Effects of ion channel blocks on electrical activity of stochastic Hodgkin–Huxley neural network under electromagnetic induction

Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model

Electromagnetic induction plays a crucial impact on the firing activity of biological neurons, since it exists along with the mutual effect between membrane potential and ions transport. Flux-controlled memristor is an available candidate in characterizing the electromagnetic induction effect. Different from the previously reported literature, a non-ideal flux-controlled memristor with cosine mem-conductance function is employed to determine the periodic magnetization and leakage flux processes in neurons. Thereafter, a three-dimensional (3D) memristive Wilson (m-Wilson) neuron model is constructed under the consideration of this kind of electromagnetic induction. Numerical simulations are performed by multiple numerical tools, which demonstrate that the 3D m-Wilson neuron model can generate abundant firing activities. Interestingly, coexisting firing activities, antimonotonicity, and firing frequency regulation are discovered under special parameter settings. Furthermore, a PCB-based analog circuit is designed and hardware measurements are executed to verify the numerical simulations. These explorations in numerical and hardware surveys might provide insights to regulate the firing activities by appropriate electromagnetic induction.

Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation

To characterize the magnetic induction flow induced by neuron membrane potential, a three-dimensional (3D) memristive Morris-Lecar (ML) neuron model is proposed in this paper. It is achieved using a memristor induction current to replace the slow modulation current in the existing 3D ML neuron model with fast-slow structure. The magnetic induction effects on firing activities are explained by the spiking/bursting firings with period-adding bifurcation and periodic/chaotic spiking-bursting patterns, and the bifurcation mechanisms of the bursting patterns are elaborated using the fast-slow analysis method to create two bifurcation sets. In particular, the 3D memristive ML model can also exhibit the homogeneous coexisting bursting patterns when switching the memristor initial states, which are effectively illustrated by the theoretical analysis and numerical simulations. Finally, a digitally FPGA-based hardware platform is developed for the 3D memristive ML model and the experimentally measured results well verify the numerical ones.

Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction

Memristive electromagnetic induction effect has been widely explored in bi-neuron network with homogeneous neurons, but rarely in bi-neuron network with heterogeneous ones. This paper builds a bi-neuron network by coupling heterogeneous Rulkov neurons with memristor and investigates the memristive electromagnetic induction effect. Theoretical analysis discloses that the bi-neuron network possesses a line equilibrium state and its stability depends on the memristor coupling strength and initial condition. That is, the stability of the line equilibrium state has a transition between unstable saddle-focus and stable node-focus via Hopf bifurcation. By employing parameters located in the stable node-focus region, dynamical behaviors related to the memristor coupling strength and initial conditions are revealed by Julia- and MATLAB-based multiple numerical tools. Numerical results demonstrate that the proposed heterogeneous bi-neuron Rulkov network can generate point attractor, period, chaos, chaos crisis, and period-doubling bifurcation. Note that extreme multistability are disclosed with respect to initial conditions of memristor and gated ion concentration. Coexisting infinitely multiple firing patterns of periodic firing patterns with different periodicities and chaotic firing patterns for different memristor initial conditions are demonstrated by phase portrait and time-domain waveform. Besides, the phase synchronization related to the memristor coupling strength and its initial condition is explored, which suggests that the two heterogeneous neurons become phase synchronization with large memristor coupling strength and initial condition. This also reflects that the plasticity of memristor synapse enables adaptive regulation in keeping energy balance between the neurons. What's more, MCU-based hardware experiments are executed to further confirm the numerical simulations.

Adaptive synapse-based neuron model with heterogeneous multistability and riddled basins

Biological neurons can exhibit complex coexisting multiple firing patterns dependent on initial conditions. To this end, this paper presents a novel adaptive synapse-based neuron (ASN) model with sine activation function. The ASN model has time-varying equilibria with the variation of externally applied current and its equilibrium stability involves transitions between stable and unstable points through fold and Hopf bifurcations, resulting in complex distributions of attractive regions with heterogeneous multi-stability. Globally coexisting heterogeneous behaviors are studied by bifurcation diagram, phase portrait, dynamical distribution, and basin of attraction. The results show that the number of coexisting heterogeneous attractors can be up to 12, but for a simple neuron model, such a large number of coexisting heterogeneous attractors has not been reported in the relevant literature. Most interestingly, the ASN model also has riddled-like complex basins of attraction and four illustrative examples are depicted by the phase portraits with small changes of the initial conditions. Besides, the ASN model is implemented using a simple microcontroller platform, and various heterogeneous coexisting attractors are acquired experimentally to validate the numerical results.

Effects of chaotic activity and time delay on signal transmission in FitzHugh-Nagumo neuronal system

The influences of chaotic activity and time delay on the transmission of the sub-threshold signal (STS) in a single FitzHugh-Nagumo neuron and coupled neuronal networks are studied. It is found that a moderate chaotic activity level can enhance the system's detection and transmission of STS. This phenomenon is known as chaotic resonance (CR). In a single neuron, the large amplitude and small period of the STS have a positive effect on the CR phenomenon. In the coupled neuronal network, however, the signal transmission performance of chemical synapses is better than that of electrical synapses. The time delay can determine the trend of the system response, and the multiple chaotic resonances phenomenon is observed upon fine-tuning the time delay length. Both sub-harmonic chaotic resonance and chaotic anti-resonance appear when the STS period and time delay are locked. In chained networks, the signal transmission performance between electrical synapses attenuates continuously. Conversely, the performance between chemical synapses reaches a steady state.

Effects of temperature and ion channel blocks on propagation of action potential in myelinated axons

Potassium ion and sodium ion channels play important roles in the propagation of action potentials along a myelinated axon. The random opening and closing of ion channels can cause the fluctuation of action potentials. In this paper, an improved Hodgkin-Huxley chain network model is proposed to study the effects of ion channel blocks, temperature, and ion channel noise on the propagation of action potentials along the myelinated axon. It is found that the chain network has minimum coupling intensity threshold and maximum tolerance temperature threshold that allow the action potentials to pass along the whole axon, and the blockage of ion channels can change these two thresholds. A striking result is that the simulated value of the optimum membrane size (inversely proportional to noise intensity) coincides with the area range of feline thalamocortical relay cells in biological experiments.

Effects of noise and time delay on E2F's expression level in a bistable Rb-E2F gene's regulatory network

The bistable Rb-E2F gene regulatory network plays a central role in regulating cellular proliferation-quiescence transition. Based on Gillespie's chemical Langevin method, the stochastic bistable Rb-E2F gene's regulatory network with time delays is proposed. It is found that under the moderate intensity of internal noise, delay in the Cyclin E synthesis rate can greatly increase the average concentration value of E2F. When the delay is considered in both E2F-related positive feedback loops, within a specific range of delay (3-13) hr , the average expression of E2F is significantly increased. Also, this range is in the scope with that experimentally given by Dong et al. [65]. By analysing the quasi-potential curves at different delay times, simulation results show that delay regulates the dynamic behaviour of the system in the following way: small delay stabilises the bistable system; the medium delay is conducive to a high steady-state, making the system fluctuate near the high steady-state; large delay induces approximately periodic transitions between high and low steady-state. Therefore, by regulating noise and time delay, the cell itself can control the expression level of E2F to respond to different situations. These findings may provide an explanation of some experimental result intricacies related to the cell cycle.

Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction

Energy supply plays a key role in metabolism and signal transmission of biological individuals, neurons in a complex electromagnetic environment must be accompanied by the absorption and release of energy. In this paper, the discharge mode and the Hamiltonian energy are investigated within the Izhikevich neuronal model driven by external signals in the presence of electromagnetic induction. It is found that multiple electrical activity modes can be observed by changing external stimulus, and the Hamiltonian energy is more dependent on the discharge mode. In particular, there is a distinct shift and transition in the Hamiltonian energy when the discharge mode is switched quickly. Furthermore, the amplitude of periodic stimulus signal has a greater effect on the neuronal energy compared to the angular frequency, and the average Hamiltonian energy decreases when the discharge rhythm becomes higher. Based on the principle of energy minimization, the system should choose the minimum Hamiltonian energy when maintaining various trigger states to reduce the metabolic energy of signal processing in biological systems. Therefore, our results give the possible clues for predicting and selecting appropriate parameters, and help to understand the sudden and paroxysmal mechanisms of epilepsy symptoms.

Effect of potassium channel noise on nerve discharge based on the Chay model

BACKGROUND:

The nervous system senses and transmits information through the firing behavior of neurons, and this process is affected by various noises. However, in the previous study of the influence of noise on nerve discharge, the channel of some noise effects is not clear, and the difference from other noises was not examined.

OBJECTIVE:

To construct ion channel noise which is more biologically significant, and to clarify the basic characteristics of the random firing rhythm of neurons generated by different types of noise acting on ion channels.

Method:

Based on the dynamics of the ion channel, we constructed ion channel noise. We simulated the nerve discharge based on the Chay model of potassium ion channel noise, and used the nonlinear time series analysis method to measure the certainty and randomness of nerve discharge.

RESULTS:

In the Chay model with potassium ion noise, the chaotic rhythm defined by the original model could be effectively unified with the random rhythm simulated by the previous random Chay model into a periodic bifurcation process.

CONCLUSION:

This method clarified the influence of ion channel noise on nerve discharge, better understood the randomness of nerve discharge and provided a more reasonable explanation for the mechanism of nerve discharge.

Ionic channel blockage in stochastic Hodgkin-Huxley neuronal model driven by multiple oscillatory signals

Ionic channel blockage and multiple oscillatory signals play an important role in the dynamical response of pulse sequences. The effects of ionic channel blockage and ionic channel noise on the discharge behaviors are studied in Hodgkin-Huxley neuronal model with multiple oscillatory signals. It is found that bifurcation points of spontaneous discharge are altered through tuning the amplitude of multiple oscillatory signals, and the discharge cycle is changed by increasing the frequency of multiple oscillatory signals. The effects of ionic channel blockage on neural discharge behaviors indicate that the neural excitability can be suppressed by the sodium channel blockage, however, the neural excitability can be reversed by the potassium channel blockage. There is an optimal blockage ratio of potassium channel at which the electrical activity is the most regular, while the order of neural spike is disrupted by the sodium channel blockage. In addition, the frequency of spike discharge is accelerated by increasing the ionic channel noise, the firing of neuron becomes more stable if the ionic channel noise is appropriately reduced. Our results might provide new insights into the effects of ionic channel blockages, multiple oscillatory signals, and ionic channel noises on neural discharge behaviors.

Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse

In this paper, the effects of asymmetry in an electrical synaptic connection between two neuronal oscillators with a small discrepancy are studied in a 2D Hindmarsh-Rose model. We have found that the introduced model possesses a unique unstable equilibrium point. We equally demonstrate that the asymmetric electrical couplings as well as external stimulus induce the coexistence of bifurcations and multiple firing patterns in the coupled neural oscillators. The coexistence of at least two firing patterns including chaotic and periodic ones for some discrete values of coupling strengths and external stimulus is demonstrated using time series, phase portraits, bifurcation diagrams, maximum Lyapunov exponent graphs, and basins of attraction. The PSpice results with an analog electronic circuit are in good agreement with the results of theoretical analyses. Of most/particular interest, multistability observed in the coupled neuronal model is further controlled based on the linear augmentation scheme. Numerical results show the effectiveness of the control strategy through annihilation of the periodic coexisting firing pattern. For higher values of the coupling strength, only a chaotic firing pattern survives. To the best of the authors' knowledge, the results of this work represent the first report on the phenomenon of coexistence of multiple firing patterns and its control ever present in a 2D Hindmarsh-Rose model connected to another one through an asymmetric electrical coupling and, thus, deserves dissemination.

Hidden Bursting Firings and Bifurcation Mechanisms in Memristive Neuron Model With Threshold Electromagnetic Induction

Memristors can be employed to mimic biological neural synapses or to describe electromagnetic induction effects. To exhibit the threshold effect of electromagnetic induction, this paper presents a threshold flux-controlled memristor and examines its frequency-dependent pinched hysteresis loops. Using an electromagnetic induction current generated by the threshold memristor to replace the external current in 2-D Hindmarsh-Rose (HR) neuron model, a 3-D memristive HR (mHR) neuron model with global hidden oscillations is established and the corresponding numerical simulations are performed. It is found that due to no equilibrium point, the obtained mHR neuron model always operates in hidden bursting firing patterns, including coexisting hidden bursting firing patterns with bistability also. In addition, the model exhibits complex dynamics of the actual neuron electrical activities, which acts like the 3-D HR neuron model, indicating its feasibility. In particular, by constructing the fold and Hopf bifurcation sets of the fast-scale subsystem, the bifurcation mechanisms of hidden bursting firings are expounded. Finally, circuit experiments on hardware breadboards are deployed and the captured results well match with the numerical results, validating the physical mechanism of biological neuron and the reliability of electronic neuron.

Temperature effect on memristive ion channels

Neuron shows distinct dependence of electrical activities on membrane patch temperature, and the mode transition of electrical activity is induced by the patch temperature through modulating the opening and closing rates of ion channels. In this paper, inspired by the physical effect of memristor, the potassium and sodium ion channels embedded in the membrane patch are updated by using memristor-based voltage gate variables, and an external stimulus is applied to detect the variety of mode selection in electrical activities under different patch temperatures. It is found that each ion channel can be regarded as a physical memristor, and the shape of pinched hysteresis loop of memristor is dependent on both input voltage and patch temperature. The pinched hysteresis loops of two ion-channel memristors are dramatically enlarged by increasing patch temperature, and the hysteresis lobe areas are monotonously reduced with the increasing of excitation frequency if the frequency of external stimulus exceeds certain threshold. However, for the memristive potassium channel, the AREA1 corresponding to the threshold frequency is increased with the increasing of patch temperature. The amplitude of conductance for two ion-channel memristors depends on the variation of patch temperature. The results of this paper might provide insights to modulate the neural activities in appropriate temperature condition completely, and involvement of external stimulus enhance the effect of patch temperature.

Spontaneous electromagnetic induction promotes the formation of economical neuronal network structure via self-organization process

Developed through evolution, brain neural system self-organizes into an economical and dynamic network structure with the modulation of repetitive neuronal firing activities through synaptic plasticity. These highly variable electric activities inevitably produce a spontaneous magnetic field, which also significantly modulates the dynamic neuronal behaviors in the brain. However, how this spontaneous electromagnetic induction affects the self-organization process and what is its role in the formation of an economical neuronal network still have not been reported. Here, we investigate the effects of spontaneous electromagnetic induction on the self-organization process and the topological properties of the self-organized neuronal network. We first find that spontaneous electromagnetic induction slows down the self-organization process of the neuronal network by decreasing the neuronal excitability. In addition, spontaneous electromagnetic induction can result in a more homogeneous directed-weighted network structure with lower causal relationship and less modularity which supports weaker neuronal synchronization. Furthermore, we show that spontaneous electromagnetic induction can reconfigure synaptic connections to optimize the economical connectivity pattern of self-organized neuronal networks, endowing it with enhanced local and global efficiency from the perspective of graph theory. Our results reveal the critical role of spontaneous electromagnetic induction in the formation of an economical self-organized neuronal network and are also helpful for understanding the evolution of the brain neural system.

Localized nonlinear excitations in diffusive memristor-based neuronal networks

We extend the existing ordinary differential equations modeling neural electrical activity to include the memory effect of electromagnetic induction through magnetic flux, used to describe time varying electromagnetic field. Through the multi-scale expansion in the semi-discrete approximation, we show that the neural network dynamical equations can be governed by the complex Ginzburg-Landau equation. The analytical and numerical envelop soliton of this equation are reported. The results obtained suggest the possibility of collective information processing and sharing in the nervous system, operating in both the spatial and temporal domains in the form of localized modulated waves. The effects of memristive synaptic electromagnetic induction coupling and perturbation on the modulated action potential dynamics examined. Large electromagnetic induction coupling strength may contribute to signal block as the amplitude of modulated waves are observed to decrease. This could help in the development of a chemical brain anaesthesia for some brain pathologies.

Modeling of mesenchymal hybrid epithelial state and phenotypic transitions in EMT and MET processes of cancer cells

Based on the transcriptional regulatory mechanisms between microRNA-200 and transcription factor ZEB in an individual cancer cell, a minimal dynamic model is proposed to study the epithelial-mesenchymal transition (EMT) and mesenchymal-epithelial transition (MET) processes of cancer cells. It is shown that each cancer cell can exit in any of three phenotypic states: the epithelial (E) state, the mesenchymal (M) state, and the epithelial/mesenchymal (E/M) hybrid state, and the state of cancer cell can interconvert between different states. The phase diagram shows that there are monostable, bistable, and tristable phenotypic states regions in a parameters plane. It is found that different pathway in the phase diagram can correspond to the EMT or the MET process of cancer cells, and there are two possible EMT processes. It is important that the experimental phenomenon of E/M hybrid state appearing in the EMT process but rather in the MET process can be understood through different pathways in the phase diagram. Our numerical simulations show that the effects of noise are opposite to these of time delay on the expression of transcription factor ZEB, and there is competition between noise and time delay in phenotypic transitions process of cancer cells.

Effect of external periodic signals and electromagnetic radiation on autaptic regulation of neuronal firing

An improved Hindmarsh-Rose (HR) neuron model, where the memristor is a bridge between membrane potential and magnetic flux, can be used to investigate the effect of periodic signals on autaptic regulation of neurons under electromagnetic radiation. Based on the improved HR model driven by periodic high-low-frequency current and electromagnetic radiation, the responses of electrical autaptic regulation with diverse high-low-frequency signals are investigated using bifurcation analysis. It is found that the electrical modes of neurons are determined by the selecting parameters of both periodic high and low-frequency current and electromagnetic radiation, and the Hamiltonian energy depends on the neuronal firing modes. The effects of Gaussian white noise on the membrane potential are discussed using numerical simulations. It is demonstrated that external high-low-frequency stimulus plays a significant role in the autaptic regulation of neural firing mode, and the electrical mode of neurons can be affected by the angular frequency of both high-low-frequency forcing current and electromagnetic radiation. The mechanism of neuronal firing regulated by high-low-frequency signal and electromagnetic radiation discussed here could be applied to research neuronal networks and synchronisation modes.

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh-Nagumo neuron

Based on the FitzHugh-Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.