Investigating the role of axonal ion channel cooperativity in action potential dynamics: Studies on Hodgkin-Huxley's model.

Voltage-gated ion channels play an important role in generating action potential in neurons. These ion channels are found to be in localized cluster form on the axonal membrane surface and behave cooperatively. However, in Hodgkin & Huxley's model of action potential the ion channels are considered to function independently. According to some recent reports, the activity of an ion channel is influenced by the neighboring ion channels' activities. We have modified the Hodgkin-Huxley's model based on our previous studies on cooperativity among ion channels. Computational analysis of the proposed model shows that the initiation of the action potential, amplitude and hyperpolarization are affected significantly by the cooperative interactions among the voltage-gated ion channels present on the axonal membrane surface. These results are qualitatively supported by the existing experimental facts.

Quantitative analysis of noninvasive deep temporal interference stimulation: A simulation and experimental study.

Background: Deep brain stimulation (DBS) is a method for stimulating deep regions of the brain for the treatment of various neurological and psychiatric disorders such as depression, obsessive-compulsive disorder, addiction, and Parkinson's disease. Generally, DBS can be performed using both invasive and non-invasive approaches. Invasive DBS is associated with several problems, including intracranial bleeding, infection, and changes in the position of the electrode tip. Temporal interference (TI) stimulation is a non-invasive technique used to stimulate deep regions of the brain by applying two high-frequency sinusoidal currents with slightly different frequencies. New method: This paper presents insights into the response of the spiking in the Hodgkin-Huxley (HH) neuron model of the rat somatosensory cortex by changing the parameters carrier frequency, current ratio, and difference frequency of TI stimulation. Furthermore, in order to experimentally evaluate the effect of TI stimulation on the activation of the left motor cortex, an experiment was conducted to measure the motion induced by the balanced and unbalanced TI stimulation. In the experiment, a three-axis accelerometer was attached to the right hand of the animal to determine the position of the hand. Results: Simulation results of the HH model showed that the frequency of the envelope of the TI stimulation is identical to the fundamental frequency of the neuron spikes. This result was obtained for difference frequencies of 6 Hz and 9 Hz in balanced and unbalanced TI stimulations. Moreover specifically, when the difference frequency is set to zero, the carrier frequency is within the range of 1300-1400 Hz, and the current range is between 140 and 250 µA/cm2, the firing rate reached to its highest value. In the experimental result, the maximum range of movement at a difference frequency of Δf = 6 Hz was approximately 1.6 mm and 5.3 mm in the z and y directions respectively. Comparison with existing method: The results of the spatial spectrum of the rat hand movement were consistent with the spectrum information of the simulation results. Additionally, steering the interfering region to the left motor cortex leads to noticeable contralateral movement of the right hand while no movement was observed in the right hand during the stimulation of the right motor cortex. Conclusion: This technique of stimulation for the deep regions of the brain is a promising tool to noninvasively treat various neurological and psychiatric disorders such as morphine dependence in addicted rats.

Joule heating involving ion currents through channel proteins.

Ion currents associated with channel proteins in the presence of membrane potential are ubiquitous in cellular and organelle membranes. When an ion current occurs through a channel protein, Joule heating should occur. However, this Joule heating seems to have been largely overlooked in biology. Here we show theoretical investigation of Joule heating involving channel proteins in biological processes. We used electrochemical potential to derive the Joule's law for an ion current through an ion transport protein in the presence of membrane potential, and we suggest that heat production and absorption can occur. Simulation of temperature distribution around a single channel protein with the Joule heating revealed that the temperature increase was as small as <10-3 K, although an ensemble of channel proteins was suggested to exhibit a noticeable temperature increase. Thereby, we theoretically investigated the Joule heating of systems containing ensembles of channel proteins. Nerve is known to undergo rapid heat production followed by heat absorption during the action potential, and our simulation of Joule heating for a squid giant axon combined with the Hodgkin-Huxley model successfully reproduced the feature of the heat. Furthermore, we extended the theory of Joule heating to uncoupling protein 1 (UCP1), a solute carrier family transporter, which is important to the non-shivering thermogenesis in brown adipose tissue mitochondria (BATM). Our calculations showed that the Joule heat involving UCP1 was comparable to the literature calorimetry data of BATM. Joule heating of ion transport proteins is likely to be one of important mechanisms of cellular thermogenesis.

Hodgkin's and Huxley's own assessments of their "quantitative description" of nerve membrane current.

Alan Hodgkin's and Andrew Huxley's mid-20th century work on the ionic currents generating neuron action potentials stands among that century's great scientific achievements. Unsurprisingly, that case has attracted widespread attention from neuroscientists, historians and philosophers of science. In this paper, I do not propose to add any new insights into the vast historical treatment of Hodgkin's and Huxley's scientific discoveries in that much- discussed episode. Instead, I focus on an aspect of it that hasn't received much attention: Hodgkin's and Huxley's own assessments about what their famous "quantitative description" accomplished. The "Hodgkin-Huxley model" is now widely recognized as a foundation of contemporary computational neuroscience. Yet Hodgkin and Huxley expressed serious caveats about their model and what it added to their scientific discoveries, as far back as their (1952d), in which they first presented their model. They were even more critical of its accomplishments in their Nobel Prize addresses a decade later. Most notably, as I argue here, some worries they raised about their quantitative description seem still to be relevant to current work in ongoing computational neuroscience.

The Goldberg-Huxley model of the pathway to psychiatric care: 21st-century systematic review.

BACKGROUND: The classification of mental disorders used to be based only on people seen by hospital psychiatrists. In fact, most people with a mental disorder were, and are, not seen by psychiatrists because of decisions made prior to psychiatric consultation. The first description of this 'pathway' to care and its levels and filters was published by Goldberg and Huxley in 1980. AIMS: To conduct a review of papers relevant to the application of the Goldberg-Huxley model in the 21st century. METHOD: Systematic review (PROSPERO registration CRD42021270603) of the pathway to psychiatric care in the 21st century. The review concentrates on community surveys and passage through the first filter (consultation in primary care or its equivalent). Ten databases were searched for papers meeting the defined inclusion criteria published between 2000 and 2019 and completed on 15 February 2020. RESULTS: In total, 1824 papers were retrieved, 137 screened fully and 31 included in this review. The results are presented in a table comparing them with previous research. Despite major social, economic and health service changes since 1980, community prevalence and consultation rates remain remarkably consistent and in line with World Health Organization findings. Passage through the first filter is largely unchanged and there is evidence that the same factors operate internationally, especially gender and social parameters. CONCLUSIONS: The Goldberg-Huxley model remains applicable internationally, but this may change owing to an increasingly mixed mental health economy and reduced access to primary care services.

A biophysical and statistical modeling paradigm for connecting neural physiology and function.

To understand single neuron computation, it is necessary to know how specific physiological parameters affect neural spiking patterns that emerge in response to specific stimuli. Here we present a computational pipeline combining biophysical and statistical models that provides a link between variation in functional ion channel expression and changes in single neuron stimulus encoding. More specifically, we create a mapping from biophysical model parameters to stimulus encoding statistical model parameters. Biophysical models provide mechanistic insight, whereas statistical models can identify associations between spiking patterns and the stimuli they encode. We used public biophysical models of two morphologically and functionally distinct projection neuron cell types: mitral cells (MCs) of the main olfactory bulb, and layer V cortical pyramidal cells (PCs). We first simulated sequences of action potentials according to certain stimuli while scaling individual ion channel conductances. We then fitted point process generalized linear models (PP-GLMs), and we constructed a mapping between the parameters in the two types of models. This framework lets us detect effects on stimulus encoding of changing an ion channel conductance. The computational pipeline combines models across scales and can be applied as a screen of channels, in any cell type of interest, to identify ways that channel properties influence single neuron computation.

Sodium channel slow inactivation normalizes firing in axons with uneven conductance distributions.

The Na+ channels that are important for action potentials show rapid inactivation, a state in which they do not conduct, although the membrane potential remains depolarized.1,2 Rapid inactivation is a determinant of millisecond-scale phenomena, such as spike shape and refractory period. Na+ channels also inactivate orders of magnitude more slowly, and this slow inactivation has impacts on excitability over much longer timescales than those of a single spike or a single inter-spike interval.3,4,5,6,7,8,9,10 Here, we focus on the contribution of slow inactivation to the resilience of axonal excitability11,12 when ion channels are unevenly distributed along the axon. We study models in which the voltage-gated Na+ and K+ channels are unevenly distributed along axons with different variances, capturing the heterogeneity that biological axons display.13,14 In the absence of slow inactivation, many conductance distributions result in spontaneous tonic activity. Faithful axonal propagation is achieved with the introduction of Na+ channel slow inactivation. This "normalization" effect depends on relations between the kinetics of slow inactivation and the firing frequency. Consequently, neurons with characteristically different firing frequencies will need to implement different sets of channel properties to achieve resilience. The results of this study demonstrate the importance of the intrinsic biophysical properties of ion channels in normalizing axonal function.

Mathematical Model for Skin Pain Sensation under Local Distributed Mechanical Compression for Electronic Skin Applications.

Skin pain resulting from mechanical compression is one of the most common pains in daily life and the indispensable information for electronic skin to perceive external signals. The external mechanical stimuli are transduced into impulses and transmitted via nerve fiber, and finally, the sensation is perceived via the procession of the nerve system. However, the mathematical mechanism for pain sensation due to mechanical stimuli remains unclear. In this paper, a mathematical model for skin pain sensation under compression is established, in which the Flament solution, the revised Hodgkin-Huxley model, and the mathematical model gate control theory are considered simultaneously. The proposed model includes three parts: a mechanical model of skin compression, a model of transduction, and a model of modulation and perception. It is demonstrated that the pain sensation degree increases with the compression amplitude and decreases with deeper nociceptor location in the skin. With the help of the proposed model, the quantitative relationship between compression pain sensation and external mechanical stimuli is revealed, which has a significant benefit in promoting the design and mechanism research of electronic skin with pain perception function.

The 70-year search for the voltage-sensing mechanism of ion channels.

This retrospective on the voltage-sensing mechanisms and gating models of ion channels begins in 1952 with the charged gating particles postulated by Hodgkin and Huxley, viewed as charges moving across the membrane and controlling its permeability to Na+ and K+ ions. Hodgkin and Huxley postulated that their movement should generate small and fast capacitive currents, which were recorded 20 years later as gating currents. In the early 1980s, several voltage-dependent channels were cloned and found to share a common architecture: four homologous domains or subunits, each displaying six transmembrane α-helical segments, with the fourth segment (S4) displaying four to seven positive charges invariably separated by two non-charged residues. This immediately suggested that this segment was serving as the voltage sensor of the channel (the molecular counterpart of the charged gating particle postulated by Hodgkin and Huxley) and led to the development of the sliding helix model. Twenty years later, the X-ray crystallographic structures of many voltage-dependent channels allowed investigation of their gating by molecular dynamics. Further understanding of how channels gate will benefit greatly from the acquisition of high-resolution structures of each of their relevant functional or structural states. This will allow the application of molecular dynamics and other approaches. It will also be key to investigate the energetics of channel gating, permitting an understanding of the physical and molecular determinants of gating. The use of multiscale hierarchical approaches might finally prove to be a rewarding strategy to overcome the limits of the various single approaches to the study of channel gating.

Multiscale simulation analysis of passive and active micro/nanoelectrodes for CMOS-based in vitro neural sensing devices.

Neuron and neural network studies are remarkably fostered by novel stimulation and recording systems, which often make use of biochips fabricated with advanced electronic technologies and, notably, micro- and nanoscale complementary metal-oxide semiconductor (CMOS). Models of the transduction mechanisms involved in the sensor and recording of the neuron activity are useful to optimize the sensing device architecture and its coupling to the readout circuits, as well as to interpret the measured data. Starting with an overview of recently published integrated active and passive micro/nanoelectrode sensing devices for in vitro studies fabricated with modern (CMOS-based) micro-nano technology, this paper presents a mixed-mode device-circuit numerical-analytical multiscale and multiphysics simulation methodology to describe the neuron-sensor coupling, suitable to derive useful design guidelines. A few representative structures and coupling conditions are analysed in more detail in terms of the most relevant electrical figures of merit including signal-to-noise ratio. This article is part of the theme issue 'Advanced neurotechnologies: translating innovation for health and well-being'.

The thermodynamic soliton theory of the nervous impulse and possible medical implications.

The textbook picture of nerve activity is that of a propagating voltage pulse driven by electrical currents through ion channel proteins, which are gated by changes in voltage, temperature, pressure or by drugs. All function is directly attributed to single molecules. We show that this leaves out many important thermodynamic couplings between different variables. A more recent alternative picture for the nerve pulse is of thermodynamic nature. It considers the nerve pulse as a soliton, i.e., a macroscopic excited region with properties that are influenced by thermodynamic variables including voltage, temperature, pressure and chemical potentials of membrane components. All thermodynamic variables are strictly coupled. We discuss the consequences for medical treatment in a view where one can compensate a maladjustment of one variable by adjusting another variable. For instance, one can explain why anesthesia can be counteracted by hydrostatic pressure and decrease in pH, suggest reasons why lithium over-dose may lead to tremor, and how tremor is related to alcohol intoxication. Lithium action as well as the effect of ethanol and the anesthetic ketamine in bipolar patients may fall in similar thermodynamic patterns. Such couplings remain obscure in a purely molecular picture. Other fields of application are the response of nerve activity to muscle stretching and the possibility of neural stimulation by ultrasound.

A Life of Biophysics.

Biophysics is a way of approaching biological problems through numbers, physical laws, models, and quantitative logic. In a long scientific career, I have seen the formation and fruition of the ion channel concept through biophysical study. Marvelous discoveries were made as our instruments evolved from vacuum tubes to transistors; computers evolved from the size of an entire building to a few chips inside our instruments; and genome sequencing, gene expression, and atom-level structural biology became accessible to all laboratories. Science is rewarding and exhilarating.

Holistic idealization: An artifactual standpoint.

Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs.

The Influence of Transcranial Magnetoacoustic Stimulation Parameters on the Basal Ganglia-Thalamus Neural Network in Parkinson's Disease.

Objective: Parkinson's disease (PD) is a degenerative disease of the nervous system that frequently occurs in the aged. Transcranial magnetoacoustic stimulation (TMAS) is a neuronal adjustment method that combines sound fields and magnetic fields. It has the characteristics of high spatial resolution and noninvasive deep brain focusing. Methods: This paper constructed a simulation model of TMAS based on volunteer's skull computer tomography, phased controlled transducer and permanent magnet. It simulates a transcranial focused sound pressure field with the Westervelt equation and builds a basal ganglia and thalamus neural network model in the PD state based on the Hodgkin-Huxley model. Results: A biased sinusoidal pulsed ultrasonic TMAS induced current with 0.3 T static magnetic field induction and 0.2 W⋅cm-2 sound intensity can effectively modulate PD states with RI ≥ 0.633. The magnitude of magnetic induction strength was changed to 0.2 and 0.4 T. The induced current was the same when the sound intensity was 0.4 and 0.1 W⋅cm-2. And the sound pressure level is in the range of -1 dB (the induced current difference is less than or equal to 0.019 µA⋅cm-2). TMAS with a duty cycle of approximately 50% can effectively modulates the error firings in the PD neural network with a relay reliability not less than 0.633. Conclusion: TMAS can modulates the state of PD.

Persistent sodium currents in SCN1A developmental and degenerative epileptic dyskinetic encephalopathy.

Pathogenic variants in the voltage-gated sodium channel gene (SCN1A) are amongst the most common genetic causes of childhood epilepsies. There is considerable heterogeneity in both the types of causative variants and associated phenotypes; a recent expansion of the phenotypic spectrum of SCN1A associated epilepsies now includes an early onset severe developmental and epileptic encephalopathy with regression and a hyperkinetic movement disorder. Herein, we report a female with a developmental and degenerative epileptic-dyskinetic encephalopathy, distinct and more severe than classic Dravet syndrome. Clinical diagnostics indicated a paternally inherited c.5053G>T; p. A1685S variant of uncertain significance in SCN1A. Whole-exome sequencing detected a second de novo mosaic (18%) c.2345G>A; p. T782I likely pathogenic variant in SCN1A (maternal allele). Biophysical characterization of both mutant channels in a heterologous expression system identified gain-of-function effects in both, with a milder shift in fast inactivation of the p. A1685S channels; and a more severe persistent sodium current in the p. T782I. Using computational models, we show that large persistent sodium currents induce hyper-excitability in individual cortical neurons, thus relating the severe phenotype to the empirically quantified sodium channel dysfunction. These findings further broaden the phenotypic spectrum of SCN1A associated epilepsies and highlight the importance of testing for mosaicism in epileptic encephalopathies. Detailed biophysical evaluation and computational modelling further highlight the role of gain-of-function variants in the pathophysiology of the most severe phenotypes associated with SCN1A.

Coherence in the Ferroelectric A3ClO (A = Li, Na) Family of Electrolytes.

Coherence is a major caveat in quantum computing. While phonons and electrons are weakly coupled in a glass, topological insulators strongly depend on the electron-phonon coupling. Knowledge of the electron-phonon interaction at conducting surfaces is relevant from a fundamental point of view as well as for various applications, such as two-dimensional and quasi-1D superconductivity in nanotechnology. Similarly, the electron-phonon interaction plays a relevant role in other transport properties e.g., thermoelectricity, low-dimensional systems as layered Bi and Sb chalcogenides, and quasi-crystalline materials. Glass-electrolyte ferroelectric energy storage cells exhibit self-charge and self-cycling related to topological superconductivity and electron-phonon coupling; phonon coherence is therefore important. By recurring to ab initio molecular dynamics, it was demonstrated the tendency of the Li3ClO, Li2.92Ba0.04ClO, Na3ClO, and Na2.92Ba0.04ClO ferroelectric-electrolytes to keep phonon oscillation coherence for a short lapse of time in ps. Double-well energy potentials were obtained while the electrolyte systems were thermostatted in a heat bath at a constant temperature. The latter occurrences indicate ferroelectric type behavior but do not justify the coherent self-oscillations observed in all types of cells containing these families of electrolytes and, therefore, an emergent type phenomenon where the full cell works as a feedback system allowing oscillations coherence must be realized. A comparison with amorphous SiO2 was performed and the specific heats for the various species were calculated.

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.

Predicting Spike Features of Hodgkin-Huxley-Type Neurons With Simple Artificial Neural Network.

Hodgkin-Huxley (HH)-type model is the most famous computational model for simulating neural activity. It shows the highest accuracy in capturing neuronal spikes, and its model parameters have definite physiological meanings. However, HH-type models are computationally expensive. To address this problem, a previous study proposed a spike prediction module (SPM) to predict whether a spike will take place 1 ms later based on three voltage values with intervals of 1 ms. Although SPM does well, it fails to evaluate the informative features of the spike. In this study, the feature prediction module (FPM) based on simple artificial neural network (ANN) was proposed to predict spike features including maximum voltage, minimum voltage, and dropping interval. Nine different HH-type models were adopted whose firing patterns cover most of the firing behaviors observed in the brain. Voltage and spike feature samples under constant external input current were collected for training and testing. Experiment results illustrated that the combination of SPM and FPM can accurately predict the spiking part of different HH-type models and can generalize to unseen types of input current. The combination of SPM and FPM may offer a possible way to simulate the action potentials of biological neurons with high accuracy and efficiency.

A Potential Mechanism of Sodium Channel Mediating the General Anesthesia Induced by Propofol.

General anesthesia has revolutionized healthcare over the past 200 years and continues to show advancements. However, many phenomena induced by general anesthetics including paradoxical excitation are still poorly understood. Voltage-gated sodium channels (Na V ) were believed to be one of the proteins targeted during general anesthesia. Based on electrophysiological measurements before and after propofol treatments of different concentrations, we mathematically modified the Hodgkin-Huxley sodium channel formulations and constructed a thalamocortical model to investigate the potential roles of Na V . The ion channels of individual neurons were modeled using the Hodgkin-Huxley type equations. The enhancement of propofol-induced GABAa current was simulated by increasing the maximal conductance and the time-constant of decay. Electroencephalogram (EEG) was evaluated as the post-synaptic potential from pyramidal (PY) cells. We found that a left shift in activation of Na V was induced primarily by a low concentration of propofol (0.3-10 µM), while a left shift in inactivation of Na V was induced by an increasing concentration (0.3-30 µM). Mathematical simulation indicated that a left shift of Na V activation produced a Hopf bifurcation, leading to cell oscillations. Left shift of Na V activation around a value of 5.5 mV in the thalamocortical models suppressed normal bursting of thalamocortical (TC) cells by triggering its chaotic oscillations. This led to irregular spiking of PY cells and an increased frequency in EEG readings. This observation suggests a mechanism leading to paradoxical excitation during general anesthesia. While a left shift in inactivation led to light hyperpolarization in individual cells, it inhibited the activity of the thalamocortical model after a certain depth of anesthesia. This finding implies that high doses of propofol inhibit the network partly by accelerating Na V toward inactivation. Additionally, this result explains why the application of sodium channel blockers decreases the requirement for general anesthetics. Our study provides an insight into the roles that Na V plays in the mechanism of general anesthesia. Since the activation and inactivation of Na V are structurally independent, it should be possible to avoid side effects by state-dependent binding to the Na V to achieve precision medicine in the future.

Statistical Approaches for the Analysis of Dependency Among Neurons Under Noise.

Neuronal noise is a major factor affecting the communication between coupled neurons. In this work, we propose a statistical toolset to infer the coupling between two neurons under noise. We estimate these statistical dependencies from data which are generated by a coupled Hodgkin-Huxley (HH) model with additive noise. To infer the coupling using observation data, we employ copulas and information-theoretic quantities, such as the mutual information (MI) and the transfer entropy (TE). Copulas and MI between two variables are symmetric quantities, whereas TE is asymmetric. We demonstrate the performances of copulas and MI as functions of different noise levels and show that they are effective in the identification of the interactions due to coupling and noise. Moreover, we analyze the inference of TE values between neurons as a function of noise and conclude that TE is an effective tool for finding out the direction of coupling between neurons under the effects of noise.