different functional couplings. With the Hindmarsh-Rose model for the dynamics of single neurons, we analyze the possible patterns of dynamics in each layer separately and report emergent patterns of activity like in-phase synchronized oscillations and amplitude death (AD) for excitatory coupling and anti-phase mixed-mode oscillations (MMO) in multi-clusters with phase regularities when the connections are inhibitory. When they are multiplexed, with neurons of one layer coupled with excitatory synaptic coupling and neurons of the other layer coupled with inhibitory synaptic coupling, we observe the transfer or selection of interesting patterns of collective behavior between the layers. While the revival of oscillations occurs in the layer with excitatory coupling, the transition from anti-phase to in-phase and vice versa is observed in the other layer with inhibitory synaptic coupling. We also discuss how the selection of these spatio temporal patterns can be controlled by tuning the intralayer or interlayer coupling strengths or increasing the range of non-local coupling. With one layer having electrical coupling while the other synaptic coupling of excitatory(inhibitory)type, we find in-phase(anti-phase) synchronized patterns of activity among neurons in both layers.

Brain Network Simulations Indicate Effects of Neuregulin-1 Genotype on Excitation-Inhibition Balance in Cortical Dynamics.

Neuregulin-1 (NRG1) represents an important factor for multiple processes including neurodevelopment, brain functioning or cognitive functions. Evidence from animal research suggests an effect of NRG1 on the excitation-inhibition (E/I) balance in cortical circuits. However, direct evidence for the importance of NRG1 in E/I balance in humans is still lacking. In this work, we demonstrate the application of computational, biophysical network models to advance our understanding of the interaction between cortical activity observed in neuroimaging and the underlying neurobiology. We employed a biophysical neuronal model to simulate large-scale brain dynamics and to investigate the role of polymorphisms in the NRG1 gene (rs35753505, rs3924999) in n = 96 healthy adults. Our results show that G/G-carriers (rs3924999) exhibit a significant difference in global coupling (P = 0.048) and multiple parameters determining E/I-balance such as excitatory synaptic coupling (P = 0.047), local excitatory recurrence (P = 0.032) and inhibitory synaptic coupling (P = 0.028). This indicates that NRG1 may be related to excitatory recurrence or excitatory synaptic coupling potentially resulting in altered E/I-balance. Moreover, we suggest that computational modeling is a suitable tool to investigate specific biological mechanisms in health and disease.

Dragon-king-like extreme events in coupled bursting neurons.

We present evidence of extreme events in two Hindmarsh-Rose (HR) bursting neurons mutually interacting via two different coupling configurations: chemical synaptic- and gap junctional-type diffusive coupling. A dragon-king-like probability distribution of the extreme events is seen for combinations of synaptic coupling where small- to medium-size events obey a power law and the larger events that cross an extreme limit are outliers. The extreme events originate due to instability in antiphase synchronization of the coupled systems via two different routes, intermittency and quasiperiodicity routes to complex dynamics for purely excitatory and inhibitory chemical synaptic coupling, respectively. For a mixed type of inhibitory and excitatory chemical synaptic interactions, the intermittency route to extreme events is only seen. Extreme events with our suggested distribution is also seen for gap junctional-type diffusive, but repulsive, coupling where the intermittency route to complexity is found. A simple electronic experiment using two diffusively coupled analog circuits of the HR neuron model, but interacting in a repulsive way, confirms occurrence of the dragon-king-like extreme events.

Inverse stochastic resonance in networks of spiking neurons.

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron’s intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.

Network-timing-dependent plasticity.

Bursts of activity in networks of neurons are thought to convey salient information and drive synaptic plasticity. Here we report that network bursts also exert a profound effect on Spike-Timing-Dependent Plasticity (STDP). In acute slices of juvenile rat somatosensory cortex we paired a network burst, which alone induced long-term depression (LTD), with STDP-induced long-term potentiation (LTP) and LTD. We observed that STDP-induced LTP was either unaffected, blocked or flipped into LTD by the network burst, and that STDP-induced LTD was either saturated or flipped into LTP, depending on the relative timing of the network burst with respect to spike coincidences of the STDP event. We hypothesized that network bursts flip STDP-induced LTP to LTD by depleting resources needed for LTP and therefore developed a resource-dependent STDP learning rule. In a model neural network under the influence of the proposed resource-dependent STDP rule, we found that excitatory synaptic coupling was homeostatically regulated to produce power law distributed burst amplitudes reflecting self-organized criticality, a state that ensures optimal information coding.

Correlated neuronal activity and its relationship to coding, dynamics and network architecture.

Correlated neuronal activity and its relationship to coding, dynamics and network architecture.

Modelling of neocortical neural dynamics during human focal seizures

Recent advances in microelectrode array (MEA) recordings have made possible the simultaneous recordings of spiking activity in ensembles of neocortical single neurons during human focal seizures. As a result, a much more detailed picture of seizure initiation and spread has begun to emerge [1]. Here, we combine single neuron spiking and local field potential (LFP) data obtained from 96-MEA recordings with mathematical modelling to characterize the synaptic coupling and parameters required to sustain the neural dynamics observed in the two main types of epileptic seizures identified in the studied patients: spike-wave-complex (SWCs ~2-3 Hz) seizures and gamma-band (40-60 Hz) seizures, respectively. We model the neocortex under a 96-MEA (4mm x 4mm) with Izhikevich type neurons [2,3]. There are 28x28 minicolumns in the model. Each minicolumn is 25μm apart from each other and has 12 excitatory neurons and 4 interneurons. The neurons are synaptically connected up to a radius of 75μm and a synaptic delay of 2ms. (Connectivity drops to zero close to the MEA boundaries). Each neuron is driven by an independent Poisson input simulating background synaptic activities (i.e. high Poisson rates close to a few kHz, but individual Poisson events are of small amplitude). We simulate each of the two types of epileptic seizures by controlling the synaptic strengths amongst neurons and the Poisson drive. Dynamics similar to that in gamma-band seizures (Fig. ​(Fig.1)1) were obtained in models that combined strong mutual inhibitory synaptic couplings (gi->i), strong inhibitory to excitatory synaptic couplings (gi->e), and strong Poisson drive to both the pyramidal and interneuronal populations. The resulting single neuron spiking patterns (in both the inhibitory and excitatory cases) remained irregular, despite that they lead to sustained narrow gamma band LFP oscillations, consistent with the observations from the neuronal spiking data recorded from the patients. Dynamics similar to SWC seizures were obtained by decreasing both mutual inhibitory coupling (gi->i ) and inhibitory to excitatory coupling (gi->e), as well as by reducing the Poisson drive to the inhibitory interneuron populations. During each SWC discharge (Figure ​(Figure1),1), we observed the spread of neuronal spiking activity and recruitment of pyramidal cells starting from a focus, accompanied by strong coherent LFP. In the model, the participation of interneurons in SWC generation is minimal due to the weak gi->i,e and low Poisson drive. Our model suggests that gamma-band seizures require strong inhibitory conductance and participation of both excitatory and inhibitory populations, while SWC seizures require weaker inhibitory conductances and are mostly driven by excitatory (pyramidal) neurons. We are working towards a conductance-based network model in which intra and extracellular ionic concentrations are included to explore how disregulation of ionic concentrations can trigger each of the two types of seizures. Figure 1 Neuronal spiking raster plots (gamma-band seizure: left; SWC seizure: right).

Conflicting effects of excitatory synaptic and electric coupling on the dynamics of square-wave bursters

Using two-cell and 50-cell networks of square-wave bursters, we studied how excitatory coupling of individual neurons affects the bursting output of the network. Our results show that the effects of synaptic excitation vs. electrical coupling are distinct. Increasing excitatory synaptic coupling generally increases burst duration. Electrical coupling also increases burst duration for low to moderate values, but at sufficiently strong values promotes a switch to highly synchronous bursts where further increases in electrical or synaptic coupling have a minimal effect on burst duration. These effects are largely mediated by spike synchrony, which is determined by the stability of the in-phase spiking solution during the burst. Even when both coupling mechanisms are strong, one form (in-phase or anti-phase) of spike synchrony will determine the burst dynamics, resulting in a sharp boundary in the space of the coupling parameters. This boundary exists in both two cell and network simulations. We use these results to interpret the effects of gap-junction blockers on the neuronal circuitry that underlies respiration.

Optimal Intrinsic Dynamics for Bursting in a Three-Cell Network

Previous numerical and analytical work has shown that synaptic coupling can allow a network of model neurons to synchronize despite heterogeneity in intrinsic parameter values. In particular, synchronous bursting oscillations can arise in a network with excitatory synaptic coupling, even in the absence of intrinsically bursting neurons. In this work, we explore how the intrinsic dynamics of neurons within a reduced three-cell network influence its ability to exhibit synchronous bursting and the frequency range over which such activity can occur. We establish necessary and sufficient conditions for the existence of synchronous bursting solutions and perform related numerical experiments in three-cell networks that include a quiescent cell, a tonically active cell, and a third added cell. Our results show that, in most cases, the addition of a quiescent cell is optimal for synchronous network bursting, in a variety of ways, and that intrinsically bursting cells can be detrimental to synchronous bursting, and we explain the mechanisms underlying these effects. These findings may help explain how robust synchronous oscillations arise in neuronal central pattern generators, such as the mammalian inspiratory network, despite the presence of significant cellular heterogeneity. They also support the idea that intrinsic burst capabilities of individual cells need not be central to these networks' rhythms.

Neurons Skip a Beat during Fast Ripples

Fast ripples are EEG transients emanating from epileptic foci, but fast-ripple frequencies far exceed maximal neuronal firing rates. In this issue of Neuron, Menendez de la Prida and coworkers propose that out-of-phase firing of a subpopulation of neurons during physiological ripple activity effectively doubles the ripple frequency to produce fast ripples.

Propagation of Seizure-like Activity in a Model of Neocortex

Seizures in pediatric epilepsy are often associated with spreading, repetitive bursting activity in neocortex. The authors examined onset and propagation of seizure-like activity using a computational model of cortical circuitry. The model includes two pyramidal cell types and four types of inhibitory interneurons. Each neuron is represented by a multicompartmental model with biophysically realistic ion channels. The authors determined the role of bursting neurons and found that their capability of driving network oscillations is most prominent in networks with either weak or relatively strong excitatory synaptic coupling. Synaptic coupling strength was varied in a separate set of simulations to examine its role in network bursting. Oscillations both between cortical layers (vertical oscillations) and between cortical areas (horizontal oscillations) emerge at moderate excitatory coupling strengths. For horizontal propagation, existence of a fast-conducting fiber system and its properties are critical. Seizure-like oscillatory activity may originate from single neurons or small networks, and that activity may propagate in two principal fashions: one that can be represented by a unidirectional (pacemaker)-type process and the other as multi- or bidirectional propagating waves. The frequency of the bursting patterns relates to underlying propagating activity that can either sustain or disrupt the ongoing oscillation.

Generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena

The integrate-and-fire (IF) neuron model and the piecewise-linear version of FitzHugh-Nagumo (PL) neuron model with a time scale parameter mu are frequently being used in the study of synchronization phenomena. Although the two models are regarded to be different type, we show a certain equivalence between them by deriving the coupled IF model of an improved version with a firing duration from the recovery variable coupled system of the PL model, under taking the limit of mu-->0 without a loss of any coupling properties. In the coupled IF model with the duration time, the synchronization behavior of a pair of neurons with excitatory or inhibitory synaptic coupling can be systematically explored in terms of three parameters in the model (synaptic strength, decaying relaxation rate of the synaptic coupling, and the parameter exhibiting the firing duration). We find some irregularly synchronous behavior with or without constant firing order alternations. We show that the duration of an impulse plays an important role in synchronization phenomena.

Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters

This work explains a mechanism through which the introduction of excitatory synaptic coupling between two model cells, one of which is excitable and the other of which is tonically active when uncoupled, leads to bursting in the resulting two-cell network. This phenomenon can arise when the individual cells are conditional relaxation oscillators, in that they can be tuned to engage in relaxation oscillations, or when they are conditional square-wave bursters. The mechanism is illustrated with a model for conditional pacemaker neurons in the pre-Bötzinger complex as well as with a reduced form of this model. In the relaxation oscillator case, a periodic bursting solution is proved to exist in the singular limit, under a pair of general conditions. These conditions relate the durations of the silent and active phases of the bursting solution to the locations of certain structures in the phase plane, at appropriate synaptic input strengths. Further, additional conditions on the relative flow rates in the silent and active phases are proved to imply the uniqueness and asymptotic stability of the bursting solution.

Instability of synchronized motion in nonlocally coupled neural oscillators

We study nonlocally coupled Hodgkin-Huxley equations with excitatory and inhibitory synaptic coupling. We investigate the linear stability of the synchronized solution, and find numerically various nonuniform oscillatory states such as chimera states, wavy states, clustering states, and spatiotemporal chaos as a result of the instability.

Surprising Effects of Synaptic Excitation

Typically, excitatory synaptic coupling is thought of as an influence that accelerates and propagates firing in neuronal networks. This paper reviews recent results explaining how, contrary to these expectations, the presence of excitatory synaptic coupling can drastically slow oscillations in a network and how localized, sustained activity can arise in a network with purely excitatory coupling, without sustained inputs. These two effects stem from interactions of excitatory coupling with two different forms of intrinsic neuronal dynamics, and both serve to highlight the fact that the influence of synaptic coupling in a network depends strongly on the intrinsic properties of cells in the network.

Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node

We give a geometric analysis of canards of folded node type in singularly perturbed systems with two-dimensional (2D) folded critical manifold using the blow-up technique. The existence of two primary canards is known provided a nonresonance condition $\mu\notin\mathbb{N}$ is satisfied, where $\mu=\lambda_1/\lambda_2$ denotes the ratio of the eigenvalues of the associated folded singularity of the reduced flow. We show that, due to resonances, bifurcation of secondary canards occurs. We give a detailed geometric explanation of this phenomenon using an extension of Melnikov theory to prove a transcritical bifurcation of canards for odd $\mu$. Furthermore, we show numerically the existence of a pitchfork bifurcation for even $\mu$ and a novel turning point bifurcation close to $\mu\in\mathbb{N}$. We conclude the existence of $[(\mu-1)/2]$ secondary canards away from the resonances. Finally, we apply our results to a network of Hodgkin--Huxley neurons with excitatory synaptic coupling and explain the observed slowing of the firing rate of the synchronized network due to the existence of canards of folded node type.

Gap junctions promote synchronous activities in a network of inhibitory interneurons

By using a single compartment biophysical model of a fast spiking interneuron the synchronization properties of a pair of cells, coupled by electrical and inhibitory synapses, are investigated. The inhibitory and excitatory synaptic couplings are modeled in order to reproduce the experimental time course of the corresponding currents. It is shown that increasing the conductance value of the electrical synapses enhances the synchronization between the spike trains of the two cells. Moreover, increasing either the decay time constant of the inhibitory current or the firing frequency of the cells favours the emergence of synchronous discharges.

Localized activity patterns in excitatory neuronal networks

The existence of localized activity patterns, or bumps, has been investigated in a variety of spatially distributed neuronal network models that contain both excitatory and inhibitory coupling between cells. Here we show that a neuronal network with purely excitatory synaptic coupling can exhibit localized activity. Bump formation ensues from an initial transient synchrony of a localized group of cells, followed by the emergence of desynchronized activity within the group. Transient synchrony is shown to promote recruitment of cells into the bump, while desynchrony is shown to be good for curtailing recruitment and sustaining oscillations of those cells already within the bump. These arguments are based on the geometric structure of the phase space in which solutions of the model equations evolve. We explain why bump formation and bump size are very sensitive to initial conditions and changes in parameters in this type of purely excitatory network, and we examine how short-term synaptic depression influences the characteristics of bump formation.

Analysis of a Canard Mechanism by Which Excitatory Synaptic Coupling Can Synchronize Neurons at Low Firing Frequencies

A population of oscillatory Hodgkin--Huxley (HH) model neurons is shown numerically to exhibit a behavior in which the introduction of excitatory synaptic coupling synchronizes and dramatically slows firing. This effect contrasts with the standard theory that recurrent synaptic excitation promotes states of rapid, sustained activity, independent of intrinsic neuronal dynamics. The observed behavior is not due to simple depolarization block nor to standard elliptic bursting, although it is related to these phenomena. We analyze this effect using a reduced model for a single, self-coupled HH oscillator. The mechanism explained here involves an extreme form of delayed bifurcation in which the development of a vortex structure through interaction of fast and slow subsystems pins trajectories near a surface that consists of unstable equilibria of a certain reduced system, in a canard-like manner. Using this vortex structure, a new passage time calculation is used to approximate the interspike time interval. We...

Localized activity patterns in excitatory neuronal networks

The existence of localized activity patterns, or bumps, has been investigated in a variety of spatially distributed neuronal network models that contain both excitatory and inhibitory coupling between cells. Here we show that a neuronal network with purely excitatory synaptic coupling can exhibit localized activity. Bump formation ensues from an initial transient synchrony of a localized group of cells, followed by the emergence of desynchronized activity within the group. Transient synchrony is shown to promote recruitment of cells into the bump, while desynchrony is shown to be good for curtailing recruitment and sustaining oscillations of those cells already within the bump. These arguments are based on the geometric structure of the phase space in which solutions of the model equations evolve. We explain why bump formation and bump size are very sensitive to initial conditions and changes in parameters in this type of purely excitatory network, and we examine how short-term synaptic depression influences the characteristics of bump formation.