Neuronal Coupling Research Articles

Stable Antiphase Oscillations in a Network of Electrically Coupled Model Neurons

We consider a model of two identical neurons with electrical coupling and give a rigorous analysis for when the network exhibits stable antiphase behavior. Each neuron is modeled as a relaxation oscillator, and the main technique used in the analysis is geometric singular perturbation theory. Using fast/slow analysis, we derive a one-dimensional map; the antiphase solution corresponds to a fixed point of this map. Detailed analysis of the map, along with its derivative, leads to precise conditions on the duty cycle of an individual cell for when there exists an antiphase solution and when it is stable, for sufficiently weak electrical coupling. The results presented here extend our previous analysis [D. Terman et al., SIAM J. Appl. Dyn. Syst., 10 (2011), pp. 1127--1153] to more biophysical neuronal models.

STDP induced synchrony in inhibitory neural networks: theory and experiments

Gamma rhythms have been the focus of significant research interest within the neuroscience community in recent years [1]. Earlier theoretical studies focused on the question: how can a network of GABA containing neurons generate gamma oscillations? The findings suggest that for non-instantaneous synaptic events, inhibition rather than excitation is a better synchronizing mechanism for the generation of gamma rhythms [2]. Synchrony in inhibitory neural networks however is extremely sensitive to intrinsic heterogeneity in the network [3]. Based on the evidence for spike timing dependent plasticity (STDP) in inhibitory neurons [4,5], we hypothesize that STDP of inhibitory synapses can promote robust neural synchrony in inhibitory neuronal networks in the presence of heterogeneity. We investigate our hypothesis in a computational (Figure ​(Figure1a)1a) and a hybrid (Figure ​(Figure1b)1b) uni-directionally coupled network (UCI) of two fast-spiking inhibitory neurons. In the computational model, each neuron is modeled using the Hodgkin-Huxley (HH) framework [4]. Heterogeneity (H) is modeled by the difference in the intrinsic firing activity of the coupled neurons resulting from different DC current input. In the presence of STDP, the strength of synaptic coupling between the coupled neurons is modeled using a linear additive rule as: gs(t) = gs(t – 1) + ΔgSTDP(Δt), where Δt = tA – tB is the time interval between successive spikes of the post-synaptic and the pre-synaptic neurons and ΔgSTDP is the STDP rule adapted from [4]. In Figure ​Figure1a,1a, we demonstrate the effect of STDP on synchrony between coupled neurons in the presence of and the absence of STDP for network heterogeneity H=12%. Theoretical analysis using the concept of spike time response curves and Arnold tongue revealed that STDP induced 1:1 synchrony in the UCI network is (i) robust against a large range of heterogeneity in the intrinsic firing activity of coupled neurons, and (ii) in-phase i.e., Δt ≈ 0. Furthermore, the time to in-phase synchronization increases with increasing heterogeneity. Figure 1 a) Theoretical model of UCI. Autaptic synapse is introduced to mimic spike frequency adaptation in neuronal firing activity. b) Hybrid UCI network. Dynamic clamp experimental results for experimental protocol with fixed static-synaptic strength gs(0)=0.5 ... We used the dynamic clamp technique to construct a hybrid UCI network consisting of an HH based model of a inhibitory neuron coupled to a living inhibitory neuron in the stratum oriens of area CA1 of the hippocampus. Whole cell patch clamp recordings were obtained from the live cell under the following experimental protocols: (i) Fix H, vary the static synapse coupling strength gs(0) and (ii) Fix static synapse coupling strength gs(0) and vary H. In Figure ​Figure1b,1b, we present results from the second experimental protocol. We see that as predicted by our theoretical model, the time to in phase neural synchrony in the hybrid UCI network increases with increasing heterogeneity. We conclude that STDP of inhibitory synapses is a putative mechanism for robust neural synchrony in inhibitory neuronal networks.

Nearly Extensive Sequential Memory Lifetime Achieved by Coupled Nonlinear Neurons

Many cognitive processes rely on the ability of the brain to hold sequences of events in short-term memory. Recent studies have revealed that such memory can be read out from the transient dynamics of a network of neurons. However, the memory performance of such a network in buffering past information has been rigorously estimated only in networks of linear neurons. When signal gain is kept low, so that neurons operate primarily in the linear part of their response nonlinearity, the memory lifetime is bounded by the square root of the network size. In this work, I demonstrate that it is possible to achieve a memory lifetime almost proportional to the network size, "an extensive memory lifetime," when the nonlinearity of neurons is appropriately used. The analysis of neural activity revealed that nonlinear dynamics prevented the accumulation of noise by partially removing noise in each time step. With this error-correcting mechanism, I demonstrate that a memory lifetime of order N/logN can be achieved.

Multiple firing coherence resonances in excitatory and inhibitory coupled neurons

The impact of inhibitory and excitatory synapses in delay-coupled Hodgkin–Huxley neurons that are driven by noise is studied. If both synaptic types are used for coupling, appropriately tuned delays in the inhibition feedback induce multiple firing coherence resonances at sufficiently strong coupling strengths, thus giving rise to tongues of coherency in the corresponding delay-strength parameter plane. If only inhibitory synapses are used, however, appropriately tuned delays also give rise to multiresonant responses, yet the successive delays warranting an optimal coherence of excitations obey different relations with regards to the inherent time scales of neuronal dynamics. This leads to denser coherence resonance patterns in the delay-strength parameter plane. The robustness of these findings to the introduction of delay in the excitatory feedback, to noise, and to the number of coupled neurons is examined. Mechanisms underlying our observations are revealed, and it is suggested that the regularity of spiking across neuronal networks can be optimized in an unexpectedly rich variety of ways, depending on the type of coupling and the duration of delays.

The fractional-order modeling and synchronization of electrically coupled neuron systems

In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald–Letnikov discretization process which is easily implemented and reliably accurate.

Transition of phase locking modes in a minimal neuronal network

We investigate the dynamics of phase locking in a minimal neuronal network, which is composed of two Morris–Lecar neurons that are coupled by inhibitory and excitatory synapses as the synaptic strength is varied. Studies show that the synaptic strength can induce various phase locking modes and complex chaotic behaviors. In particular, two coupled neurons may display the complicated transitions between various periodic phase locking modes and chaotic states. It is shown that those transitions are accompanied by the tangent bifurcation, where the different phase locking modes can be related to the appearance of periodic windows. Furthermore, we explore the dynamical mechanism of the phase locking modes by means of the phase plane analysis. Interestingly, we have found two types of 2:1 phase locking modes, which are characterized by a thin tadpole tail and a fat tadpole tail, respectively. And then, two types of 2:1 phase locking modes are analyzed in detail for understanding their dynamical mechanism. The obtained results can be helpful to explore realistic neuronal activities.

Bistability induces episodic spike communication by inhibitory neurons in neuronal networks

Bistability is one of the important features of nonlinear dynamical systems. In neurodynamics, bistability has been found in basic Hodgkin-Huxley equations describing the cell membrane dynamics. When the neuron is clamped near its threshold, the stable rest potential may coexist with the stable limit cycle describing periodic spiking. However, this effect is often neglected in network computations where the neurons are typically reduced to threshold firing units (e.g., integrate-and-fire models). We found that the bistability may induce spike communication by inhibitory coupled neurons in the spiking network. The communication is realized in the form of episodic discharges with synchronous (correlated) spikes during the episodes. A spiking phase map is constructed to describe the synchronization and to estimate basic spike phase locking modes.

Intermittent synchronization in a network of bursting neurons

Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical network of the basal ganglia, formed by excitatory and inhibitory bursters of the subthalamic nucleus and globus pallidus, involved in motor control and affected in Parkinson’s disease. Recent experiments have demonstrated the intermittent nature of the phase-locking of neural activity in this network. Here, we explore one potential mechanism to explain the intermittent phase-locking in a network. We simplify the network to obtain a model of two inhibitory coupled elements and explore its dynamics. We used geometric analysis and singular perturbation methods for dynamical systems to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently, synchronous oscillations are generated by overlapped spiking which crucially depends on the geometry of the slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of activity patterns with overlapped spiking, and the other slower variable enhances the robustness of an irregular and intermittent activity pattern. While the analyzed network and the explored mechanism of intermittent synchrony appear to be quite generic, the results of this analysis can be used to trace particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson’s disease.

Gap Junctions and Epileptic Seizures – Two Sides of the Same Coin?

Electrical synapses (gap junctions) play a pivotal role in the synchronization of neuronal ensembles which also makes them likely agonists of pathological brain activity. Although large body of experimental data and theoretical considerations indicate that coupling neurons by electrical synapses promotes synchronous activity (and thus is potentially epileptogenic), some recent evidence questions the hypothesis of gap junctions being among purely epileptogenic factors. In particular, an expression of inter-neuronal gap junctions is often found to be higher after the experimentally induced seizures than before. Here we used a computational modeling approach to address the role of neuronal gap junctions in shaping the stability of a network to perturbations that are often associated with the onset of epileptic seizures. We show that under some circumstances, the addition of gap junctions can increase the dynamical stability of a network and thus suppress the collective electrical activity associated with seizures. This implies that the experimentally observed post-seizure additions of gap junctions could serve to prevent further escalations, suggesting furthermore that they are a consequence of an adaptive response of the neuronal network to the pathological activity. However, if the seizures are strong and persistent, our model predicts the existence of a critical tipping point after which additional gap junctions no longer suppress but strongly facilitate the escalation of epileptic seizures. Our results thus reveal a complex role of electrical coupling in relation to epileptiform events. Which dynamic scenario (seizure suppression or seizure escalation) is ultimately adopted by the network depends critically on the strength and duration of seizures, in turn emphasizing the importance of temporal and causal aspects when linking gap junctions with epilepsy.

Chaotic Synchronization of Two Electrical Coupled Neurons with Unknown Parameters Based on Adaptive Control

Chaotic synchronization of two electrical coupled FitzHugh—Nagumo (FHN) neurons with unknown parameters via adaptive control is investigated. Based on the Lyapunov stability theory, an adaptive controller and a parameter update law are designed, which can achieve the synchronization of the two gap junction coupled FHN neurons when the individual neuron is chaotic, without considering the coupling strength. Moreover, the unknown parameters are identified successfully and the controller is robust to the random noise. The numerical simulation results confirm the effectiveness of the designed controller.

Synchronization of Coupled Neurons Controlled by a Pacemaker

We investigate synchronization of Hindmarsh—Rose neurons with gap junctions under the control of a pacemaker. In a ring Hindmarsh—Rose neuronal network, the coupled neurons with the pacemaker can occur in synchronization more easily than those without the pacemaker. Furthermore, the pacemaker can induce phase synchronization or nearly-complete synchronization of nonidentical neurons. This synchronization can occur more easily when time delay is considered. Theses results can be helpful to understand the activities of the real neuronal system.

Synchronization in Two Coupled Hindmarsh-Rose Neurons

Synchronization in Two Coupled Hindmarsh-Rose Neurons

Synchronization in Two Coupled Fitzhugh-Nagumo Neurons with Time Delay

Synchronization in Two Coupled Fitzhugh-Nagumo Neurons with Time Delay

Coupled Noisy Spiking Neurons as Velocity-Controlled Oscillators in a Model of Grid Cell Spatial Firing

One of the two primary classes of models of grid cell spatial firing uses interference between oscillators at dynamically modulated frequencies. Generally, these models are presented in terms of idealized oscillators (modeled as sinusoids), which differ from biological oscillators in multiple important ways. Here we show that two more realistic, noisy neural models (Izhikevich's simple model and a biophysical model of an entorhinal cortex stellate cell) can be successfully used as oscillators in a model of this type. When additive noise is included in the models such that uncoupled or sparsely coupled cells show realistic interspike interval variance, both synaptic and gap-junction coupling can synchronize networks of cells to produce comparatively less variable network-level oscillations. We show that the frequency of these oscillatory networks can be controlled sufficiently well to produce stable grid cell spatial firing on the order of at least 2-5 min, despite the high noise level. Our results suggest that the basic principles of oscillatory interference models work with more realistic models of noisy neurons. Nevertheless, a number of simplifications were still made and future work should examine increasingly realistic models.

A Novel Method of Wire Detection Combined PCNN with HT

The traditional method of wire detection is implemented artificially, and that is heavy-worked, inefficient and low-accurate. This paper proposes a novel method to complete the job by using image technology to improve production efficiency and product qualification rate. In this paper, Pulse Coupled Neuron Network (PCNN) has been applied to the wire image preprocessing, and then Hough Transform (HT) is used to extract features of lines, and detect them according to these features from the processed image. After that, whether the wires were qualified was determined by the criterion of parallelism and isometry. Comparison between different wire images was given in the experimental study. Experimental results showed that the proposed method was feasible and this method could achieve higher detection accuracy and efficiency compared with the traditional method.

Electrotonic Coupling between Pyramidal Neurons in the Neocortex

Electrotonic couplings (i.e., electrical synapses or gap junctions) are fundamental to neuronal synchronization, and thus essential for many physiological functions and pathological disorders. Interneuron electrical synapses have been studied intensively. Although studies on electrotonic couplings between pyramidal cells (PCs) are emerging, particularly in the hippocampus, evidence is still rare in the neocortex. The electrotonic coupling of PCs in the neocortex is therefore largely unknown in terms of electrophysiological, anatomical and synaptological properties. Using multiple patch-clamp recording with differential interference contrast infrared videomicroscopy (IR-DIC) visualization, histochemical staining, and 3D-computer reconstruction, electrotonic coupling was recorded between close PCs, mainly in the medial prefrontal cortex as well as in the visual cortical regions of ferrets and rats. Compared with interneuron gap junctions, these electrotonic couplings were characterized by several special features. The recording probability of an electrotonic coupling between PCs is extremely low; but the junctional conductance is notably high, permitting the direct transmission of action potentials (APs) and even tonic firing between coupled neurons. AP firing is therefore perfectly synchronized between coupled PCs; Postjunctional APs and spikelets alternate following slight changes of membrane potentials; Postjunctional spikelets, especially at high frequencies, are summated and ultimately reach AP-threshold to fire. These properties of pyramidal electrotonic couplings largely fill the needs, as predicted by simulation studies, for the synchronization of a neuronal assembly. It is therefore suggested that the electrotonic coupling of PCs plays a unique role in the generation of neuronal synchronization in the neocortex.

Triggering bursts in all-to-all coupled neurons with global inhibition

Event Abstract Back to Event Triggering bursts in all-to-all coupled neurons with global inhibition Hong-Viet V Ngo1, 2, 3*, Jan Köhler4, Jörg Mayer3, 4, Jens Christian Claussen1, 3 and Heinz G. Schuster4 1 University of Lübeck, Institute for Neuro- and Bioinformatics, Germany 2 University of Lübeck, Graduate School for Computing in Medicine and Life Sciences, Germany 3 University of Lübeck, SFB 654 “Plasticity and Sleep”, Germany 4 University of Kiel, Institute for Astrophysics and Theoretical Physics, Germany Slow-wave sleep in mammals is characterized by a change of large-scale cortical activity currently paraphrased as cortical up/down states. Recently Shu et al. [3] demonstrated experimentally a bistable collective behaviour in ferret brain slices, with the remarkable property that up states can be switched on and off with pulses, or excitations, of same polarity; whereby the effect of the second pulse depends on the time delay to the first pulse. We present a time discrete model of a neural network that reproduces this type of stimulation response and quantitatively the time-dependence found in the experiments.

Coupled nonlinear neurons achieve extensive scaling of a working memory lifetime

Coupled nonlinear neurons achieve extensive scaling of a working memory lifetime

A computational study of the interdependencies between neuronal impulse pattern, noise effects and synchronization

Alterations of individual neurons dynamics and associated changes of the activity pattern, especially the transition from tonic firing (single-spikes) to bursts discharges (impulse groups), play an important role for neuronal information processing and synchronization in many physiological processes (sensory encoding, information binding, hormone release, sleep–wake cycles) as well as in disease (Parkinson, epilepsy). We have used Hodgkin–Huxley-type model neurons with subthreshold oscillations to examine the impact of noise on neuronal encoding and thereby have seen significant differences depending on noise implementation as well as on the neuron’s dynamic state. The importance of the individual neurons’ dynamics is further elucidated by simulation studies with electrotonically coupled model neurons which revealed mutual interdependencies between the alterations of the network’s coupling strength and neurons’ activity patterns with regard to synchronization. Remarkably, a pacemaker-like activity pattern which revealed to be much more noise sensitive than the bursting patterns also requires much higher coupling strengths for synchronization. This seemingly simple pattern is obviously governed by more complex dynamics than expected from a conventional pacemaker which may explain why neurons more easily synchronize in the bursting than in the tonic firing mode.

Asymmetric STDP in excitatory-inhibitory coupled neurons: a self-stabilizing mechanism?

Spike Timing Dependent Plasticity (STDP), where the modification of a synapse depends on the time difference between preand post-synaptic spikes, has been observed in various types of neurons. In general, the STDP window function of excitatory synapses has a causal shape; a causal firing order (where the pre-synaptic neuron fires before the post-synaptic neuron) induces LTP, and an anti-causal firing order induces LTD. In contrast, anti-causal STDP has been described in some inhibitory neurons [1].