K+ conduction in the selectivity filter of potassium channels is monitored by the charge distribution along their sequence

Impact of geometry changes in the channel pore by the gating movements on the channel's conductance

Kv 1.2 are voltage-dependent potassium channels of great biological importance. Despite the existence of many reports considering structure - function relations of the Kv 1.2 channel's quantitative domains, some details of the voltage gating remain ambiguous, or even unknown. One of the examples is the range of the S4-S6 domains motions involved in channel activation and gating. Another important question is to what extent the channel geometry influences the observable channel conductance at different voltages, and what mechanism stands behind. Does the narrowing of the pore reduce the conductance by ohmic resistance growth? The answer is surprisingly negative. But it can be explained in an alternative way by considering the fluctuations. To address these problems, we formulate geometric models that mimic the generic features of voltage sensor movement and trigger the movement of the other domains involved in gating. We carry out a complete simulation of S4-S6 domains translations and tilts. The obtained pore profiles allow to estimate the (ohmic) conductance dependency on the voltage. From a family of analysed models, we choose the one most concurring with the experimental data. The results allow to suggest the most probable scenario of S4-S6 domains movement during channel activation by membrane depolarization.

Origin of the Shape of Current-Voltage Curve through Nanopores: A Molecular Dynamics Study

Ion transports through ion channels, biological nanopores, are essential for life: Living cells generate electrical signals by utilizing ion permeation through channels. The measured current-voltage (i-V) relations through most ion channels are sublinear, however, its physical meaning is still elusive. Here we calculated the i-V curves through anion-doped carbon nanotubes, a model of an ion channel, using molecular dynamics simulation. It was found the i-V curve reflects the physical origin of the rate-determining step: the i-V curve is sublinear when the permeation is entropy bottlenecked, while it is superlinear in the case of the energy bottlenecked permeation. Based on this finding, we discuss the relation between the molecular mechanism of ion permeation through the biological K⁺ channels and the shape of the i-V curves through them. This work also provides a clue for a novel design of nanopores that show current rectification.

Self-Optimized Biological Channels in Facilitating the Transmembrane Movement of Charged Molecules

We consider an anisotropically two-dimensional diffusion of a charged molecule (particle) through a large biological channel under an external voltage. The channel is modeled as a cylinder of three structure parameters: radius, length, and surface density of negative charges located at the channel interior-lining. These charges induce inside the channel a potential that plays a key role in controlling the particle current through the channel. It was shown that to facilitate the transmembrane particle movement the channel should be reasonably self-optimized so that its potential coincides with the resonant one, resulting in a large particle current across the channel. Observed facilitation appears to be an intrinsic property of biological channels, regardless of the external voltage or the particle concentration gradient. This facilitation is very selective in the sense that a channel of definite structure parameters can facilitate the transmembrane movement of only particles of proper valence at corresponding temperatures. Calculations also show that the modeled channel is nonohmic with the ion conductance which exhibits a resonance at the same channel potential as that identified in the current.

Energetics of Multi-Ion Conduction Pathways in Potassium Ion Channels

Potassium ion channels form pores in cell membranes, allowing potassium ions through while preventing the passage of sodium ions. Despite numerous high-resolution structures, it is not yet possible to relate their structure to their single molecule function other than at a qualitative level. Over the past decade, there has been a concerted effort using molecular dynamics to capture the thermodynamics and kinetics of conduction by calculating potentials of mean force (PMF). These can be used, in conjunction with the electro-diffusion theory, to predict the conductance of a specific ion channel. Here, we calculate seven independent PMFs, thereby studying the differences between two potassium ion channels, the effect of the CHARMM CMAP forcefield correction, and the sensitivity and reproducibility of the method. Thermodynamically stable ion-water configurations of the selectivity filter can be identified from all the free energy landscapes, but the heights of the kinetic barriers for potassium ions to move through the selectivity filter are, in nearly all cases, too high to predict conductances in line with experiment. This implies it is not currently feasible to predict the conductance of potassium ion channels, but other simpler channels may be more tractable.

Pore waters regulate ion permeation in a calcium release-activated calcium channel

The recent crystal structure of Orai, the pore unit of a calcium release-activated calcium (CRAC) channel, is used as the starting point for molecular dynamics and free-energy calculations designed to probe this channel's conduction properties. In free molecular dynamics simulations, cations localize preferentially at the extracellular channel entrance near the ring of Glu residues identified in the crystal structure, whereas anions localize in the basic intracellular half of the pore. To begin to understand ion permeation, the potential of mean force (PMF) was calculated for displacing a single Na(+) ion along the pore of the CRAC channel. The computed PMF indicates that the central hydrophobic region provides the major hindrance for ion diffusion along the permeation pathway, thereby illustrating the nonconducting nature of the crystal structure conformation. Strikingly, further PMF calculations demonstrate that the mutation V174A decreases the free energy barrier for conduction, rendering the channel effectively open. This seemingly dramatic effect of mutating a nonpolar residue for a smaller nonpolar residue in the pore hydrophobic region suggests an important role for the latter in conduction. Indeed, our computations show that even without significant channel-gating motions, a subtle change in the number of pore waters is sufficient to reshape the local electrostatic field and modulate the energetics of conduction, a result that rationalizes recent experimental findings. The present work suggests the activation mechanism for the wild-type CRAC channel is likely regulated by the number of pore waters and hence pore hydration governs the conductance.

Detailed Examination of a Single Conduction Event in a Potassium Channel

Although extensively studied, it has proved difficult to describe in detail how potassium ion channels conduct cations and water. We present a computational study that, by using stratified umbrella sampling, examines nearly an entire conduction event of the Kv1.2/2.1 paddle chimera and thereby identifies the expected stable configurations of ions and waters in the selectivity filter of the channel. We describe in detail the motions of the ions and waters during a conduction event, focusing on how waters and ions enter the filter, the rotation of water molecules inside the filter, and how potassium ions are coordinated as they move from a water to a protein environment. Finally, we analyze the small conformational changes undergone by the protein, showing that the stable configurations are most similar to the experimental crystal structure.

The mechanism of Na⁺/K⁺ selectivity in mammalian voltage-gated sodium channels based on molecular dynamics simulation

Voltage-gated sodium (Nav) channels and their Na⁺/K⁺ selectivity are of great importance in the mammalian neuronal signaling. According to mutational analysis, the Na⁺/K⁺ selectivity in mammalian Nav channels is mainly determined by the Lys and Asp/Glu residues located at the constriction site within the selectivity filter. Despite successful molecular dynamics simulations conducted on the prokaryotic Nav channels, the lack of Lys at the constriction site of prokaryotic Nav channels limits how much can be learned about the Na⁺/K⁺ selectivity in mammalian Nav channels. In this work, we modeled the mammalian Nav channel by mutating the key residues at the constriction site in a prokaryotic Nav channel (NavRh) to its mammalian counterpart. By simulating the mutant structure, we found that the Na⁺ preference in mammalian Nav channels is collaboratively achieved by the deselection from Lys and the selection from Asp/Glu within the constriction site.

Ion conduction through the hERG potassium channel

The inward rectifier voltage-gated potassium channel hERG is of primary importance for the regulation of the membrane potential of cardiomyocytes. Unlike most voltage-gated K⁺-channels, hERG shows a low elementary conductance at physiological voltage and potassium concentration. To investigate the molecular features underlying this unusual behavior, we simulated the ion conduction through the selectivity filter at a fully atomistic level by means of molecular dynamics-based methods, using a homology-derived model. According to our calculations, permeation of potassium ions can occur along two pathways, one involving site vacancies inside the filter (showing an energy barrier of about 6 kcal mol⁻¹), and the other characterized by the presence of a knock-on intermediate (about 8 kcal mol⁻¹). These barriers are indeed in accordance with a low conductance behavior, and can be explained in terms of a series of distinctive structural features displayed by the hERG ion permeation pathway.

Ion solvation and structural stability in a sodium channel investigated by molecular dynamics calculations

The stability and ion binding properties of the homo-tetrameric pore domain of a prokaryotic, voltage-gated sodium channel are studied by extensive all-atom molecular dynamics simulations, with the channel protein being embedded in a fully hydrated lipid bilayer. It is found that Na(+) ion presents in a mostly hydrated state inside the wide pore of the selectivity filter of the sodium channel, in sharp contrast to the nearly fully dehydrated state for K(+) ions in potassium channels. Our results also indicate that Na(+) ions make contact with only one or two out of the four polypeptide chains forming the selectivity filter, and surprisingly, the selectivity filter exhibits robust stability for various initial ion configurations even in the absence of ions. These findings are quite different from those in potassium channels. Furthermore, an electric field above 0.5V/nm is suggested to be able to induce Na(+) permeation through the selectivity filter.

Molecular dynamics simulations of voltage-gated cation channels: insights on voltage-sensor domain function and modulation

Since their discovery in the 1950s, the structure and function of voltage-gated cation channels (VGCC) has been largely understood thanks to results stemming from electrophysiology, pharmacology, spectroscopy, and structural biology. Over the past decade, computational methods such as molecular dynamics (MD) simulations have also contributed, providing molecular level information that can be tested against experimental results, thereby allowing the validation of the models and protocols. Importantly, MD can shed light on elements of VGCC function that cannot be easily accessed through “classical” experiments. Here, we review the results of recent MD simulations addressing key questions that pertain to the function and modulation of the VGCC’s voltage-sensor domain (VSD) highlighting: (1) the movement of the S4-helix basic residues during channel activation, articulating how the electrical driving force acts upon them; (2) the nature of the VSD intermediate states on transitioning between open and closed states of the VGCC; and (3) the molecular level effects on the VSD arising from mutations of specific S4 positively charged residues involved in certain genetic diseases.

Computer Simulations of Voltage-Gated Cation Channels

The relentless growth in computational power has seen increasing applications of molecular dynamics (MD) simulation to the study of membrane proteins in realistic membrane environments, which include explicit membrane lipids, water and ions. The concomitant increasing availability of membrane protein structures for ion channels, and transporters -- to name just two examples -- has stimulated many of these MD studies. In the case of voltage-gated cation channels (VGCCs) recent computational works have focused on ion-conduction and gating mechanisms, along with their regulation by agonist/antagonist ligands. The information garnered from these computational studies is largely inaccessible to experiment and is crucial for understanding the interplay between the structure and function as well as providing new directions for experiments. This article highlights recent advances in probing the structure and function of potassium channels and offers a perspective on the challenges likely to arise in making analogous progress in characterizing sodium channels.

Counting ion and water molecules in a streaming file through the open-filter structure of the K channel

The mechanisms underlying the selective permeation of ions through channel molecules are a fundamental issue related to understanding how neurons exert their functions. The "knock-on" mechanism, in which multiple ions in the selectivity filter are hit by an incoming ion, is one of the leading concepts. This mechanism has been supported by crystallographic studies that demonstrated ion distribution in the structure of the Streptomyces lividans (KcsA) potassium channel. These still pictures under equilibrium conditions, however, do not provide a snapshot of the actual, ongoing permeation processes. To understand the dynamics of permeation, we determined the ratio of the ion and water flow [the water-ion coupling ratio (CR(w-i))] through the KcsA channel by measuring the streaming potential (V(stream)) electrophysiologically. The V(stream) value was converted to the CR(w-i) value, which reveals how individual ion and water molecules are queued in the narrow and short filter during permeation. At high K(+) concentrations, the CR(w-i) value was 1.0, indicating that turnover between the alternating ion and water arrays occurs in a single-file manner. At low K(+), the CR(w-i) value was increased to a point over 2.2, suggesting that the filter contained mostly one ion at a time. These average behaviors of permeation were kinetically analyzed for a more detailed understanding of the permeation process. Here, we envisioned the permeation as queues of ion and water molecules and sequential transitions between different patterns of arrays. Under physiological conditions, we predicted that the knock-on mechanism may not be predominant.

Comparative study of the energetics of ion permeation in Kv1.2 and KcsA potassium channels

Biological ion channels rely on a multi-ion transport mechanism for fast yet selective permeation of ions. The crystal structure of the KcsA potassium channel provided the first microscopic picture of this process. A similar mechanism is assumed to operate in all potassium channels, but the validity of this assumption has not been well investigated. Here, we examine the energetics of ion permeation in Shaker Kv1.2 and KcsA channels, which exemplify the six-transmembrane voltage-gated and two-transmembrane inward-rectifier channels. We study the feasibility of binding a third ion to the filter and the concerted motion of ions in the channel by constructing the potential of mean force for K(+) ions in various configurations. For both channels, we find that a pair of K(+) ions can move almost freely within the filter, but a relatively large free-energy barrier hinders the K(+) ion from stepping outside the filter. We discuss the effect of the CMAP dihedral energy correction that was recently incorporated into the CHARMM force field on ion permeation dynamics.

A High-Throughput Steered Molecular Dynamics Study on the Free Energy Profile of Ion Permeation through Gramicidin A

Steered molecular dynamics (SMD) simulations for the calculation of free energies are well suited for high-throughput molecular simulations on a distributed infrastructure due to the simplicity of the setup and parallel granularity of the runs. However, so far, the computational cost limited the estimation of the free energy typically over just a few pullings, thus impeding the evaluation of statistical uncertainties involved. In this work, we performed two thousand pulls for the permeation of a potassium ion in the gramicidin A pore by all-atom molecular dynamics in order to assess the bidirectional SMD protocol with a proper amount of sampling. The estimated free energy profile still shows a statistical error of several kcal/mol, while the work distributions are estimated to be non-Gaussian at pulling speeds of 10 Å/ns. We discuss the methodology and the confidence intervals in relation to increasing amounts of computed trajectories and how different permeation pathways for the potassium ion, knock-on and sideways, affect the sampling and the free energy estimation.

Affinity of C60 neat fullerenes with membrane proteins: a computational study on potassium channels

Most studies of the interactions of neat and functionalized fullerenes with cells have focused so far on their ability to cross the cell membrane envelopes. Membranes are, however, also host to a large number of proteins responsible for various cellular functions. Among these, ion channels are prominent components of the nervous system. Recently, it was shown that fullerenes may act as blockers or modulators of a variety of K+ channels. Here we use computer simulations to investigate the propensity of such nanocompounds to bind to K+ channels. Our results based on extensive atomistic molecular dynamics simulations reveal a variety of specific binding sites depending on the structure and properties of the channel. The corresponding binding free energies and putative mechanisms suggest that C60 may indeed effectively hinder the function of K+ channels and hence induce toxicity.

Computational analysis of membrane proteins: the largest class of drug targets

Given the key roles of integral membrane proteins as transporters and channels, it is necessary to understand their structures and, hence, mechanisms and regulation at the molecular level. Membrane proteins represent approximately 30% of all proteins of currently sequenced genomes. Paradoxically, however, only approximately 2% of crystal structures deposited in the protein data bank are of membrane proteins, and very few of these are at high resolution (better than 2A). The great disparity between our understanding of soluble proteins and our understanding of membrane proteins is because of the practical problems of working with membrane proteins - specifically, difficulties in expression, purification and crystallization. Thus, computational modeling has been utilized extensively to make crucial advances in understanding membrane protein structure and function.

Importance of the peptide backbone description in modeling the selectivity filter in potassium channels

A dihedral energy correction (CMAP) term has been recently included in the CHARMM force field to obtain a more accurate description of the peptide backbone. Its importance in improving dynamical properties of proteins and preserving their stability in long molecular-dynamics simulations has been established for several globular proteins. Here we investigate its role in maintaining the structure and function of two potassium channels, Shaker K(v)1.2 and KcsA, by performing molecular-dynamics simulations with and without the CMAP correction in otherwise identical systems. We show that without CMAP, it is not possible to maintain the experimentally observed orientations of the carbonyl groups in the selectivity filter in Shaker, and the channel loses its selectivity property. In the case of KcsA, the channel retains some selectivity even without CMAP because the carbonyl orientations are relatively better preserved compared to Shaker.

Molecular modeling and simulation studies of ion channel structures, dynamics and mechanisms

Ion channels are integral membrane proteins that enable selected ions to flow passively across membranes. Channel proteins have been the focus of computational approaches to relate their three-dimensional (3D) structure to their physiological function. We describe a number of computational tools to model ion channels. Homology modeling may be used to construct structural models of channels based on available X-ray structures. Electrostatics calculations enable an approximate evaluation of the energy profile of an ion passing through a channel. Molecular dynamics simulations and free-energy calculations provide information on the thermodynamics and kinetics of channel function.

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.

Molecular dynamics simulations of potassium channels

Despite the complexity of ion-channels, MD simulations based on realistic all-atom models have become a powerful technique for providing accurate descriptions of the structure and dynamics of these systems, complementing and reinforcing experimental work. Successful multidisciplinary collaborations, progress in the experimental determination of three-dimensional structures of membrane proteins together with new algorithms for molecular simulations and the increasing speed and availability of supercomputers, have made possible a considerable progress in this area of biophysics. This review aims at highlighting some of the work in the area of potassium channels and molecular dynamics simulations where numerous fundamental questions about the structure, function, folding and dynamics of these systems remain as yet unresolved challenges.