Collective responses in electrical activities of neurons under field coupling

A neuron model with nonlinear membranes

One-layer membrane separates the gradient field in and out of the cell, while some two-layer membranes filled with excitable media/material are important to regulate the energy flow when ions are propagated and diffused. The intracellular and extracellular media can be effectively separated by the membrane. It is important to clarify and describe the biophysical function and then the capacitive property can be reproduced in equivalent neural circuit. Here, we suggest the cell membrane has certain thickness and becomes flexible under external stimuli, therefore, it is considered as a kind of nonlinear media. To mimic the physical property of the two-layer cell membrane, a nonlinear resistor is used to connect two linear circuits, which is used to describe the electrical characteristic of two sides of the cell membrane, respectively. The combination of two linear circuits via a nonlinear resistor can describe the energy characteristic and firing mode in the flexible membrane of biophysical neurons. Circuit equations are defined and converted into equivalent nonlinear oscillator like a neuron. The voltage difference for the two capacitors can be consistent with the membrane potential for the neuron. The Hamilton energy function for this neuron can be mapped from the field energy in the electronic components, and it is also derived by using Helmholtz's theorem. The neuron can show similar spiking and bursting firing patterns, and uncertain diversity in membrane potentials is effective to support continuous firing patterns and mode transition under external stimulus. Furthermore, noisy disturbance is applied to induce coherence resonance. The results indicate that the lower coefficient variability and higher average energy level supports periodic firing in the neuron under coherence resonance. Therefore, this neuron model with nonlinear membranes (or two-layer form) is more suitable for identifying the biophysical property of biological neuron.

Hamilton energy balance and synchronization behaviors of two functional neurons

The nervous system is composed of various functional neurons, some of which perceive sound or light, and these physical signals can be converted into bioelectrical signals. From the biophysical point of view, piezoelectric ceramic embedded in neuronal circuits can detect the external auditory waves, while phototube can capture light signals, so as to obtain two functional neurons with auditory recognition and light-dependent recognition. Considering the two identical or different functional neurons are connected by an induction coil to stimulate magnetic field coupling, and there will be energy diversity when they are driven by different initial conditions or external stimulation. Thus, synaptic connections can be activated and awakened in an adaptive manner when field energy is exchanged, and the coupling channel remains open until the energy diversity between neurons is controlled at a limited threshold. For this purpose, a criterion of the coupling strength increases exponentially is proposed to discuss the enhancement of neuronal synaptic connections. It is found that two neurons can be coupled adaptively to achieve complete synchronization, quasi-synchronization or intermittent quasi-synchronization. These results could help in designing functional assistive devices for patients with hearing or vision impairment.

Proteinoid Microspheres as Protoneural Networks

Proteinoids, also known as thermal proteins, possess a fascinating ability to generate microspheres that exhibit electrical spikes resembling the action potentials of neurons. These spiking microspheres, referred to as protoneurons, hold the potential to assemble into proto-nanobrains. In our study, we investigate the feasibility of utilizing a promising electrochemical technique called differential pulse voltammetry (DPV) to interface with proteinoid nanobrains. We evaluate DPV's suitability by examining critical parameters such as selectivity, sensitivity, and linearity of the electrochemical responses. The research systematically explores the influence of various operational factors, including pulse width, pulse amplitude, scan rate, and scan time. Encouragingly, our findings indicate that DPV exhibits significant potential as an efficient electrochemical interface for proteinoid nanobrains. This technology opens up new avenues for developing artificial neural networks with broad applications across diverse fields of research.

Recent Development of Neural Microelectrodes with Dual-Mode Detection

Neurons communicate through complex chemical and electrophysiological signal patterns to develop a tight information network. A physiological or pathological event cannot be explained by signal communication mode. Therefore, dual-mode electrodes can simultaneously monitor the chemical and electrophysiological signals in the brain. They have been invented as an essential tool for brain science research and brain-computer interface (BCI) to obtain more important information and capture the characteristics of the neural network. Electrochemical sensors are the most popular methods for monitoring neurochemical levels in vivo. They are combined with neural microelectrodes to record neural electrical activity. They simultaneously detect the neurochemical and electrical activity of neurons in vivo using high spatial and temporal resolutions. This paper systematically reviews the latest development of neural microelectrodes depending on electrode materials for simultaneous in vivo electrochemical sensing and electrophysiological signal recording. This includes carbon-based microelectrodes, silicon-based microelectrode arrays (MEAs), and ceramic-based MEAs, focusing on the latest progress since 2018. In addition, the structure and interface design of various types of neural microelectrodes have been comprehensively described and compared. This could be the key to simultaneously detecting electrochemical and electrophysiological signals.

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.

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.

Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization

The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the prediction and the realization of self-sustained oscillations in different kinds of excitable networks are the challenging tasks. In this paper, we extensively investigate the prediction and the realization of a Winfree loop sustained oscillation (WLSO) in two-dimensional (2D) excitable lattices. By analyzing the network structure, the fundamental oscillation source structure (FOSS) of WLSO in a 2D excitable lattice is exposed explicitly. For the suitable combinations of system parameters, the Winfree loop can self-organize on the FOSS to form an oscillation source sustaining the oscillation, and these suitable parameter combinations are predicted by calculating the minimum Winfree loop length and have been further confirmed in numerical simulations. However, the FOSS cannot spontaneously offer the WLSO in 2D excitable lattices in usual cases due to the coupling bidirectionality and the symmetry properties of the lattice. A targeted protection scheme of the oscillation source is proposed by overcoming these two drawbacks. Finally, the WLSO is realized in the 2D excitable lattice successfully.

Spiral waves in externally excited neuronal network: Solvable model with a monotonically differentiable magnetic flux

Spiral waves are particular spatiotemporal patterns connected to specific phase singularities representing topological wave dislocations or nodes of zero amplitude, witnessed in a wide range of complex systems such as neuronal networks. The appearance of these waves is linked to the network structure as well as the diffusion dynamics of its blocks. We report a novel form of the Hindmarsh-Rose neuron model utilized as a square neuronal network, showing the remarkable multistructure of dynamical patterns ranging from characteristic spiral wave domains of spatiotemporal phase coherence to regions of hyperchaos. The proposed model comprises a hyperbolic memductance function as the monotone differentiable magnetic flux. Hindmarsh-Rose neurons with an external electromagnetic excitation are considered in three different cases: no excitation, periodic excitation, and quasiperiodic excitation. We performed an extensive study of the neuronal dynamics including calculation of equilibrium points, bifurcation analysis, and Lyapunov spectrum. We have found the property of antimonotonicity in bifurcation scenarios with no excitation or periodic excitation and identified wide regions of hyperchaos in the case of quasiperiodic excitation. Furthermore, the formation and elimination of the spiral waves in each case of external excitation with respect to stimuli parameters are investigated. We have identified novel forms of Hindmarsh-Rose bursting dynamics. Our findings reveal multipartite spiral wave formations and symmetry breaking spatiotemporal dynamics of the neuronal model that may find broad practical applications.

Hindmarsh-Rose neuron model with memristors

We analyze single and coupled Hindmarsh-Rose neurons in the presence of a time varying electromagnetic field which results from the exchange of ions across the membrane. Memristors are used to model the relation between magnetic flux of the electromagnetic field and the membrane potential of interacting neurons. The bifurcation analysis of Hindmarsh-Rose neurons has been carried out by varying the modulation intensity of induced current on the membrane potential. Many important dynamical behaviors such as synchrony, desynchrony, amplitude death, anti-phase oscillations, coexistence of resting and spiking state, and near death rare spikes are observed when the neurons are coupled using electrical and chemical synapses. In all cases the transverse Lyapunov exponents are plotted to observe the point of transition from desynchrony to synchrony. The memristor based analysis on neural networks can contribute to biological system modeling and can be used as a synapse in hardware of artificial neural networks.

Constraints of Metabolic Energy on the Number of Synaptic Connections of Neurons and the Density of Neuronal Networks

Neuronal networks in the brain are the structural basis of human cognitive function, and the plasticity of neuronal networks is thought to be the principal neural mechanism underlying learning and memory. Dominated by the Hebbian theory, researchers have devoted extensive effort to studying the changes in synaptic connections between neurons. However, understanding the network topology of all synaptic connections has been neglected over the past decades. Furthermore, increasing studies indicate that synaptic activities are tightly coupled with metabolic energy, and metabolic energy is a unifying principle governing neuronal activities. Therefore, the network topology of all synaptic connections may also be governed by metabolic energy. Here, by implementing a computational model, we investigate the general synaptic organization rules for neurons and neuronal networks from the perspective of energy metabolism. We find that to maintain the energy balance of individual neurons in the proposed model, the number of synaptic connections is inversely proportional to the average of the synaptic weights. This strategy may be adopted by neurons to ensure that the ability of neurons to transmit signals matches their own energy metabolism. In addition, we find that the density of neuronal networks is also an important factor in the energy balance of neuronal networks. An abnormal increase or decrease in the network density could lead to failure of energy metabolism in the neuronal network. These rules may change our view of neuronal networks in the brain and have guiding significance for the design of neuronal network models.

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.