Huxley Neurons Research Articles

Formation of multi-armed spiral waves in neuronal network induced by adjusting ion channel conductance

The Hodgkin–Huxley neuron model is used to describe the local dynamics of nodes in a two-dimensional regular network with nearest-neighbor connections. Multi-armed spiral waves emerge when a group of spiral waves rotate the same core synchronously. Here we have numerically investigated how multi-armed spiral waves are formed in such a system. Under the appropriate conditions, multi-armed spiral waves were able to develop as a result of adjusting the conductance of ion channels of particular neurons in the network. In a realistic neuron model, it can be practiced by blocking potassium of ion channels embedded in the membrane of neurons. For example, decreasing the potassium channel conductance in some neurons with a certain transient period can lead to the development of a group of double spirals in a localized area of the network. Furthermore, decreasing the excitability and the external forcing current to zero led to the growth of these double spirals and the formation of a stable multi-armed spiral wave that occupied the network under inhomogeneity.

Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron

We study the effect of the delayed feedback loop on the weak periodic signal detection performance of a stochastic Hodgkin–Huxley neuron. We consider an electrical autapse characterized by its coupling strength and delay time. The stochastic Hodgkin–Huxley neuron exhibits subthreshold oscillations, and thus has an intrinsic time scale with the subthreshold oscillations. Therefore, we investigate the interplay of the subthreshold oscillations, coupling strength and delay time on the weak periodic signal detection. Results indicate that the delayed feedback either enhances or suppresses the weak signal detection depending on its parameters, when compared to that without the feedback. The delayed feedback augments the weak periodic signal detection for the optimal values of the intrinsic noise and the coupling strength when the delay time is close to the integer multiples of the period of the intrinsic oscillations, due to the multiple resonance among the weak signal, the intrinsic oscillations, and the delayed feedback.We analyze the interspike interval histograms and show that the delayed feedback enhances or suppresses the weak periodic signal detection by increasing or decreasing the phase locking (synchronization) between the spiking and the weak periodic signal. We also show that an optimal phase locking is obtained when the delay time is close to the period of the intrinsic oscillations, leading a single dominant time scale in the spike trains.

Optimization of Intrinsic Stochastic Resonance in Adaptive Newman–Watts Network of Channel Blocked Hodgkin–Huxley Neurons

In this paper, we study stochastic resonance (SR) induced by channel noise in adaptive weighted Newman–Watts networks of Hodgkin–Huxley neurons with channel blocking (CB). It is found that the intrinsic SR is dependent on adaptive coupling and is strongly enhanced when the changing rate of adaptive coupling is optimal, and this phenomenon is independent of sodium and potassium CB levels. As CB increases, the channel noise for SR decreases, but the strength of intrinsic SR nearly does not change in the presence of adaptive coupling, which is different from the case for fixed coupling. These results show that intrinsic SR can be enhanced and optimized by adaptive coupling, and CB's effect on the intrinsic SR can be reduced by adaptive coupling. This implies that adaptive coupling could more efficiently improve the time precision of information processing in neural systems.

Pinning impulsive directed coupled delayed dynamical network and its applications

The main objective of the present paper is to further investigate pinning synchronisation of a complex delayed dynamical network with directionally coupling by a single impulsive controller. By developing the analysis procedure of pinning impulsive stability for undirected coupled dynamical network previously, some simple yet general criteria of pinning impulsive synchronisation for such directed coupled network are derived analytically. It is shown that a single impulsive controller can always pin a given directed coupled network to a desired homogenous solution, including an equilibrium point, a periodic orbit, or a chaotic orbit. Subsequently, the theoretical results are illustrated by a directed small-world complex network which is a cellular neural network (CNN) and a directed scale-free complex network with the well-known Hodgkin–Huxley neuron oscillators. Numerical simulations are finally given to demonstrate the effectiveness of the proposed control methodology.

Synchronization limit of weakly forced nonlinear oscillators

Nonlinear oscillators exhibit synchronization (injection-locking) to external periodic forcings, which underlies the mutual synchronization in networks of nonlinear oscillators. Despite its history of synchronization and the practical importance of injection-locking to date, there are many important open problems of an efficient injection-locking for a given oscillator. In this work, I elucidate a hidden mechanism governing the synchronization limit under weak forcings, which is related to a widely known inequality; Hölderʼs inequality. This mechanism enables us to understand how and why the efficient injection-locking is realized; a general theory of synchronization limit is constructed where the maximization of the synchronization range or the stability of synchronization for general forcings including pulse trains, and a fundamental limit of general m : n phase locking, are clarified systematically. These synchronization limits and their utility are systematically verified in the Hodgkin–Huxley neuron model as an example.

Independent Noise Enhances Synchronization in Heterogeneous Systems

We investigated effects of noise inputs on synchronous firing in a simple model neuron system with electrophysiological heterogeneity. The system consists of two leaky integrate-and-fire (LIF) neurons with different membrane time constants. They are uncoupled and driven by Gaussian white noise inputs. We found that correlation between spike trains of two LIF neurons was maximized at input correlation slightly smaller than one. The same result was obtained for a more realistic system consisting of two non-identical Hodgkin–Huxley neurons. We also revealed the mechanism underlying the effect.

Dynamic range in small-world networks of Hodgkin–Huxley neurons with chemical synapses

According to Stevens’ law the relationship between stimulus and response is a power-law within an interval called the dynamic range. The dynamic range of sensory organs is found to be larger than that of a single neuron, suggesting that the network structure plays a key role in the behavior of both the scaling exponent and the dynamic range of neuron assemblies. In order to verify computationally the relationships between stimulus and response for spiking neurons, we investigate small-world networks of neurons described by the Hodgkin–Huxley equations connected by chemical synapses. We found that the dynamic range increases with the network size, suggesting that the enhancement of the dynamic range observed in sensory organs, with respect to single neurons, is an emergent property of complex network dynamics.

Influence of autapse on mode-locking structure of a Hodgkin–Huxley neuron under sinusoidal stimulus

We investigated the mode-locking behaviors of a Hodgkin–Huxley neuron with an autapse under sinusoidal stimulus. A neuron without an autapse can exhibit rich p:q mode-locking (i.e. p output action potentials generated by q cycles stimulations) behaviors with periodic stimuli. In the presence of the autaptic connection, the p:q mode-locking behaviors are completely reset. The autapse extends the scope of mode-locking. The autapse can enhance or suppress the status of mode-locking. Even for some specified autaptic parameters, the neuron could be driven into the sub-threshold oscillation. Our results suggested that the autapse can serve as a potential control option for adjusting the mode-locking firing behaviors. We also found that changing the delay time is much more effectively operable to regulate the response behavior than the autaptic intensity.

Stochastic and Coherence Resonance in a Dressed Neuron Model

The noise induced stochastic behaviors, in terms of stochastic resonance (SR) and coherence resonance (CR), have been widely reported in many nonlinear systems in different disciplines. In particular, in neuroscience, both the phenomena of SR and CR have been discovered. However, the traditional studies only focus on the dynamical behaviors of the neurons without considering the effects of other biological cells. It is known that neurons are surrounded by a number of glial cells. Being a subgroup of glial cells, astrocytes have been argued to take part in neuronal signal processing. Therefore, it is more reasonable to study the dynamics of a neuron by incorporating the effect of astrocyte, which is termed as dressed neuron. In this paper, the stochastic behaviors of a dressed Hodgkin–Huxley neuron with mutual neuron-astrocyte interaction are studied, and the effects of astrocyte on different resonance mechanisms are analyzed. Simulation results show that the astrocyte plays a similar role as noise in the stochastic behaviors of a neuron, which enhances the performance of a neuron in signal transduction via resonance mechanisms.

Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin—Huxley neuron

How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin—Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional (1D) map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm — symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.

Bifurcation analysis of delay-induced patterns in a ring of Hodgkin–Huxley neurons

Rings of delay-coupled neurons possess a striking capability to produce various stable spiking patterns. In order to reveal the mechanisms of their appearance, we present a bifurcation analysis of the Hodgkin-Huxley (HH) system with delayed feedback as well as a closed loop of HH neurons. We consider mainly the effects of external currents and communication delays. It is shown that typically periodic patterns of different spatial form (wavenumber) appear via Hopf bifurcations as the external current or time delay changes. The Hopf bifurcations are shown to occur in relatively narrow regions of the external current values, which are independent of the delays. Additional patterns, which have the same wavenumbers as the existing ones, appear via saddle-node bifurcations of limit cycles. The obtained bifurcation diagrams are evidence for the important role of communication delays for the emergence of multiple coexistent spiking patterns. The effects of a short-cut, which destroys the rotational symmetry of the ring, are also briefly discussed.

Dynamics, control and information in delay-coupled systems: an overview

Dynamics, control and information in delay-coupled systems: an overview

Periodic coupling strength-dependent multiple coherence resonance by time delay in Newman–Watts neuronal networks

Recently, multiple coherence resonance induced by time delay has been observed in neuronal networks with constant coupling strength. In this paper, by employing Newman–Watts Hodgkin–Huxley neuron networks with time-periodic coupling strength, we study how the temporal coherence of spiking behavior and coherence resonance by time delay change when the frequency of periodic coupling strength is varied. It is found that delay induced coherence resonance is dependent on periodic coupling strength and increases when the frequency of periodic coupling strength increases. Periodic coupling strength can also induce multiple coherence resonance, and the coherence resonance occurs when the frequency of periodic coupling strength is approximately multiple of the spiking frequency. These results show that for periodic coupling strength time delay can more frequently optimize the temporal coherence of spiking activity, and periodic coupling strength can repetitively optimize the temporal coherence of spiking activity as well. Frequency locking may be the mechanism for multiple coherence resonance induced by periodic coupling strength. These findings imply that periodic coupling strength is more efficient for enhancing the temporal coherence of spiking activity of neuronal networks, and thus it could play a more important role in improving the time precision of information processing and transmission in neural networks.

Noise-induced synchronization in a lattice Hodgkin–Huxley neural network

We examine how the synchronization of the series of action potentials (APs) of realistic neurons interconnected in a lattice is influenced by variations of both the direction and magnitude of neuron–neuron connectivity in a noisy environment. We first demonstrate the existence of an optimal noise level that brings about the highest average number of APs per unit time, for a single Hodgkin–Huxley neuron. We then show that synchronization, as a collective response of interconnected neurons forming an N×N lattice, is optimal at different noise strengths σc=σc(p), depending on the degree of random-link malfunction parameterized by flipping direction probability p. Thus, even without the scale-free structure of neuronal networks, proper combinations of both randomness in reconnection (flipping) and noisy environment can be beneficial to the collective functioning of neurons.

Soliton Solutions and Applications on Neuronal Hodgkin-Huxley Model

from one neuron to another neuron fibers generate action potentials of nerve cells, leading to nervous excitement along. Hodgkin - Huxley neuron model has been used to solve many physiological phenomenon. This paper presents Neuralfiber conduction theory, based on the Hodgkin - Huxley model, considering the propagation of nerve impulses nerve fiber soliton solutions, and to further discuss the application of numerical results are two aspects raised.

Impact of the variations in the temperature on the first spike latency of a Hodgkin-Huxley neuron model

For stimuli just beyond threshold and certain noise strength, the Hodgkin–Huxley (HH) neuron model shows sensitivity to noise with respect to latency to first spike after stimulus onset. This effect has been called “noise delayed decay” (NDD). Here we investigate how the NDD is affected by the variation in temperature using a HH model that includes stochastic ion channels. We show that the NDD effect increases and emerges for smaller noise strengths (or larger cell sizes) as the temperature increases. We also show that the potassium channel noise plays a key role on the appearance of the NDD effect.

In-phase and anti-phase synchronization in noisy Hodgkin–Huxley neurons

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 characteristic stochastic synchronization patterns which exhibit multiple phase-flip bifurcations: The phase-flip bifurcations occur in form of alternate transitions from an in-phase spiking activity towards an anti-phase spiking activity. Interestingly, these phase-flips remain robust for strong channel noise and in turn cause a striking stabilization of the spiking frequency.

Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potassium, Sodium) is investigated, the dynamics of the node is described by Hodgkin—Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio xNa (and xK), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio xNa (and xK) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.

Simulating the formation of spiral wave in the neuronal system

Some experimental results have confirmed that a spiral wave could be observed in the cortex of brain. The biological Hodgkin–Huxley neurons are used to construct a regular network with nearest-neighbor connection, artificial line defects are generated to block the traveling wave in the network, and the potential mechanism for formation of spiral wave is investigated. A target wave is generated in a local area by imposing two external forcing currents with diversity (I0−I1) in different areas of the network. It is confirmed that spiral wave could be induced by the defects even if no specific initial values are used. A single perfect spiral wave can occupy the network when the coupling intensity exceeds certain threshold; otherwise, a group of spiral waves emerges in the network. Certain channel noise can enhance the diversity (I0−I1) for generating target wave, and then spiral waves are induced by blocking the target wave with defects under no-flux and/or periodic boundary conditions in the network.

Enhanced Response to Subthreshold Signals by Phase Noise in a Hodgkin—Huxley Neuron

Noise has been revealed as an important cue for understanding the extraordinary ability of sensory neurons to detect or amplify external weak signals. We demonstrate that phase noise originating from the time-varying signal phase can enable an excitable neuron to excite spikes upon a periodic signal even though the signal amplitude is subthreshold. In addition, we find that there exists an optimal value on the phase noise at which the neuron's response to the subthreshold periodic signal can be significantly improved, resulting in a resonance-like behavior. Since phase noise makes the external signal aperiodic, our findings show that sensory neurons might evolve with a better performance on detecting aperiodic signals than periodic signals.