Ion Channel Models Research Articles

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.

Behavior of Spiral Wave Spectra with a Rank-Deficient Diffusion Matrix

Spiral waves emerge in numerous pattern forming systems and are commonly modeled with reaction-diffusion systems. Some systems used to model biological processes, such as ion-channel models, fall under the reaction-diffusion category and often have one or more non-diffusing species which results in a rank-deficient diffusion matrix. Previous theoretical research focused on spiral spectra for strictly positive diffusion matrices. In this paper, we use a general two-variable reaction-diffusion system to compare the essential and absolute spectra of spiral waves for strictly positive and rank-deficient diffusion matrices. We show that the essential spectrum is not continuous in the limit of vanishing diffusion in one component. Moreover, we predict locations for the absolute spectrum in the case of a non-diffusing slow variable. Predictions are confirmed numerically for the Barkley and Karma models.

In‐Silico Investigation of Castration on Vas Deferens Smooth Muscle Electrophysiology

OBJECTIVEThe vas deferens smooth muscle (VDSM) generates spontaneous contractions for the sperm transportation. The underlying electrical activities of the VDSM cell are prominently correlated with these contractions. According to a recent experimental study, the castration has down regulated the A‐type K+channel activities in the VDSM cell. However, the modulating properties of castration into VDSM electrophysiology are not investigated yet. In the present time, the in‐silico study plays a key role in understanding various complex physiological systems. To explore the quantitative contribution of castration to the VDSM membrane action potential (AP), a biophysically detailed single VDSM in‐silico cell model is simulated.METHODSThe in‐silico guinea‐pig VDSM cell model is constructed after incorporating a voltage‐gated Na+ ion channel, two voltage‐gated Ca2+ ion channels, a hyperpolarization‐activated ion channel, two voltage‐gated K+ ion channels, a Ca2+‐activated K+ ion channel, and a nonspecific background leak ion channel. All ion channel models are validated by comparing the simulated currents and current‐voltage relationship with those reported in the experimental studies. The modulating properties of the castration are simulated by mimicking the A‐type K+ channel on VDSM cell excitability.RESULTSThe ion channel conductnaces are set to maintain the resting membrane potential (RMP) at ̶ 50 mV as the physiological range of RMP in VDSM cell varies from ̶ 45 mV to ̶ 70 mV (Figure 1). The AP and membrane depolarization are generated in the whole cell model by applying an external current stimulus (10‐30 pA), as a brief square pulse of 10 ms duration. The A‐type K+ current is elicited by a 1000 ms depolarizing‐voltage‐step between ̶ 70 and +40 mV from a holding potential (̶ 80 mV) with 10 mV increments. The maximum conductance of A‐type K+ channel is altered to observe the changes in VDSM AP. The RMP, AP width, and AP peak are elevated by 2 mV, 15 ms, and 1 mV respectively after the castration (Figure 1). It reveals that the VDSM cell is more electrically excited due to the castration.CONCLUSIONSThe present in‐silico model, constrained heavily by physiological data, provides a powerful tool to investigate the ionic mechanisms underlying the genesis of VDSM electrical activity. In the guinea‐pig, following castration, the VDSM cell is excited by membrane depolarization, which causes to evoke more spontaneous contractions. The new biological insight from this investigation shows the agonist of the A‐type K+ channel might control the much‐diminished sex drive experiences for men after the castration.

A strategy for determining the equilibrium constants for heteromeric ion channels in a complex model.

Ligand-gated ion channels are oligomers containing several binding sites for the ligands. However, the signal transmission from the ligand binding site to the pore has not yet been fully elucidated for any of these channels. In heteromeric channels, the situation is even more complex than in homomeric channels. Using published data for concatamers of heteromeric cyclic nucleotide-gated channels, we show that, on theoretical grounds, multiple functional parameters of the individual subunits can be determined with high precision. The main components of our strategy are (1) the generation of a defined subunit composition by concatenating multiple subunits, (2) the construction of 16 concatameric channels, which differ in systematically permutated binding sites, (3) the determination of respectively differing concentration-activation relationships, and (4) a complex global fit analysis with corresponding intimately coupled Markovian state models. The amount of constraints in this approach is exceedingly high. Furthermore, we propose a stochastic fit analysis with a scaled unitary start vector of identical elements to avoid any bias arising from a specific start vector. Our approach enabled us to determine 23 free parameters, including 4 equilibrium constants for the closed-open isomerizations, 4 disabling factors for the mutations of the different subunits, and 15 virtual equilibrium-association constants in the context of a 4-D hypercube. From the virtual equilibrium-association constants, we could determine 32 equilibrium-association constants of the subunits at different degrees of ligand binding. Our strategy can be generalized and is therefore adaptable to other ion channels.

Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux.

Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.

Creating a Novel Mathematical Model of the Kv10.1 Ion Channel and Controlling Channel Activity with Nanoelectromechanical Systems

The use of nanoelectromechanical systems or nanorobots offers a new concept for sensing and controlling subcellular structures, such as ion channels. We present here a novel method for mathematical modeling of ion channels based on control system theory and system identification. We investigated the use of nanoelectromechanical devices to control the activity of ion channels, particularly the activity of the voltage-gated ion channel Kv10.1, an important channel in cancer development and progression. A mathematical model of the dynamic behavior of the selected ion channel Kv10.1 in the Laplace (s) domain was developed, which is given in the representation of a transfer function. In addition, we addressed the possibilities of controlling ion channel activity by nanoelectromechanical devices and nanorobots and finally presented a control algorithm for the Kv10.1 as a control object. A use case demonstrates the potential of a Kv10.1 controlled nanorobot for cancer treatment at a single-cell level.

Pacemaking function of two simplified cell models.

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

Creating Ion Channel Kinetic Models Using Cloud Computing.

Computational modeling of ion channels provides key insight into experimental electrophysiology results and can be used to connect channel dynamics to emergent phenomena observed at the tissue and organ levels. However, creation of these models requires substantial mathematical and computational background. This tutorial seeks to lower the barrier to creating these models by providing an automated pipeline for creating Markov models of an ion channel kinetics dataset. We start by detailing how to encode sample voltage-clamp protocols and experimental data into the program and its implementation in a cloud computing environment. We guide the reader on how to build a containerized instance, push the machine image, and finally run the routine on cluster nodes. While providing open-source code has become more standard in computational studies, this tutorial provides unprecedented detail on the use of the program and the creation of channel models, starting from inputting the raw experimental data. © 2022 Wiley Periodicals LLC. Basic Protocol: Creation of ion channel kinetic models with a cloud computing environment Alternate Protocol: Instructions for use in a standard high-performance compute cluster.

Structural and functional comparison of cation-selective claudin channels

Tight junctions seal the paracellular space and provide a selective barrier for the passage of ions and small molecules. Claudins are one of the major components of tight junctions that control ion selectivity. Based on our previously determined model of claudin-15 ion channels, we constructed an atomic model of claudin-2 and refined it using molecular dynamics simulations. Using all-atom molecular dynamics simulations, we calculated the relative permeability of the channels to alkali metal ions as well as organic cations and compared them to in vitro measurements of channel permeability.

Markov-type kinetic models for sodium and potassium ion channels for generation of action potential in synthetic neurons

Synthetic biology is an exciting area of research that hopes to understand the building blocks of life. With the goal of constructing a predictive model to ultimately guide the bottom-up construction of a synthetic neuron that can qualitatively recapitulate the electrophysiology of biological neurons, we construct and investigate Markov-type models of voltage-gated sodium (Nav) and potassium (Kv3.1) ion channels that capture their complex kinetics. We also mapped a Hodgkin-Huxley model of an inward rectifying potassium channel (Kir2.1) to a Markov-type model.

Nanoparticle tracking analysis and statistical mixture distribution analysis to quantify nanoparticle–vesicle binding

Nanoparticle tracking analysis (NTA) is a single particle tracking technique that in principle provides a more direct measure of particle size distribution compared to dynamic light scattering (DLS). Here, we demonstrate how statistical mixture distribution analysis can be used in combination with NTA to quantitatively characterize the amount and extent of particle binding in a mixture of nanomaterials. The combined approach is used to study the binding of gold nanoparticles to two types of phospholipid vesicles, those containing and lacking the model ion channel peptide gramicidin A. This model system serves as both a proof of concept for the method and a demonstration of the utility of the approach in studying nano-bio interactions. Two diffusional models (Stokes–Einstein and Kirkwood–Riseman) were compared in the determination of particle size, extent of binding, and nanoparticle:vesicle binding ratios for each vesicle type. The combination of NTA and statistical mixture distributions is shown to be a useful method for quantitative assessment of the extent of binding between particles and determination of binding ratios.

A Poisson-Nernst-Planck Single Ion Channel Model and its Effective Finite Element Solver

A Poisson-Nernst-Planck Single Ion Channel Model and its Effective Finite Element Solver

Parameter Optimization for Ion Channel Models: Integrating New Data with Known Channel Properties.

Ion channels play a central role in membrane physiology, but to fully understand how they operate, one must have accurate kinetic mechanisms. Estimating kinetics is not trivial when the mechanism is complex, and a large number of parameters must be extracted from data. Furthermore, the information contained in the data is often limited, and the model may not be fully determined. The solution is to reduce the number of parameters and to estimate them in such a way that they not only describe well the new data but also agree with the existing knowledge. In a previous study, we presented a comprehensive formalism for estimating kinetic parameters subject to a variety of explicit and implicit constraints that define quantitative relationships between parameters and describe specific mechanism properties. Here, we introduce the reader to the QuB software, which implements this constraining formalism. QuB features a powerful visual interface and a high-level scripting language that can be used to formulate kinetic models and constraints of arbitrary complexity, and to efficiently estimate the parameters from a variety of experimental data.

Macroscopic currents of ionic channels using Mass Action Law: A mathematical model

In this work it proposes a mathematical model for ion channels based on two concepts, the Hodgkin and Huxley's as well as the Law of Mass Action in addition, we consider the kinetics of channels as a dynamic process of Markov`s chain. With the previous premises, a system of differential equations is proposed that when it is solved, all properties of the macroscopic currents are determined. The activation, deactivation, inactivation, and recovery of the inactivation concepts remain as processes that are part of a chemical reaction. With this system of equations, all the experimental protocols used in electrophysiology to characterize macroscopic currents can be modeled. Another advantage is that the model allows, with the same system of equations, to determine the properties of voltage-dependent channels regardless of the type of ion that pass through in the channel.

Photoswitching of model ion channels in lipid bilayers.

Membrane proteins can be regulated by alterations in material properties intrinsic to the hosting lipid bilayer. Here, we investigated whether the reversible photoisomerization of bilayer-embedded diacylglycerols (OptoDArG) with two azobenzene-containing acyl chains may trigger such regulatory events. We observed an augmented open probability of the mechanosensitive model channel gramicidin A (gA) upon photoisomerizing OptoDArG's acyl chains from trans to cis: integral planar bilayer conductance brought forth by hundreds of simultaneously conducting gA dimers increased by typically >50% - in good agreement with the observed increase in single-channel lifetime. Further, (i) increments in the electrical capacitance of planar lipid bilayers and protrusion length of aspirated giant unilamellar vesicles into suction pipettes, as well as (ii) changes of small-angle X-ray scattering of multilamellar vesicles indicated that spontaneous curvature, hydrophobic thickness, and bending elasticity decreased upon switching from trans- to cis-OptoDArG. Our bilayer elasticity model for gA supports the causal relationship between changes in gA activity and bilayer material properties upon photoisomerization. Thus, we conclude that photolipids are deployable for converting bilayers of potentially diverse origins into light-gated actuators for mechanosensitive proteins.

The amyloid concentric β-barrel hypothesis: Models of synuclein oligomers, annular protofibrils, lipoproteins, and transmembrane channels.

Amyloid beta (Aβ of Alzheimer's disease) and α-synuclein (α-Syn of Parkinson's disease) form large fibrils. Evidence is increasing however that much smaller oligomers are more toxic and that these oligomers can form transmembrane ion channels. We have proposed previously that Aβ42 oligomers, annular protofibrils, and ion channels adopt concentric β-barrel molecular structures. Here we extend that hypothesis to the superfamily of α, β, and γ-synucleins. Our models of numerous synuclein oligomers, annular protofibrils, tubular protofibrils, lipoproteins, and ion channels were developed to be consistent with sizes, shapes, molecular weights, and secondary structures of assemblies as determined by electron microscopy and other studies. The models have the following features: (1) all subunits have identical structures and interactions; (2) they are consistent with conventional β-barrel theory; (3) the distance between walls of adjacent β-barrels is between 0.6 and 1.2 nm; (4) hydrogen bonds, salt bridges, interactions among aromatic side-chains, burial and tight packing of hydrophobic side-chains, and aqueous solvent exposure of hydrophilic side-chains are relatively optimal; and (5) residues that are identical among distantly related homologous proteins cluster in the interior of most oligomers whereas residues that are hypervariable are exposed on protein surfaces. Atomic scale models of some assemblies were developed.

Toward a More General Understanding of Bohr's Complementarity: Insights from Modeling of Ion Channels.

Some contemporary theorists such as Mazzocchi, Theise and Kafatos are convinced that the reformed complementarity may redefine how we might exploit the complexity theory in 21st-century life sciences research. However, the motives behind the profound re-invention of "biological complementarity" need to be substantiated with concrete shreds of evidence about this principle's applicability in real-life science experimentation, which we found missing in the literature. This paper discusses such pieces of evidence by confronting Bohr's complementarity and ion channel modeling practice. We examine whether and to what extent this principle might assist in developing ion channel models incorporating both deterministic and stochastic solutions. According to the "mutual exclusiveness of experimental setups" version of Bohr's complementarity, this principle is needed when two mutually exclusive perspectives or approaches are right, necessary in a particular context, and are not contradictory as they arise in mutually exclusive conditions (mutually exclusive experimental or modeling setups).A detailed examination of the modeling practice reveals that both solutions are often used simultaneously in a single ion channel model, suggesting that the opposite conceptual frameworks can coexist in the same modeling setup. We concluded that Bohr's complementarity might find applications in these complex modeling setups but only through its realistic phenomenological interpretation that allows applying different modes of description regardless of the nature of the underlying ion channel opening process. Also, we propose the combined use of complementarity and Complex thinking in building the multifaceted ion channel models. Overall, this paper's results support the efforts to establish a more general form of complementarity to meet today's complexity theory-inspired life sciences modeling demands.

A New Neuron Ion Channel Model Under Time Varying Input Currents

In recent years, it has been argued and shown experimentally that ion channel noise in neurons can cause fundamental effects on the neuron’s dynamical behavior. Most profoundly, ion channel noise was seen to be able to cause spontaneous firing and stochastic resonance. However, Hodgkin-Huxley model affected when inserting some colored noise terms inside the conductance’s, where those effects captured by colored noise due to the gate multiplicity. This paper presents a new ion channel model under time varying periodic input currents. It firstly introduced the effect of without, with (colored noise), on the proposed model and the comparison of ion channel based on HH, Fox- Lu, and Linaro models. Additionally, in order to overcome the limitations of other parameter estimation methods, the proposed method fully constraints their models and obtains all models capabilities of reproducing the data. Finally, the relationship between the sequence of colored noise and the spike frequency are simulated efficiently each gate compared with microscopic simulations of the stochastic Markov process method. The simulation results revealed that above a critical value of the input frequency and also below a certain amplitude value, the colored terms play a very prominent role on the firing statistics. In addition, the spiking rate generated from the proposed model very close to microscopic simulations and doesn’t effect by the membrane size.

MODULATING EFFECTS OF CASTRATION ON VAS DEFERENS SMOOTH MUSCLE ELECTRICAL ACTIVITIES: INSIGHTS FROM A QUANTITATIVE STUDY

The vas deferens smooth muscle (VDSM), which is dependent on testosterone, generates spontaneous contraction. Although the factors modulating the spontaneous contraction are not completely understood, different experimental studies have supported that the VDSM cell electrophysiological phenomena is eminently correlated to it. According to a recent study, the castration has down regulated the A-type K+ channel activities in VDSM cell [Ohya et al., 2019]. In the present time, computational modeling plays a powerful role in understanding various complex biological/physiological systems. To explore the quantitative contribution of castration into the VDSM membrane electrical activities, a biophysically detailed single VDSM cell model is presented. First, we constructed computational models for seven ion channels found in guinea-pig VDSM cells based on published experimental data: One voltage gated Na+ ion channel, two voltage gated Ca2+ ion channels, a hyperpolarization-activated ion channel, two voltage-gated K+ ion channels, one Ca2+-activated K+ ion channels and a nonspecific background leak ion channel. All ion channel models were validated by comparing the simulated currents and current-voltage relationship with those reported in experimental work. Then, all ion channels were integrated to simulate the VDSM electrical activities towards neurotransmitter/current stimulus. We investigated the contribution of the castration by mimicking the testosterone as down regulation of A-type K+ channel on VDSM cell excitability. The ion channel conductnaces are set to maintain the resting membrane potential (RMP) at — 50 mV as the physiological range of RMP in VDSM cell varies from — 45 mV to — 70 mV. The action potential (AP) and membrane depolarization are simulated in the whole cell model by applying an external stimulus current (10-30 pA), as a brief square pulse of 10 ms duration. The results showed both L-type Ca2+ and Na+ channel are indispensable for generating the spike, although the L-type Ca2+ channel is the major contributor to the total inward current. The results also revealed that both BK and A-type K+ channel channels are essential in maintaining the RMP and repolarization. Because of castration, A-type K+ current is reduced, and as a result, it elevated the RMP from — 50 mV to — 47 mV (more positive). The model was able to evoke an AP with a reduced current stimulus. To date, a biophysically detailed computational model does not exist for VDSM cells. Our model, constrained heavily by physiological data, provides a powerful tool to investigate the ionic mechanisms underlying the genesis of VDSM electrical activity. In the guinea-pig, following castration, VDSM was accompanied by cell membrane depolarization, which caused to evoke more spontaneous contractions.

Cover Image

The cover image is based on the Full Paper An improved Poisson-Nernst-Planck ion channel model and numerical studies on effects of boundary conditions, membrane charges, and bulk concentrations by Zhen Chao and Dexuan Xie., https://doi.org/10.1002/jcc.26723.