Langevin approach for stochastic Hodgkin–Huxley dynamics with discretization of channel open fraction

The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K⁺$10{\text{K}}^{+}$ channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.     

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.     

Effects of channel noise on synchronization transitions in delayed scale-free network of stochastic Hodgkin–Huxley neurons

We numerically study the effect of the channel noise on the spiking synchronization of a scale-free Hodgkin–Huxley neuron network with time delays. It is found that the time delay can induce synchronization transitions at an intermediate and proper channel noise intensity, and the synchronization transitions become strongest when the channel noise intensity is optimal. The neurons can also exhibit synchronization transitions as the channel noise intensity is varied, and this phenomenon is enhanced at around the time delays that can induce the synchronization transitions. It is also found that the synchronization transitions induced by the channel noise are dependent on the coupling strength and the network average degree, and there is an optimal coupling strength or network average degree with which the synchronization transitions become strongest. These results show that by inducing synchronization transitions, the channel noise has a big regulation effect on the synchronization of the neuronal network. These findings could find potential implications for the information transmission in neural systems.     

Analysis of inverse stochastic resonance and the long-term firing of Hodgkin–Huxley neurons with Gaussian white noise

In order to explain the occurrence of a minimum in firing rate which occurs for certain mean input levels μ$\mu$ as noise level σ$\sigma$ increases (inverse stochastic resonance, ISR) in Hodgkin–Huxley (HH) systems, we analyze the underlying transitions from a stable equilibrium point to limit cycle and vice-versa. For a value of μ$\mu$ at which ISR is pronounced, properties of the corresponding stable equilibrium point are found. A linearized approximation around this point has oscillatory solutions from whose maxima spikes tend to occur. A one dimensional diffusion is also constructed for small noise. Properties of the basin of attraction of the limit cycle (spike) are investigated heuristically. Long term trials of duration 500000 ms are carried out for values of σ$\sigma$ from 0 to 2.0. The graph of mean spike count versus σ$\sigma$ is divided into 4 regions _R1,…,_R4$R_1,\dots ,R_4$, where _R3$R_3$ contains the minimum associated with ISR. In _R1$R_1$ transitions to the basin of attraction of the rest point are not observed until a small critical value of σ=_σc1$\sigma ={\sigma }_{c_1}$ is reached, at the beginning of _R2$R_2$. The sudden decline in firing rate when σ$\sigma$ is just greater than _σc1${\sigma }_{c_1}$ implies that there is only a small range of noise levels 0<σ<_σc1$0<\sigma <{\sigma }_{c_1}$ where repetitive spiking is safe from annihilation by noise. The firing rate remains small throughout _R3$R_3$. At a larger critical value σ=_σc2$\sigma ={\sigma }_{c_2}$ which signals the beginning of _R4$R_4$, the probability of transitions from the basin of attraction of the equilibrium point to that of the limit cycle apparently becomes greater than zero and the spike rate thereafter increases with increasing σ$\sigma$. The quantitative scheme underlying the ISR curve is outlined in terms of the properties of exit time random variables. In the final subsection, several statistical properties of the main random variables associated with long term spiking activity are given, including distributions of exit times from the two relevant basins of attraction and the interspike interval.     

Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin–Huxley neurons

The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.     

Effects of temperature and electromagnetic induction on action potential of Hodgkin–Huxley model

Based on an improved the Hodgkin–Huxley (HH) neuron model which is driven by the electromagnetic induction, the effects of temperature and electromagnetic induction on the action potential of neuron are investigated by numerical computations. It is very interesting that, under the fixed condition of electromagnetic induction, there is a region for the electrical activity of neuron in the external current and temperature parameters plane, the region of electrical firing is similar to the Arnold’ tongue-like structure, and the Arnold’ tongue originates from the nonlinear variation of temperature with the increasing of threshold external current. The effects of temperature and electromagnetic induction on neuronic electrical activity are respectively discussed by using numerical simulations. Our results provide new insights into the roles of temperature in the improved HH neuron model, the existence of Arnold’ tongue-like structure might give some insights for the treatment of neurological diseases such as the epilepsia.     

Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal

We consider a scale-free network of stochastic HH neurons driven by a subthreshold periodic stimulus and investigate how the collective spiking regularity or the collective temporal coherence changes with the stimulus frequency, the intrinsic noise (or the cell size), the network average degree and the coupling strength. We show that the best temporal coherence is obtained for a certain level of the intrinsic noise when the frequencies of the external stimulus and the subthreshold oscillations of the network elements match. We also find that the collective regularity exhibits a resonance-like behavior depending on both the coupling strength and the network average degree at the optimal values of the stimulus frequency and the cell size, indicating that the best temporal coherence also requires an optimal coupling strength and an optimal average degree of the connectivity.     

An efficient method for solving fractional Hodgkin–Huxley model

In this paper, we present an accurate numerical method for solving fractional Hodgkin–Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald–Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model.     

Characteristics of critical amplitude of a sinusoidal stimulus in a model neuron

The characteristics of the critical amplitude of a sinusoidal stimulus in a model neuron, Morris－Lecar model, are investigated numerically. It is important in the study of stochastic resonance to determine whether a periodic stimulus is subthreshold or not. The critical amplitude as a function of the stimulus frequency is not a constant, but a curve, which is the boundary between subthreshold and suprathreshold stimulation. It has been considered that this curve is U-shaped in the previous investigations, and this has been accepted as a universal phenomenon. Nevertheless, we think that it is only true for a type of neuron: namely, resonators. Actually, there exists another type of neuron, integrators, which can undergo a saddle-node on invariant circle bifurcation from the rest state to the firing state. For the latter we find that the critical amplitude increases monotonically as the frequency of sinusoidal stimulus is increased. This is shown by way of the Morris－Lecar model. As a consequence, the critical amplitude curve is studied further, and the dynamical mechanisms underlying the change in critical amplitude curve are uncovered. The results of this paper can provide a reference to choose the subthreshold periodic stimulus.     

Spiking sychronization regulated by noise in three types of Hodgkin—Huxley neuronal networks

In this paper,we study spiking synchronization in three different types of Hodgkin-Huxley neuronal networks,which are the small-world,regular,and random neuronal networks.All the neurons are subjected to subthreshold stimulus and external noise.It is found that in each of all the neuronal networks there is an optimal strength of noise to induce the maximal spiking synchronization.We further demonstrate that in each of the neuronal networks there is a range of synaptic conductance to induce the effect that an optimal strength of noise maximizes the spiking synchronization.Only when the magnitude of the synaptic conductance is moderate,will the effect be considerable.However,if the synaptic conductance is small or large,the effect vanishes.As the connections between neurons increase,the synaptic conductance to maximize the effect decreases.Therefore,we show quantitatively that the noise-induced maximal synchronization in the Hodgkin-Huxley neuronal network is a general effect,regardless of the specific type of neuronal network.     

An alternating periodic－chaotic ISI sequence of HH neuron under external sinusoidal stimulus

A study of Hodgkin－Huxley (HH) neuron under external sinusoidal excited stimulus is presented in this paper. As is well known, the stimulus frequency is to be considered as a bifurcate parameter, and numerous phenomena, such as synchronization, period, and chaos appear alternatively with the changing of the stimulus frequency. For the stimulus frequency less than 2f_B (f_B being the base frequency in this paper), the simulation results demonstrate that the single HH neuron could completely convey the sinusoidal signal in anti-phase into interspike interval (ISI) sequences. We also report, perhaps for the first time, another kind of phenomenon, the beat phenomenon, which exists in the phase dynamics of the ISI sequences of the HH neuron stimulated by a sinusoidal current. It is shown furthermore that intermittent transition results in the general route to chaos.     

Response of Alanine Dosemeter to Heavy Ions

The amino acid L-α-alanine has been investigated for use as a radiation detector in low and high LET radiation fields[1]. The radiatioa detector is cheap and easy to handle. The radiation inducing free radicals are stable at normal laboratory conditions for doses below 10^4 Gy over a long period of time, which makes the detector useful for intercomparison and documentation purposes. The dosimetric features of alanine-based electron spin resonance (ESR) detectors in high energy electron beams used in radiotherapy were considered[2]. The 5 mm long alanine detectors were found to be the most suitable for carrying out in vivo dosimetry on patients undergoing electron beam radiotherapy. However, data concerning dosimetry of the alanine dosemeter to heavy charged particles are lacking, especially in China.     

Response of a uniformly accelerated detector to massless Rarita–Schwinger fields in vacuum

We study the response of a uniformly accelerated detector modeled by a two-level atom nonlinearly coupled to vacuum massless Rarita–Schwinger fields. We first generalize the formalism developed by Dalibard, Dupont-Roc, and Cohen-Tannoudji in the linear coupling case, and we then calculate the mean rate of change of the atomic energy of the accelerated atom. Our result shows that a uniformly accelerated atom in its ground state interacting with vacuum Rarita–Schwinger field fluctuations would spontaneously transition to an excited state and the unique feature in contrast to the case of the atom coupled to the scalar, electromagnetic and Dirac fields is the appearance of terms in the excitation rate which are proportional to the sixth and eighth powers of acceleration.     

Response of adaptive matched filter to multipath channel

Response of adaptive matched filter,also called adaptivecorrelator,to multipath channel is discussed in this paper.It has beenproved that the new type processor can better match with multipath chan-nel.The results of experiment carried out on lake and in laboratory arepresented.It shows that the processor has good detecting performance intime domain.     

Response of nevus of Ota to Q-switched alexandrite laser according to treatment interval

In order to determine the appropriate treatment interval, 267 patients who underwent 3 sessions of treatment with Q-switched alexandrite laser were divided into 4 groups according to treatment interval, and their clinical responses were compared. Among them, 187 were asked about the process of pigment fading. Moreover, light and transmission electron microscopy were performed. It was noted that the clinical response of the 5 - 6 month interval group was significantly better than that of the 3 - 4 month group, but showed no significant difference from that of the 7 - 8 or ≥ 9 month group. 80.21% of investigated patients stated that marked pigment fading could no longer be observed 7 months after irradiation. 4 months after irradiation, the degenerated melanosomes and cell debris were still scattered among collagen fibers, scavenged gradually by macrophage. In conclusion, an appropriate treatment interval is 5 - 6 months.     

Critical behavior of a stochastic anisotropic Bak–Sneppen model

In this paper we present our study on the critical behavior of a stochastic anisotropic Bak–Sneppen (saBS) model, in which a parameter α is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness f _c and the critical exponent τ _r by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents.     

Independent Component Analysis to enhance performances of Karhunen–Loeve expansions for non-Gaussian stochastic processes: Application to uncertain systems

In the context of engineering systems, an essential step in uncertainty quantification is the development of accurate and efficient representation of the random input parameters. For such input parameters modeled as stochastic processes, Karhunen–Loeve expansion is a classical approach providing efficient representations using a set of uncorrelated, but generally statistically dependent random variables. The dependence structure among these random variables may be difficult to estimate statistically and is thus ignored in many practical applications. This simplifying assumption of independence may lead to considerable errors in estimating the variability in the system state, thus limiting the effectiveness of Karhunen–Loeve expansion in certain cases. In this paper, Independent Component Analysis is exploited to linearly transform the random variables used in Karhunen–Loeve expansion resulting into a set of random variables exhibiting higher order decorrelation. The stochastic wave equation is investigated for numerical illustration whereby the random stiffness coefficient is modeled as a non-Gaussian stochastic process. Under the assumption of independence among the random variables used in the Karhunen–Loeve expansion and Independent Component Analysis representations, the latter provides more accurate statistical characterization of the output process for the specific cases examined.     

Periodic solutions of Wick-type stochastic Korteweg–de Vries equations

Nonlinear stochastic partial differential equations have a wide range of applications in science and engineering. Finding exact solutions of the Wick-type stochastic equation will be helpful in the theories and numerical studies of such equations. In this paper, Kudrayshov method together with Hermite transform is implemented to obtain exact solutions of Wick-type stochastic Korteweg–de Vries equation. Further, graphical illustrations in two- and three-dimensional plots of the obtained solutions depending on time and space are also given with white noise functionals.     

The Norton–Simon hypothesis and the onset of non-genetic resistance to chemotherapy induced by stochastic fluctuations

By studying a simple but realistic biophysical model of tumor growth in the presence of a constant continuous chemotherapy, we show that if an extended Norton–Simon hypothesis holds, the system may have multiple equilibria. Thus, the stochastic bounded fluctuations that affect both the tumor carrying capacity and/or the drug pharmacodynamics (and/or the drug pharmacokinetics) may cause the transition from a small equilibrium to a far larger one, not compatible with the life of the host. In particular, we mainly investigated the effects of fluctuations that involve parameters nonlinearly affecting the deterministic model. We propose to frame the above phenomena as a new and non-genetic kind of resistance to chemotherapy.