Excitatory Coupling Research Articles

Computational model prospective on the observation of proictal states in epileptic neuronal systems

Epilepsy is a pathological condition of the human central nervous system in which normal brain functions are impaired by unexpected transitions to states called seizures. We developed a lumped neuronal model that has the property of switching between two states as a result of intrinsic or extrinsic perturbations, such as noisy fluctuations. In one version of the model, seizure risk is controlled by a single connectivity parameter representing excitatory couplings between two model lumps. We show that this risk can be reconstructed from calculation of the cross-covariance between the activities of the two neural populations during the nonictal phase. In a second simulation sequence, we use a system of 10 interconnected lumps with randomly generated connectivity matrices. We show again that the tendency to develop seizures can be inferred from the cross-covariances calculated during the nonictal states. Our conclusion is that the risk of epileptic transitions in biological systems can be objectively quantified. This article is part of a Supplemental Special Issue entitled The Future of Automated Seizure Detection and Prediction.

Serotonin Transporter Genotype Modulates Subgenual Response to Fearful Faces Using an Incidental Task

This study assessed the impact of serotonin transporter genotype (5-HTTLPR) on regional responses to emotional faces in the amygdala and subgenual cingulate cortex (sgACC), while subjects performed a gender discrimination task. Although we found no evidence for greater amygdala reactivity or reduced amygdala-sgACC coupling in short variant 5-HTTLPR homozygotes (s/s), we observed an interaction between genotype and emotion in sgACC. Only long variant homozygotes (la/la) exhibited subgenual deactivation to fearful versus neutral faces, whereas the effect in s/s subjects was in the other direction. This absence of subgenual deactivation in s/s subjects parallels a recent finding in depressed subjects [Grimm, S., Boesiger, P., Beck, J., Schuepbach, D., Bermpohl, F., Walter, M., et al. Altered negative BOLD responses in the default-mode network during emotion processing in depressed subjects. Neuropsychopharmacology, 34, 932-943, 2009]. Taken together, the findings suggest that subgenual cingulate activity may play an important role in regulating the impact of aversive stimuli, potentially conferring greater resilience to the effects of aversive stimuli in la/la subjects. Using dynamic causal modeling of functional magnetic resonance imaging data, we explored the effects of genotype on effective connectivity and emotion-specific changes in coupling across a network of regions implicated in social processing. Viewing fearful faces enhanced bidirectional excitatory coupling between the amygdala and the fusiform gyrus, and increased the inhibitory influence of the amygdala over the sgACC, although this modulation of coupling did not differ between the genotype groups. The findings are discussed in relation to the role of sgACC and serotonin in moderating responses to aversive stimuli [Dayan, P., & Huys, Q. J., Serotonin, inhibition, and negative mood. PLoS Comput Biol, 4, e4, 2008; Mayberg, H. S., Liotti, M., Brannan, S. K., McGinnis, S., Mahurin, R. K., Jerabek, P. A., et al. Reciprocal limbic-cortical function and negative mood: Converging PET findings in depression and normal sadness. Am J Psychiatry, 156, 675-682, 1999].

Spectral properties of directed random networks with modular structure

We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different values of correlation among their entries. Spectra of random networks with completely uncorrelated entries show a circular distribution with delocalized eigenvectors, whereas networks with correlated entries have localized eigenvectors. In order to understand the origin of localization we track the spectra as a function of connection probability and directionality. As connections are made directed, eigenstates start occurring in complex-conjugate pairs and the eigenvalue distribution combined with the localization measure shows a rich pattern. Moreover, for a very well distinguished community structure, the whole spectrum is localized except few eigenstates at the boundary of the circular distribution. As the network deviates from the community structure there is a sudden change in the localization property for a very small value of deformation from the perfect community structure. We search for this effect for the whole range of correlation strengths and for different community configurations. Furthermore, we investigate spectral properties of a metabolic network of zebrafish and compare them with those of the model networks.

Chimera states and collective chaos in pulse-coupled neural networks

Understanding the collective motion of networks of oscillators is crucial in many contexts, starting from neuronal circuits [1]. So far, most of the efforts have been devoted to the characterization of strong forms of synchronization. However, more subtle phenomena, like the onset of coherent oscillations in an ensemble of neurons can also play a relevant role for information coding. A peculiar coherent state, termed Chimera, appears in two symmetrically coupled populations of oscillators, where a population fully synchronizes while the other exhibit an asynchronous dynamics [2]. This can represents an idealized mathematical representation of the so-called unihemispheric sleep. Many creatures sleep with only half their brain at a time [3]. Such phenomenon was first reported in dolphins and other sea mammals and, recently, in birds; when brain waves are recorded, the awake side of the brain shows desynchronized electrical activity, corresponding to millions of neurons oscillating out of phase, whereas the sleeping side is highly synchronized. In our study we have investigated the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by excitatory coupling [4]. Upon varying the coupling strengths between and within the two populations, we found symmetry-breaking transitions that lead to the onset of various chimera states. To be more specific, in the observed chimera states one population is fully synchronized, while the other one is in the so-called Partially Synchronous (PS) regime. This regime is characterized by a coherent periodic activity at a collective level (somehow corresponding to to the Local Field Potential), while the single neurons behaves quasi-periodically [5]. To our knowledge this represents the first evidence of chimera states in pulse-coupled neural networks. Furthermore a new regime, where the two populations are both PS but with a different degree of synchronization have been also observed. Even more interesting is the identification of a regions of parameters where the coherent activity of the network, characterized by collective variables, becomes chaotic. Collective chaos, meant as irregular dynamics of coarse-grained observables, has been found in ensembles of fully coupled one-dimensional maps as well as in two-dimensional continuous-time oscillators. In both classes of models, the single dynamical unit can behave chaotically under the action of a periodic forcing. Only a few examples of low-dimensional chaotic collective motion have been found in ensembles of phase oscillators because in this setup there is little space for a high-dimensional dynamics [6]. Our results reveal for the first time chaos at a macroscopic level in a neural network. The computation of the the finite-amplitude Lyapunov exponent allows us to firmly establish the chaoticity of the (collective) dynamics in a finite region of the phase plane. The further numerical study of the standard Lyapunov spectrum reveals the presence of several positive exponents, indicating that the microscopic dynamics is high-dimensional.

Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity

Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.

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.

Quantifying the Relative Contributions of Divisive and Subtractive Feedback to Rhythm Generation

Biological systems are characterized by a high number of interacting components. Determining the role of each component is difficult, addressed here in the context of biological oscillations. Rhythmic behavior can result from the interplay of positive feedback that promotes bistability between high and low activity, and slow negative feedback that switches the system between the high and low activity states. Many biological oscillators include two types of negative feedback processes: divisive (decreases the gain of the positive feedback loop) and subtractive (increases the input threshold) that both contribute to slowly move the system between the high- and low-activity states. Can we determine the relative contribution of each type of negative feedback process to the rhythmic activity? Does one dominate? Do they control the active and silent phase equally? To answer these questions we use a neural network model with excitatory coupling, regulated by synaptic depression (divisive) and cellular adaptation (subtractive feedback). We first attempt to apply standard experimental methodologies: either passive observation to correlate the variations of a variable of interest to system behavior, or deletion of a component to establish whether a component is critical for the system. We find that these two strategies can lead to contradictory conclusions, and at best their interpretive power is limited. We instead develop a computational measure of the contribution of a process, by evaluating the sensitivity of the active (high activity) and silent (low activity) phase durations to the time constant of the process. The measure shows that both processes control the active phase, in proportion to their speed and relative weight. However, only the subtractive process plays a major role in setting the duration of the silent phase. This computational method can be used to analyze the role of negative feedback processes in a wide range of biological rhythms.

Traveling echo waves in an array of excitable elements with time-delayed coupling

We study time-delayed coupling in one-dimensional arrays of discrete excitable FitzHugh-Nagumo elements. For small time delays in an excitatory coupling, noise-triggered spikes undergo a slight prolongation. For larger delay times, the coupling to adjacent elements leads to a splitting of spikes and an "echo" effect that produces dampened series of spikes. For very large delay times, a transition to a stationary regime appears, as the spikes are sustained by mutual excitations, resulting in antiphase synchronization of all elements. We characterize several features exhibited by the system, such as speed and duration of pulses as well as bifurcations leading to the stationary regime.

Dynamic interplay of excitatory and inhibitory coupling modes of neuronal L-type calcium channels

L-type voltage-gated calcium channels (LTCCs) have long been considered as crucial regulators of neuronal excitability. This role is thought to rely largely on coupling of LTCC-mediated Ca(2+) influx to Ca(2+)-dependent conductances, namely Ca(2+)-dependent K(+) (K(Ca)) channels and nonspecific cation (CAN) channels, which mediate afterhyperpolarizations (AHPs) and afterdepolarizations (ADPs), respectively. However, in which manner LTCCs, K(Ca) channels, and CAN channels co-operate remained scarcely known. In this study, we examined how activation of LTCCs affects neuronal depolarizations and analyzed the contribution of Ca(2+)-dependent potassium- and cation-conductances. With the use of hippocampal neurons in primary culture, pulsed current-injections were applied in the presence of tetrodotoxin (TTX) for stepwise depolarization and the availability of LTCCs was modulated by BAY K 8644 and isradipine. By varying pulse length and current strength, we found that weak depolarizing stimuli tend to be enhanced by LTCC activation, whereas in the course of stronger depolarizations LTCCs counteract excitation. Both effect modes appear to involve the same channels that mediate ADP and AHP, respectively. Indeed, ADPs were activated at lower stimulation levels than AHPs. In the absence of TTX, activation of LTCCs prolonged or shortened burst firing, depending on the initial burst duration, and invariably augmented brief unprovoked (such as excitatory postsynaptic potentials) and provoked electrical events. Hence, regulation of membrane excitability by LTCCs involves synchronous activity of both excitatory and inhibitory Ca(2+)-activated ion channels. The overall enhancing or dampening effect of LTCC stimulation on excitability does not only depend on the relative abundance of the respective coupling partner but also on the stimulus intensity.

Computer simulations of neural mechanisms explaining upper and lower limb excitatory neural coupling

BackgroundWhen humans perform rhythmic upper and lower limb locomotor-like movements, there is an excitatory effect of upper limb exertion on lower limb muscle recruitment. To investigate potential neural mechanisms for this behavioral observation, we developed computer simulations modeling interlimb neural pathways among central pattern generators. We hypothesized that enhancement of muscle recruitment from interlimb spinal mechanisms was not sufficient to explain muscle enhancement levels observed in experimental data.MethodsWe used Matsuoka oscillators for the central pattern generators (CPG) and determined parameters that enhanced amplitudes of rhythmic steady state bursts. Potential mechanisms for output enhancement were excitatory and inhibitory sensory feedback gains, excitatory and inhibitory interlimb coupling gains, and coupling geometry. We first simulated the simplest case, a single CPG, and then expanded the model to have two CPGs and lastly four CPGs. In the two and four CPG models, the lower limb CPGs did not receive supraspinal input such that the only mechanisms available for enhancing output were interlimb coupling gains and sensory feedback gains.ResultsIn a two-CPG model with inhibitory sensory feedback gains, only excitatory gains of ipsilateral flexor-extensor/extensor-flexor coupling produced reciprocal upper-lower limb bursts and enhanced output up to 26%. In a two-CPG model with excitatory sensory feedback gains, excitatory gains of contralateral flexor-flexor/extensor-extensor coupling produced reciprocal upper-lower limb bursts and enhanced output up to 100%. However, within a given excitatory sensory feedback gain, enhancement due to excitatory interlimb gains could only reach levels up to 20%. Interconnecting four CPGs to have ipsilateral flexor-extensor/extensor-flexor coupling, contralateral flexor-flexor/extensor-extensor coupling, and bilateral flexor-extensor/extensor-flexor coupling could enhance motor output up to 32%. Enhancement observed in experimental data exceeded 32%. Enhancement within this symmetrical four-CPG neural architecture was more sensitive to relatively small interlimb coupling gains. Excitatory sensory feedback gains could produce greater output amplitudes, but larger gains were required for entrainment compared to inhibitory sensory feedback gains.ConclusionsBased on these simulations, symmetrical interlimb coupling can account for much, but not all of the excitatory neural coupling between upper and lower limbs during rhythmic locomotor-like movements.

A numerical solver for a nonlinear Fokker–Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [15,14], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker–Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker–Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker–Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [15] to further simplify the kinetic theory.

The interplay of excitatory and inhibitory coupling modes is crucial for the regulation of neuronal electrical activities by L-type calcium channels

Background Neuronal L-type voltage-gated calcium channels (LTCCs) have long been implicated in the regulation of excitability. This function appears to be related to the coupling of LTCC-mediated Ca influx to Ca-dependent conductances, such as KCa channels, e.g. KV2.x (SK), and nonspecific cation (CAN) channels. However, despite numerous data related to the molecular functioning of LTCCs, little is known about the actual role of these channels in cellular electrical excitation. In this study, we examined how activation of LTCCs affects neuronal depolarizations and analyzed the contribution of Ca-dependent potassium and cation conductances.

A network of pyramidal neurons is sensitive to the timing of its excitatory inputs

The transmission of excitatory inputs by a network of coupled pyramidal cells is investigated by means of numerical simulations. The pyramidal cell models are coupled by excitatory synapses and each one receives an excitatory pulse at a random time extracted from a Gaussian distribution. Moreover, each cell model is injected with a noisy current. It was found that the excitatory coupling promotes the transmission of the synaptic inputs on a time scale of a few ms.

Epileptic seizures: Quakes of the brain?

A dynamical analogy supported by five scale-free statistics (the Gutenberg-Richter distribution of event sizes, the distribution of interevent intervals, the Omori and inverse Omori laws, and the conditional waiting time until the next event) is shown to exist between two classes of seizures ("focal" in humans and generalized in animals) and earthquakes. Increments in excitatory interneuronal coupling in animals expose the system's dependence on this parameter and its dynamical transmutability: moderate increases lead to power-law behavior of seizure energy and interevent times, while marked ones to scale-free (power-law) coextensive with characteristic scales and events. The coextensivity of power law and characteristic size regimes is predicted by models of coupled heterogeneous threshold oscillators of relaxation and underscores the role of coupling strength in shaping the dynamics of these systems.

Analysis of firing behaviors in networks of pulse-coupled oscillators with delayed excitatory coupling

In this paper, we investigate the firing behaviors in networks of pulse-coupled oscillators with delayed excitatory coupling according to the coupling strength epsilon and delay tau. We find out that the parameter space A={(epsilon,tau)|0<tau<1,0<epsilon<1} can be partitioned into two regions A(1), A(2) in such a way that the network will have apparently different firing properties on them. In A(1), the firing behavior is relatively simple for rigorous analysis, while it is more complicated on A(2). First, we show that the delay tau is a lower bound for the inter-spike intervals of each oscillator on A(1). Using this lower bound, three important properties of the firing on A(1) are obtained: (a) Any complete synchronized solution is a solution with period 1; (b) If two oscillators fire at same time, and they have the same coupling strength from each other and from other oscillators, then, they will be synchronized forever; (c) The firing order of two oscillators is always preserved. However, examples can be provided to show that these properties do not hold for the region A(2). Yet, numerical simulation still reveals some interesting phenomenon on A(2): (a) Completely synchronized solutions are prevalent; (b) Given (tau,epsilon)inA(2), the fraction of the initial values that will lead to complete synchronization will converge along with increasing network size.

Mechanism for the Universal Pattern of Activity in Developing Neuronal Networks

Spontaneous episodic activity is a fundamental mode of operation of developing networks. Surprisingly, the duration of an episode of activity correlates with the length of the silent interval that precedes it, but not with the interval that follows. Here we use a modeling approach to explain this characteristic, but thus far unexplained, feature of developing networks. Because the correlation pattern is observed in networks with different structures and components, a satisfactory model needs to generate the right pattern of activity regardless of the details of network architecture or individual cell properties. We thus developed simple models incorporating excitatory coupling between heterogeneous neurons and activity-dependent synaptic depression. These models robustly generated episodic activity with the correct correlation pattern. The correlation pattern resulted from episodes being triggered at random levels of recovery from depression while they terminated around the same level of depression. To explain this fundamental difference between episode onset and termination, we used a mean field model, where only average activity and average level of recovery from synaptic depression are considered. In this model, episode onset is highly sensitive to inputs. Thus noise resulting from random coincidences in the spike times of individual neurons led to the high variability at episode onset and to the observed correlation pattern. This work further shows that networks with widely different architectures, different cell types, and different functions all operate according to the same general mechanism early in their development.

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.

IMPOSSIBILITY OF ASYMPTOTIC SYNCHRONIZATION FOR PULSE-COUPLED OSCILLATORS WITH DELAYED EXCITATORY COUPLING

Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.

Analysis of stability of neural network with inhibitory neurons

Phase coding in a neural network composed of neural oscillators with inhibitory neurons was studied based on the theory of stochastic phase dynamics. We found that with increasing the coupling coefficients of inhibitory neural oscillators, the firing density in excitatory population transits to a critical state. In this case, when we increase the inhibitory coupling, the firing density will come into dynamic balance again and tend to a fixed value gradually. According to the phenomenon, in the paper we found parameter regions to exhibit those different population states, called dividing zones including flat fading zone, rapid fading zone and critical zone. Based on the dividing zones we can choose the number ratio between inhibitory neurons and excitatory neurons in the neural network, and estimate the coupling action of inhibitory population and excitatory population. Our research also shows that the balance value, enabling the firing density to reach the dynamic balance, does not depend on initial conditions. In addition, the critical value in critical state is only related to the number ratio between inhibitory neurons and excitatory neurons, but is independent of inhibitory coupling and excitatory coupling.

Pulse-coupled neuron models as investigative tools for musical consonance

We investigate the mode locking properties of simple dynamical models of pulse-coupled neurons to two tones, i.e., simple musical intervals. A recently proposed nonlinear synchronization theory of musical consonance links the subjective ranking from consonant to dissonant intervals to the universal ordering of robustness of mode locking ratios in forced nonlinear oscillators. The theory was illustrated using two leaky integrate-and-fire neuron models with mutual excitatory coupling, with each neuron firing at one of the two frequencies in the musical interval. We show that the ordering of mode locked states in such models is not universal, but depends on coupling strength. Further, unless the coupling is weak, the observed ratio of firing frequencies is higher than that of the input tones. We finally explore generic aspects of a possible synchronization theory by driving the model neurons with sinusoidal forcing, leading to down-converted, more realistic firing rates. This model exhibits one-to-one entrainment when the input frequencies are in simple ratios. We also consider the robustness to the presence of noise that is present in the neural firing activity. We briefly discuss agreements and discrepancies between predictions from this theory and physiological/psychophysical data, and suggest directions in which to develop this theory further.