Coupled Hodgkin-Huxley Neurons Research Articles

EFFECT OF NON-GAUSSIAN CHANNEL NOISE ON COHERENCE RESONANCE IN COUPLED STOCHASTIC HODGKIN–HUXLEY NEURONS

In this paper, we study the effect of non-Gaussian channel noise (NCN) on the spiking coherence of a single and an array of bi-directionally coupled Hodgkin–Huxley neurons, mainly investigating how the non-Gaussian character of channel noise affects the coherence resonance (CR) induced by channel noise and by the number of neurons. It is found that, when NCN's deviation q from Gaussian distribution is increased, the CR moves to larger patch area (smaller channel noise) and smaller neuron number, which means that CR occurs in bigger ion channel clusters and smaller neuron number when q is increased. This result shows that, depending on the type of NCN, CR occurs in different sizes of ion channel clusters and numbers of neurons. The underlying mechanism is briefly discussed in terms of the property of NCN. These findings may help to better understand the roles of NCN for improving the time precision of the information processing in coupled stochastic neurons.

DYNAMICS OF SPIRAL WAVE IN THE COUPLED HODGKIN–HUXLEY NEURONS

In this paper, the dynamics of the coupled Hodgkin–Huxley neurons (HHn) is investigated. At first, appropriate initial values and reasonable parameters are used to induce spiral wave in the coupled HHn. The temperature and channel noise are also considered to induce the birth and transition of spiral wave, respectively. It is found that the spiral wave can be generated in the absence of channel noise, and the seed of spiral wave cannot grow up when the intensity of channel noise exceeds the threshold (the noise is distributed on all the channels and s describes the membrane patch, the threshold is suggested with s = 3.2). The spiral wave disappears and all the coupled HHn become homogeneous when the temperature exceeds the threshold about T = 22° C .

Coherence resonance induced by the deviation of non-Gaussian noise in coupled Hodgkin–Huxley neurons

Neurons are noisy elements. Noise arises from both intrinsic and extrinsic sources. In this paper, we numerically study the effect of a particular kind of colored non-Gaussian noise (NGN), mainly of its deviation q from Gaussian noise, on the collective firing in bidirectionally coupled deterministic Hodgkin-Huxley neurons. It is found that the coefficient of variation (CV), characterizing the temporal regularity of the collective spikes, nonlinearly changes with increasing q and passes through a minimum at an intermediate optimal q where the collective spiking becomes most regular, which represents the presence of coherence resonance (CR). We also present a global view of CV as a function of q and neuron number N under various appropriate values of noise intensity. For each value of noise intensity, there is an island present in the contour plot, which sufficiently demonstrates the phenomenon of "q-induced CR." This phenomenon, termed as q-induced CR, shows that there is an optimal deviation of the NGN by which the coupled neurons may behave most periodically in time. Our results provide a novel constructive role of the deviation of the NGN in information processing and signal transduction in real neural systems.

Controlling neural clustering using delayed inputs*

Coupled Hodgkin-Huxley neurons are considered when finite-speed signal propagation introduces time delays into the coupling. Bifurcations of the fully synchronous and partially synchronized cluster states are studied by varying the coupling delay. Based on these investigations a controller is constructed that uses delayed inputs to destroy full synchrony and stabilize clustering. A generalization of such a controller may be useful to drive neural systems away from pathological synchronous states associated with Parkinson's disease.

Spatial coherence resonance on diffusive and small-world networks of Hodgkin–Huxley neurons

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin–Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining the impact of diffusive and small-world network topology that determines the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.

Effect of channel block on the collective spiking activity of coupled stochastic Hodgkin-Huxley neurons

Toxins, such as tetraethylammonium (TEA) and tetrodotoxin (TTX), can make potassium or sodium ion channels poisoned, respectively, and hence reduce the number of working ion channels and lead to the diminishment of conductance. In this paper, we have studied by numerical simulations the effects of sodium and potassium ion channel poisoning on the collective spiking activity of an array of coupled stochastic Hodgkin-Huxley (HH) neurons. It is found for a given number of neurons sodium or potassium ion channel block can either enhance or reduce the collective spiking regularity, depending on the membrane patch size. For a given smaller or larger patch size, potassium and sodium ion channel block can reduce or enhance the collective spiking regularity, but they have different patch size ranges for the transformation. This result shows that sodium or potassium ion channel block might have different effects on the collective spiking activity in coupled HH neurons from the effects for a single neuron, which represents the interplay among the diminishment of maximal conductance and the increase of channel noise strength due to the channel blocks, as well as the bi-directional coupling between the neurons.

Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed coupling

We study the synchronization dynamics for a system of two Hodgkin-Huxley (HH) neurons coupled diffusively or through pulselike interactions. By calculating the maximum transverse Lyapunov exponent, we found that, with diffusive coupling, there are three regions in the parameter space, corresponding to qualitatively distinct behaviors of the coupled dynamics. In particular, the two neurons can synchronize in two regions and desynchronize in the third. When excitatory and inhibitory pulse coupling is considered, we found that synchronized dynamics becomes more difficult to achieve in the sense that the parameter regions where the synchronous state is stable are smaller. Numerical simulations of the coupled system are presented to validate these results. The stability of a network of coupled HH neurons is then analyzed and the stability regions in the parameter space are exactly obtained.

Optimal network size for Hodgkin–Huxley neurons

The collective behavior of an array of coupled Hodgkin–Huxley neurons, which are subject to subthreshold signal and external noise, is investigated by numerical methods. It is found that the network size, the number of Hodgkin–Huxley neurons in the network, has an optimal value, at which the collective behavior shows the best performance. The value of the optimal network size goes up when the coupling strength increases. Such a nontrivial dependence on the network size is not found if we only consider the response of an individual neuron in the network.

Double‐System‐Size Resonance for Spiking Activity of Coupled Hodgkin–Huxley Neurons

Double‐System‐Size Resonance for Spiking Activity of Coupled Hodgkin–Huxley Neurons

Synchronization of two Hodgkin–Huxley neurons due to internal noise

It is well known that a strong coupling can synchronize a population of nonlinear oscillators. This fact has deep implications for the current understanding of information processing by the brain. The focus of this Letter is on the role of conductance noise on a system of two coupled Hodgkin–Huxley neurons in the so-called excitable region, where both neurons are at rest in the absence of noise. It is shown that, in this region, conductance noise allows the neurons to achieve both frequency and phase synchronization. This suggests that internal noise could play a role in the emergence of synchronous neural activity in populations of weakly coupled neurons.

BIFURCATIONS IN SYNAPTICALLY COUPLED BVP NEURONS

We investigate bifurcations of periodic solutions in model equations of two and three Bonhöffer–van der Pol (BVP) neurons coupled through the characteristics of synaptic transmissions with a time delay. Bifurcations of the coupled BVP neurons are compared with bifurcations of synaptically coupled Hodgkin–Huxley neurons. We obtained a parameter set of the BVP system, such that the two systems are qualitatively very similar from a bifurcational point of view. This study is a base for the analysis of synaptically coupled neurons with a large number of coupling strategies.

Synchronization and Clustering in a Network of Three Globally Coupled Neural Oscillators

Collective dynamics of three globally coupled Hodgkin–Huxley neurons with a symmetric synaptic coupling has been studied as a paradigm of one of the simplest but nontrivial example of physiology-based coupled oscillator networks capable of displaying synchrony and clustering. Rich phase dynamics have been observed and the phase diagram for various phase states, in particular the synchronized state and clustered states, have been constructed by direct numerical simulations of the full system. We find that the computed phase diagram in the synaptic parameter space of the reversal potential and the signal propagation time delay reveals a rich bifurcation structure and agrees with one from bifurcation analysis of the reduced phase model. Implication of our findings in connection with two-coupled neurons and larger neural networks is discussed.

Synchrony and Clustering in Two and Three Synaptically Coupled Hodgkin–Huxley Neurons with a Time Delay

Synchrony and clustering in phase dynamics of two and three Hodgkin–Huxley neurons coupled globally by excitatory synapses with a time delay have been studied by numerical simulations and bifurcation analysis. In particular, we have obtained phase diagrams for the synchronous state and various cluster states in the parameter space of the synaptic coupling strength, G syn , and the synaptic time delay, τd, by computing the phase shifts of action potential spikes. In the weak coupling limit the computed phase diagrams are found to be consistent with the results of phase model analysis. The bifurcation analysis shows the phase model predictions break down at G syn ~ 0.3 and new complex phase dynamics appear. For all numbers of neurons explored, the critical time delay at which the nature of synaptic coupling changes completely is found to be typically about 2–4 msec, which may have some implications in modeling cortical dynamics.