Nerve Impulse Propagation Research Articles

Nonlinear dynamic wave characteristics of optical soliton solutions in ion-acoustic wave

Traveling wave solutions are utilized to depict reaction-diffusion and analyze electrical signal transmission and propagation in space-time nonlinear fractional order partial differential equations like the space-time fractional Telegraph and Kolmogorov-Petrovsky Piskunov equations, and that are used in physical science to model combustion, biological research to model nerve impulse propagation, chemical dynamics to model concentration in order wave propagation, and plasma to model the progression of a set of duffing oscillators. In this study, the new generalized (G′/G)−expansion technique was employed to construct some novel and more universal closed-form traveling wave solutions in the sense of conformable derivatives which explain the above-stated phenomena properly. By utilizing complex fractional transformation, the ordinary differential equations are generated from fractional order differential equations. The recommended technique allowed us to produce some dynamical wave patterns of kink, single soliton, compacton, periodic shape, multiple periodic waves, anti-kink, and other structures are developed, which are shown using 3D plots and contour plots to illustrate the physical layout clearly. The traveling waveform responses can be defined in terms of functions based on trigonometry, hyperbolic operations, and rational functions and that are quick, flexible, and simple to reproduce. Furthermore, the obtained closed-form solutions for nonlinear fractional evolution equations make stability analysis and accuracy comparison amongst numerical solvers easier, which asserts that the new generalized (G′/G)−expansion technique is one of the most proficient and effective approaches.

Multiwaves, breathers, lump and other solutions for the Heimburg model in biomembranes and nerves

In this manuscript, a mathematical model known as the Heimburg model is investigated analytically to get the soliton solutions. Both biomembranes and nerves can be studied using this model. The cell membrane’s lipid bilayer is regarded by the model as a substance that experiences phase transitions. It implies that the membrane responds to electrical disruptions in a nonlinear way. The importance of ionic conductance in nerve impulse propagation is shown by Heimburg’s model. The dynamics of the electromechanical pulse in a nerve are analytically investigated using the Hirota Bilinear method. The various types of solitons are investigates, such as homoclinic breather waves, interaction via double exponents, lump waves, multi-wave, mixed type solutions, and periodic cross kink solutions. The electromechanical pulse’s ensuing three-dimensional and contour shapes offer crucial insight into how nerves function and may one day be used in medicine and the biological sciences. Our grasp of soliton dynamics is improved by this research, which also opens up new directions for biomedical investigation and medical developments. A few 3D and contour profiles have also been created for new solutions, and interaction behaviors have also been shown.

Regulators of Oligodendrocyte Differentiation.

Myelination has evolved as a mechanism to ensure fast and efficient propagation of nerve impulses along axons. Within the central nervous system (CNS), myelination is carried out by highly specialized glial cells, oligodendrocytes. The formation of myelin is a prolonged aspect of CNS development that occurs well into adulthood in humans, continuing throughout life in response to injury or as a component of neuroplasticity. The timing of myelination is tightly tied to the generation of oligodendrocytes through the differentiation of their committed progenitors, oligodendrocyte precursor cells (OPCs), which reside throughout the developing and adult CNS. In this article, we summarize our current understanding of some of the signals and pathways that regulate the differentiation of OPCs, and thus the myelination of CNS axons.

A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method

In this manuscript, the collocation approach using the higher order extended cubic B-spline (ECBS) as the basis function is efficiently used to numerically solve the generalized time fractional Burger-Huxley equation (TFBHE). The Burger-Huxley equation is a widely studied nonlinear partial differential equation that models the propagation of nerve impulses in excitable systems such as the neurons in the brain. The time fractional versions of the Burger-Huxley equation (BHE), which incorporate fractional derivatives in time direction to model the anomalous diffusion, reaction mechanism, and memory effects observed in many physical and biological systems. The θ−weighted technique and the Atangana–Baleanu operator are employed to discretize the equation. The higher order EBCS method is used in space direction. The stability and convergence analysis are also presented. Numerous examples are carried out to show the validity of the technique. The graphical representations and computed results are observed the good agreement with the literature.

Analysis of two spectral Galerkin approximation schemes for solving the perturbed FitzHugh-Nagumo neuron model

In this paper, we mainly study two spectral Galerkin approximation schemes of the FitzHugh-Nagumo (FHN) neuron model for the nerve impulse propagation, which contains a small parameter perturbation and strong nonlinearity. To this end, we consider two kinds of temporal discretization by a semi-implicit Euler method and a Crank-Nicolson method, and the spatial discretization by the spectral Galerkin method for the perturbed FHN neuron model. In particular, in order to obtain the second-order approximation in time for the numerical scheme, we modify the nonlinear term f(un) in the Crank-Nicolson spectral Galerkin (CNSG) scheme. We derive the error estimations with optimal convergence rates of the numerical solutions by the first-order semi-implicit spectral Galerkin (SISG) approximation scheme and the second-order modified CNSG (MCNSG) approximation scheme for the perturbed FHN neuron model. Finally, some numerical examples of one-dimensional and two-dimensional nonlinear FHN models with periodic boundary conditions are carried out to verify that the approximate solutions of the proposed SISG and MCNSG schemes satisfy the proved theoretical results.

Overview of myelin, major myelin lipids, and myelin-associated proteins.

Myelin is a modified cell membrane that forms a multilayer sheath around the axon. It retains the main characteristics of biological membranes, such as lipid bilayer, but differs from them in several important respects. In this review, we focus on aspects of myelin composition that are peculiar to this structure and differentiate it from the more conventional cell membranes, with special attention to its constituent lipid components and several of the most common and important myelin proteins: myelin basic protein, proteolipid protein, and myelin protein zero. We also discuss the many-fold functions of myelin, which include reliable electrical insulation of axons to ensure rapid propagation of nerve impulses, provision of trophic support along the axon and organization of the unmyelinated nodes of Ranvier, as well as the relationship between myelin biology and neurologic disease such as multiple sclerosis. We conclude with a brief history of discovery in the field and outline questions for future research.

Myelin protein zero - the structural foundation behind peripheral compact myelin.

Schwann cells are the myelinating glia of the peripheral nervous system (PNS). During PNS development, Schwann cell precursors differentiate into mature Schwann cells after the radial sorting of axons and form myelin around selected axonal segments. This multilayered, highly lipid-rich and insulative membrane structure significantly accelerates nerve impulse propagation, which is a pre-requisite for the efficient function of the PNS. During this differentiation process, protein zero (P0), a single-pass transmembrane protein, is expressed in high amounts. P0 is the most abundant PNS myelin protein, at up to 50% of total protein, and its accumulation in membranes eventually forms stable compact myelin. Failure to do so, like in the case of mutated or truncated protein, results in non-compacted myelin and demyelination. This subsequently causes incurable peripheral neuropathies, such as Charcot-Marie-Tooth disease (CMT) and Dejerine-Sottas syndrome (DSS), where CMT alone afflicts nearly 3 million people globally. To understand the compaction and maturation of PNS myelin, and the molecular etiology of disease, uncovering the structure-function relationships of P0 are of great importance. We demonstrate the molecular foundation of P0-mediated membrane stacking using a hybrid structural biology approach: on the extracellular side, immunoglobulin (Ig)-like domains form a zipper-like assembly of apposing protein monomers, whereas on the cytoplasmic side, the short, positively charged P0 tail (P0ct) glues membranes together. P0ct undergoes a substantial folding event during membrane binding, and we provide rationale to why membrane stacking is affected in diseases through functional in vitro mutagenesis studies. Additionally, we speculate on how post-translational modifications in P0ct help P0 locate to its target compartments, without inducing premature membrane stacking. Our results shed light on the essential role of P0 in during myelin maturation, and why other proteins fail to replace P0 when its function is compromised.

Основные нервные процессы – возбуждение и торможение как адаптивные реакции (обзор). Сообщение 1. Критический анализ эволюции теорий об основных нервных процессах и доказательство зависимости тормозного ответа нейронов от их текущего адаптационного состояния

In the work is criticized the paradigm about excitation and inhibition as the main nervous processes caused by the activity of specific excitatory and inhibitory systems. Analysis of the literature shows that the currently in neurophysiology dominant approach, justifying the existence of such systems, relies mainly on facts obtained in vitro, which are far from normal for the existence of nerve cells. Literature data are presented that indicate the dependence of the nature of the neuron response on its current adaptive (biological) state and the cytotoxicity of the neurotransmitter. In particular, in the review (part 1) it is shown that in response to the action of GABA (less toxic than neurotransmitter glutamate), brain neurons in both good (in vivo) and relatively bad (which is often in vitro) vital state will respond by hyperpolarizing postsynaptic potential (HPSP), either without excitation – the phenomenon of hyperpolarizational inhibition, or with the generation of nerve impulses, by posthyperpolarization recoil mechanism. In very poor living conditions (in vivo or in vitro), the neuronal response to GABA will always be a depolarizing postsynaptic potential (DPSP) with or without generation of action potentials (AP).

A new mouse model of Charcot-Marie-Tooth 2J neuropathy replicates human axonopathy and suggest alteration in axo-glia communication.

Myelin is essential for rapid nerve impulse propagation and axon protection. Accordingly, defects in myelination or myelin maintenance lead to secondary axonal damage and subsequent degeneration. Studies utilizing genetic (CNPase-, MAG-, and PLP-null mice) and naturally occurring neuropathy models suggest that myelinating glia also support axons independently from myelin. Myelin protein zero (MPZ or P0), which is expressed only by Schwann cells, is critical for myelin formation and maintenance in the peripheral nervous system. Many mutations in MPZ are associated with demyelinating neuropathies (Charcot-Marie-Tooth disease type 1B [CMT1B]). Surprisingly, the substitution of threonine by methionine at position 124 of P0 (P0T124M) causes axonal neuropathy (CMT2J) with little to no myelin damage. This disease provides an excellent paradigm to understand how myelinating glia support axons independently from myelin. To study this, we generated targeted knock-in MpzT124M mutant mice, a genetically authentic model of T124M-CMT2J neuropathy. Similar to patients, these mice develop axonopathy between 2 and 12 months of age, characterized by impaired motor performance, normal nerve conduction velocities but reduced compound motor action potential amplitudes, and axonal damage with only minor compact myelin modifications. Mechanistically, we detected metabolic changes that could lead to axonal degeneration, and prominent alterations in non-compact myelin domains such as paranodes, Schmidt-Lanterman incisures, and gap junctions, implicated in Schwann cell-axon communication and axonal metabolic support. Finally, we document perturbed mitochondrial size and distribution along MpzT124M axons suggesting altered axonal transport. Our data suggest that Schwann cells in P0T124M mutant mice cannot provide axons with sufficient trophic support, leading to reduced ATP biosynthesis and axonopathy. In conclusion, the MpzT124M mouse model faithfully reproduces the human neuropathy and represents a unique tool for identifying the molecular basis for glial support of axons.

Detailed magnetoelectric analysis of a nerve impulse propagation along the brachial plexus

ObjectiveTo visualize impulse conduction along the brachial plexus through simultaneous electromagnetic measurements. MethodsNeuromagnetic fields following median nerve stimulation were recorded above the clavicle with a superconducting quantum interference device biomagnetometer system in 7 healthy volunteers. Compound nerve action potentials (CNAPs) were obtained from 12 locations. Pseudocolor maps of equivalent currents reconstructed from magnetic fields and isopotential contour maps were superimposed onto X-ray images. Surface potentials and current waveforms at virtual electrodes along the brachial plexus were compared. ResultsIn magnetic field analysis, the leading axonal current followed by a trailing backward current traveled rostrally along the brachial plexus. The spatial extent of the longitudinal intra-axonal currents corresponded to the extent of the positive–negative-positive potential field reflecting transmembrane volume currents. The peaks and troughs of the intra-axonal biphasic current waveforms coincided with the zero-crossings of triphasic CNAP waveforms. The amplitudes of CNAPs and current moments were linearly correlated. ConclusionsReconstructed neural activity in magnetic field analysis visualizes not only intra-axonal currents, but also transmembrane volume currents, which are in good agreement with the surface potential field. SignificanceMagnetoneurography is a novel non-invasive functional imaging modality for the brachial plexus whose performance can surpass that of electric potential measurement.

Models of Nerve Impulse Generation and Conduction

Models of Nerve Impulse Generation and Conduction

Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

We systematically study the evolution of modulated nerve impulses in a myelinated nerve fiber, where both the ionic current and membrane capacitance provide the necessary nonlinear feedbacks. This is achieved by using a perturbation technique, in which the Liénard form of the modified discrete Fitzhugh–Nagumo equation is reduced to the complex Ginzburg–Landau amplitude equation. Three distinct values of the capacitive feedback parameter are considered. At the critical value of the capacitive feedback parameter, it is shown that the dynamics of the system is governed by the dissipative nonlinear Schrödinger equation. Linear stability analysis of the system depicts the instability of plane waves, which is manifested as burst of modulated nerve impulses that fulfills the Benjamin–Feir criteria. Variations of the capacitive feedback parameter generally influences the plane wave stability and hence the type of wave profile identified in the neural network. Results of numerical simulations mainly confirm the propagation, collision, and annihilation of nerve impulses in the myelinated axon.

On a Model for Nerve Impulse Generation Mediated by Electromechanical Processes

On a Model for Nerve Impulse Generation Mediated by Electromechanical Processes

Spatiotemporal characteristics in systems of diffusively coupled excitable slow-fast FitzHugh-Rinzel dynamical neurons.

In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the formation of spatiotemporal patterns. We focus on local, nonlinear excitations and diverse neural responses in an excitable one- and two-dimensional configuration of diffusively coupled FitzHugh-Rinzel neurons. The study of the emerging spatiotemporal patterns is essential in understanding the working mechanism in different brain areas. We derive analytically the coefficients of the amplitude equations in the vicinity of Hopf bifurcations and characterize various patterns, including spirals exhibiting complex geometric substructures. Furthermore, we derive analytically the condition for the development of antispirals in the neighborhood of the bifurcation point. The emergence of broken target waves can be observed to form spiral-like profiles. The spatial dynamics of the excitable system exhibits two- and multi-arm spirals for small diffusive couplings. Our results reveal a multitude of neural excitabilities and possible conditions for the emergence of spiral-wave formation. Finally, we show that the coupled excitable systems with different firing characteristics participate in a collective behavior that may contribute significantly to irregular neural dynamics.

Membrane-Mediated Activity of Local Anesthetics

The activity of local anesthetics (LAs) has been attributed to the inhibition of ion channels, causing anesthesia. However, there is a growing body of research showing that LAs act on a wide range of receptors and channel proteins far beyond simple analgesia. The current concept of ligand recognition may no longer explain the multitude of protein targets influenced by LAs. We hypothesize that LAs can cause anesthesia without directly binding to the receptor proteins just by changing the physical properties of the lipid bilayer surrounding these proteins and ion channels based on LAs' amphiphilicity. It is possible that LAs act in one of the following ways: They 1) dissolve raft-like membrane microdomains, 2) impede nerve impulse propagation by lowering the lipid phase transition temperature, or 3) modulate the lateral pressure profile of the lipid bilayer. This could also explain the numerous additional effects of LAs besides anesthesia. Furthermore, the concepts of membrane-mediated activity and binding to ion channels do not have to exclude each other. If we were to consider LA as the middle part of a continuum between unspecific membrane-mediated activity on one end and highly specific ligand binding on the other end, we could describe LA as the link between the unspecific action of general anesthetics and toxins with their highly specific receptor binding. This comprehensive membrane-mediated model offers a fresh perspective to clinical and pharmaceutical research and therapeutic applications of local anesthetics. SIGNIFICANCE STATEMENT: Local anesthetics, according to the World Health Organization, belong to the most important drugs available to mankind. Their rediscovery as therapeutics and not only anesthetics marks a milestone in global pain therapy. The membrane-mediated mechanism of action proposed in this review can explain their puzzling variety of target proteins and their thus far inexplicable therapeutic effects. The new concept presented here places LAs on a continuum of structures and molecular mechanisms in between small general anesthetics and the more complex molecular toxins.

Memory in Ion Channel Kinetics.

Ion channels are transport proteins present in the lipid bilayers of biological membranes. They are involved in many physiological processes, such as the generation of nerve impulses, hormonal secretion, and heartbeat. Conformational changes in the ion channel-forming protein allow the opening or closing of pores to control the ionic flux through the cell membranes. The opening and closing of the ion channel have been classically treated as a random kinetic process, known as a Markov process. Here the time the channel remains in a given state is assumed to be independent of the condition it had in the previous state. More recently, however, several studies have shown that this process is not random but a deterministic one, where both the open and closed dwell-times and the ionic current flowing through the channel are history-dependent. This property is called long memory or long-range correlation. However, there is still much controversy regarding how this memory originates, which region of the channel is responsible for this property, and which models could best reproduce the memory effect. In this article, we provide a review of what is, where it is, its possible origin, and the mathematical methods used to analyze the long-term memory present in the kinetic process of ion channels.

Statistical Field Theory of the Transmission of Nerve Impulses

Background Stochastic processes leading voltage-gated ion channel dynamics on the nerve cell membrane are a sufficient condition to describe membrane conductance through statistical mechanics of disordered and complex systems. Results Voltage-gated ion channels in the nerve cell membrane are described by the Ising model. Stochastic circuit elements called “Ising Neural Machines” are introduced. Action potentials are described as quasi-particles of a statistical field theory for the Ising system. Conclusions The particle description of action potentials is a new point of view and a powerful tool to describe the generation and propagation of nerve impulses, especially when classical electrophysiological models break down. The particle description of action potentials allows us to develop a new generation of devices to study neurodegenerative and demyelinating diseases as Multiple Sclerosis and Alzheimer’s disease, even integrated by connectomes. It is also suitable for the study of complex networks, quantum computing, artificial intelligence, machine and deep learning, cryptography, ultra-fast lines for entanglement experiments and many other applications of medical, physical and engineering interest.

Statistical field theory of the transmission of nerve impulses

BackgroundStochastic processes leading voltage-gated ion channel dynamics on the nerve cell membrane are a sufficient condition to describe membrane conductance through statistical mechanics of disordered and complex systems.ResultsVoltage-gated ion channels in the nerve cell membrane are described by the Ising model. Stochastic circuit elements called “Ising Neural Machines” are introduced. Action potentials are described as quasi-particles of a statistical field theory for the Ising system.ConclusionsThe particle description of action potentials is a new point of view and a powerful tool to describe the generation and propagation of nerve impulses, especially when classical electrophysiological models break down.The particle description of action potentials allows us to develop a new generation of devices to study neurodegenerative and demyelinating diseases as Multiple Sclerosis and Alzheimer’s disease, even integrated by connectomes. It is also suitable for the study of complex networks, quantum computing, artificial intelligence, machine and deep learning, cryptography, ultra-fast lines for entanglement experiments and many other applications of medical, physical and engineering interest.

Numerical Study of the Unique Solvability of the Showalter - Sidorov Problem for a Mathematical Model of the Propagation of Nerve Impulses in the Membrane

Numerical Study of the Unique Solvability of the Showalter - Sidorov Problem for a Mathematical Model of the Propagation of Nerve Impulses in the Membrane

МОРФОЛОГИЯ ФАЗОВОГО ПРОСТРАНСТВА ОДНОЙ МАТЕМАТИЧЕСКОЙ МОДЕЛИ РАСПРОСТРАНЕНИЯ НЕРВНОГО ИМПУЛЬСА В МЕМБРАННОЙ ОБОЛОЧКЕ

The article is devoted to the study of the morphology of the phase space of a degenerate two-component mathematical model of a nerve impulse propagation in the membrane shell. A mathematical model is studied in the case when the parameter at the time derivative of the component responsible for the dynamics of the membrane potential is equal to zero, and the theorem about the fact that the phase space is simple in this case is proved. A mathematical model is also considered in the case when the parameter at the time derivative of the component responsible for the ion currents is equal to zero, and the theorem on the presence of singularities of Whitney assemblies is proved. Based on the results obtained, the phase space of the mathematical model is constructed in the case when the parameters at the time derivative of both components of the system are equal to zero. The author gives examples of the construction of the phase space, illustrating the presence of features in the phase space of the studied problems based on the Galerkin method.