A historical biophysical dogma vs. an understanding of the structure and function of voltage-gated tetrameric ion channels. A review.

The outstanding work of several eminent biophysicists has allowed the functional features of voltage-gated tetrameric ion channels to be disclosed using ingenious and sophisticated electrophysiological techniques. However, the kinetics and mechanism underlying these functions have been heavily conditioned by an arbitrary interpretation of the groundbreaking results obtained by Hodgkin and Huxley (HH) in their investigation of sodium and potassium currents using the voltage clamp technique. Thus, the heavy parametrization of their results was considered to indicate that any proposed sequence of closed states terminates with a single open state. This 'dogma' of HH parametrization has influenced the formulation of countless mechanistic models, mainly stochastic, requiring a high number of free parameters and of often unspecified conformational states. This note aims to point out the advantages of a deterministic kinetic model that simulates the main features of tetrameric ion channels using only two free parameters by assuming their stepwise opening accompanied by a progressively increasing cation flow. This model exploits the electrostatic attractive interactions stemming from the charge distribution shared by all tetrameric ion channels, providing a close connection between their structure and function. Quite significantly, a stepwise opening of all ligand-gated tetrameric ion channels, such as glutamate receptors (GluRs), with concomitant ion flow, is nowadays generally accepted, not having been influenced by this dogma. This provides a unified picture of both voltage-gated and ligand-gated tetrameric ion channels.

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.

The effects of temperature on the dynamics of the biological neural network.

The nerve cells are responsible for transmitting messages through the action potential, which generates electrical stimulation. One of the methods and tools of electrical stimulation is infrared neural stimulation (INS). Since the mechanism of INS is based on electromagnetic radiation, it explains how a neuron is stimulated by the heat distribution which is generated by the laser. The present study is focused on modeling and simulating the conditions in which deformed temperature related to the Hodgkin and Huxley model can be effectively and safely used to activate the neurons, the fires of which depend on temperature. The results explain ionic channels in the single and network neurons, which behave differently when thermal stimulation is applied to the cell. It causes the variation of the pattern of the action potential in the Hodgkin-Huxley (HH) model. The stability of the phase-plane at high temperatures has lower fluctuations than at low temperatures, so the channel gates open and close faster. The behavior of these channels under various membrane temperatures shows that the firing rate increases with temperature. Also, the domain of the spikes reduces and the spikes occur faster with increasing temperature.

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.

Capturing Multiple Timescales of Adaptation to Second-Order Statistics With Generalized Linear Models: Gain Scaling and Fractional Differentiation.

Single neurons can dynamically change the gain of their spiking responses to take into account shifts in stimulus variance. Moreover, gain adaptation can occur across multiple timescales. Here, we examine the ability of a simple statistical model of spike trains, the generalized linear model (GLM), to account for these adaptive effects. The GLM describes spiking as a Poisson process whose rate depends on a linear combination of the stimulus and recent spike history. The GLM successfully replicates gain scaling observed in Hodgkin-Huxley simulations of cortical neurons that occurs when the ratio of spike-generating potassium and sodium conductances approaches one. Gain scaling in the GLM depends on the length and shape of the spike history filter. Additionally, the GLM captures adaptation that occurs over multiple timescales as a fractional derivative of the stimulus envelope, which has been observed in neurons that include long timescale afterhyperpolarization conductances. Fractional differentiation in GLMs requires long spike history that span several seconds. Together, these results demonstrate that the GLM provides a tractable statistical approach for examining single-neuron adaptive computations in response to changes in stimulus variance.

Estimating neuronal conductance model parameters using dynamic action potential clamp.

BACKGROUND: Parameterization of neuronal membrane conductance models relies on data acquired from current clamp (CC) or voltage clamp (VC) recordings. Although the CC approach provides key information on a neuron's firing properties, it is often difficult to disentangle the influence of multiple conductances that contribute to the excitation properties of a real neuron. Isolation of a single conductance using pharmacological agents or heterologous expression simplifies analysis but requires extensive VC evaluation to explore the complete state behavior of the channel of interest. NEW METHOD: We present an improved parameterization approach that uses data derived from dynamic action potential clamp (DAPC) recordings to extract conductance equation parameters. We demonstrate the utility of the approach by applying it to the standard Hodgkin-Huxley conductance model although other conductance models could be easily incorporated as well. RESULTS: Using a fully simulated setup we show that, with as few as five action potentials previously recorded in DAPC mode, sodium conductance equation parameters can be determined with average parameter errors of less than 4% while action potential firing accuracy approaches 100%. In real DAPC experiments, we show that by "training" our model with five or fewer action potentials, subsequent firing lasting for several seconds could be predicted with ˜96% mean firing rate accuracy and 94% temporal overlap accuracy. COMPARISON WITH EXISTING METHODS: Our DAPC-based approach surpasses the accuracy of VC-based approaches for extracting conductance equation parameters with a significantly reduced temporal overhead. CONCLUSION: DAPC-based approach will facilitate the rapid and systematic characterization of neuronal channelopathies.

Desarrollo de un Simulador de los Experimentos Clásicos y Actualizados de Fijación de Voltaje de Hodgkin y Huxley / Developing a simulation program for classic and updated Hodgkin and Huxley's voltage clamp experiments

Resumen: Los estudios de Hodgkin y Huxley fueron el punto de partida de la generación de modelos matemáticos que explican, reproducen y predicen los resultados experimentales del comportamiento de los canales iónicos sensibles a voltaje del axón. Los altos costos de estos experimentos impiden su implementación en la práctica docente de licenciatura. Una alternativa didáctica son los experimentos virtuales mediante simuladores computacionales. En este trabajo se presenta el desarrollo de un simulador que reproduce paso a paso los experimentos clásicos de Hodgkin y Huxley sobre las conductancias de los canales dependientes de voltaje del axón gigante de calamar. El simulador fue desarrollado en lenguaje Visual Basic ver 5.0 para ambiente Wiindows® . Está formado de cuatro módulos: (1) simulación de corrientes iónicas; (2) experimentos clásicos de Hodgkin y Huxley; (3) versión actual del modelo; (4) potenciales de acción. Consta de pantallas de interfaz que permiten simular y calcular los valores de las variables relacionadas con la conductancia de los canales. El usuario puede realizar una cantidad ilimitada de experimentos virtuales que le facilitarán la comprensión del tema.

Abstract: Hodgkin and Huxley ́s works were the starting point to generating mathematical models for explain, reproduce the experimental results and predict the behavior of voltage-sensitive ion channels in the axon. The high costs of these experiments avoid its implementation in teaching degree. An educational alternative is virtual experiments using computer simulations. In this work the development of a simulator that reproduces step by step the classic experiments of Hodgkin and Huxley on the conductance of voltage-dependent channels in squid giant axon is presented. The simulator was developed in Visual Basic language, ver 5.0 for Windows environment. It consists of four modules: (1) ionic currents simulation; (2) classical Hodgkin and Huxley ́s experiments; (3) current version model; (4) action potentials. It comprises connecting interface screens that allow simulate and compute the values of the variables associated with the channel conductance. The user can perform an unlimited number of virtual experiments that will facilitate the understanding of the subject.

Cell-Type-Selective Effects of Intramembrane Cavitation as a Unifying Theoretical Framework for Ultrasonic Neuromodulation.

Diverse translational and research applications could benefit from the noninvasive ability to reversibly modulate (excite or suppress) CNS activity using ultrasound pulses, however, without clarifying the underlying mechanism, advanced design-based ultrasonic neuromodulation remains elusive. Recently, intramembrane cavitation within the bilayer membrane was proposed to underlie both the biomechanics and the biophysics of acoustic bio-effects, potentially explaining cortical stimulation results through a neuronal intramembrane cavitation excitation (NICE) model. Here, NICE theory is shown to provide a detailed predictive explanation for the ability of ultrasonic (US) pulses to also suppress neural circuits through cell-type-selective mechanisms: according to the predicted mechanism T-type calcium channels boost charge accumulation between short US pulses selectively in low threshold spiking interneurons, promoting net cortical network inhibition. The theoretical results fit and clarify a wide array of earlier empirical observations in both the cortex and thalamus regarding the dependence of ultrasonic neuromodulation outcomes (excitation-suppression) on stimulation and network parameters. These results further support a unifying hypothesis for ultrasonic neuromodulation, highlighting the potential of advanced waveform design for obtaining cell-type-selective network control.

Computational modeling of neurons: intensity-duration relationship of extracellular electrical stimulation for changes in intracellular calcium.

In many instances of extensive nerve damage, the injured nerve never adequately heals, leaving lack of nerve function. Electrical stimulation (ES) has been shown to increase the rate and orient the direction of neurite growth, and is a promising therapy. However, the mechanism in which ES affects neuronal growth is not understood, making it difficult to compare existing ES protocols or to design and optimize new protocols. We hypothesize that ES acts by elevating intracellular calcium concentration ([Ca(2+)]i) via opening voltage-dependent Ca(2+) channels (VDCCs). In this work, we have created a computer model to estimate the ES Ca(2+) relationship. Using COMSOL Multiphysics, we modeled a small dorsal root ganglion (DRG) neuron that includes one Na(+) channel, two K(+) channels, and three VDCCs to estimate [Ca(2+)]i in the soma and growth cone. As expected, the results show that an ES that generates action potentials (APs) can efficiently raise the [Ca(2+)]i of neurons. More interestingly, our simulation results show that sub-AP ES can efficiently raise neuronal [Ca(2+)]i and that specific high-voltage ES can preferentially raise [Ca(2+)]i in the growth cone. The intensities and durations of ES on modeled growth cone calcium rise are consistent with directionality and orientation of growth cones experimentally shown by others. Finally, this model provides a basis to design experimental ES pulse parameters, including duration, intensity, pulse-train frequency, and pulse-train duration to efficiently raise [Ca(2+)]i in neuronal somas or growth cones.

The CNP signal is able to silence a supra threshold neuronal model.

Several experimental results published in the literature showed that weak pulsed magnetic fields affected the response of the central nervous system. However, the specific biological mechanisms that regulate the observed behaviors are still unclear and further scientific investigation is required. In this work we performed simulations on a neuronal network model exposed to a specific pulsed magnetic field signal that seems to be very effective in modulating the brain activity: the Complex Neuroelectromagnetic Pulse (CNP). Results show that CNP can silence the neurons of a feed-forward network for signal intensities that depend on the strength of the bias current, the endogenous noise level and the specific waveforms of the pulses. Therefore, it is conceivable that a neuronal network model responds to the CNP signal with an inhibition of its activity. Further studies on more realistic neuronal networks are needed to clarify if such an inhibitory effect on neuronal tissue may be the basis of the induced analgesia seen in humans and the antinociceptive effects seen in animals when exposed to the CNP.