Molecular dynamics of the KcsA K(+) channel in a bilayer membrane

The life of the cell membrane: A paradigmatic reading from Deleuze and Guattari

While the Fluid Mosaic model (FMM) is widely accepted as an account of the cell membrane's structure-function, its inability to explain certain phenomena has led to the lipid rafts hypothesis (nanodomains) that spontaneous spatiotemporal enriched zones of sphingolipids-cholesterol-protein exist within the membrane. In this text, we propose a novel approach that conceives the cell membrane as a living entity. The questions regarding the FMM revolve around the fact that, although these molecular components are present in many cell types, the membrane does not react in the same way to every external agent; for example, a virus evokes a particular response: why is there some marked specificity of virus (or toxin) attack on one (or some) of these cell types and not to other cell types that nevertheless have a similar membrane protein constitution? The crucial question, to explain this selectivity, would be what determines the specificity of attack on some cells and not others? While FMN assumes a dynamism between macrostates at the intramolecular, intermolecular, and/or collective levels in the membrane, the approach of the lipid raft model presupposes a much greater and more complex dynamics of microstates (even nano-states) of these molecular components. In other words, it implies higher and instantaneous mobility as assemblages ("intentional") and thus, of the membrane itself (as a collective), in response to changes in the internal and external physicochemical environment over a broad spatiotemporal scale. This suggests a mechanism of membrane adaptation in the face of evolutionary constraints. In this text, we propose a paradigmatic approach, from Deleuze-Guattari's philosophy: to conceive the cell membrane as living and not as a mere molecular conglomerate with particular functions and mechanical processes between molecules. For this, we employ the functional concepts of territory and machinic assemblage, whence the vitality of the membrane would allow us to postulate instantaneous updates, within wider spatiotemporal scales in its composition in contrast with the model that dominates as a more plausible explanation nowadays, that does not include smaller spatiotemporal events. If we resort to the concept of territory and its different media components, we could offer a more plausible explanation of the vigorous dynamism in the composition of the cell membrane since it would allow more subtle and complex differentiations between media and thus make visible the constant and instant changes. We propose that the model of nanodomains, understood as a process of dynamic territorialization, offers a more complex and subtle explanation of the instantaneous changes in the cell membrane's composition. This approach expands the explanatory framework for cellular phenomena and reveals their spatiotemporal complexity in accordance with other research.

Stepwise hydration of [CH3COOMg]+ studied by cold ion trap infrared spectroscopy: insights into interactions in the magnesium channel selection filters

The magnesium channel controls Mg2+ concentration in the cell and plays an indispensable role in biological functions. The crystal structure of the Magnesium Transport E channel suggested that Mg2+ hydrated by 6 water molecules is transported through a selection filter consisting of COO- groups on two Asp residues. This Mg2+ motion implies successive pairing with -OOC-R and dissociation mediated by water molecules. For another divalent ion, however, it is known that RCOO-⋯Ca2+ cannot be separated even with 12 water molecules. From this discrepancy, we probe the structure of Mg2+(CH3COO-)(H2O)4-17 clusters by measuring the infrared spectra and monitoring the vibrational frequencies of COO- with the help of quantum chemistry calculations. The hydration by (H2O)6 is not enough to induce ion separation, and partially-separated or separated pairs are formed from 10 water molecules at least. These results suggest that the ion separation between Mg2+ and carboxylate ions in the selection-filter of the MgtE channel not only results from water molecules in their first hydration shell, but also from additional factors including water molecules and protein groups in the second solvation shell of Mg2+.

Probing Ion Configurations in the KcsA Selectivity Filter with Single-Isotope Labels and 2D IR Spectroscopy

The potassium ion (K+) configurations of the selectivity filter of the KcsA ion channel protein are investigated with two-dimensional infrared (2D IR) spectroscopy of amide I vibrations. Single 13C-18O isotope labels are used, for the first time, to selectively probe the S1/S2 or S2/S3 binding sites in the selectivity filter. These binding sites have the largest differences in ion occupancy in two competing K+ transport mechanisms: soft-knock and hard-knock. According to the former, water molecules alternate between K+ ions in the selectivity filter while the latter assumes that K+ ions occupy the adjacent sites. Molecular dynamics simulations and computational spectroscopy are employed to interpret experimental 2D IR spectra. We find that in the closed conductive state of the KcsA channel, K+ ions do not occupy adjacent binding sites. The experimental data is consistent with simulated 2D IR spectra of soft-knock ion configurations. In contrast, the simulated spectra for the hard-knock ion configurations do not reproduce the experimental results. 2D IR spectra of the hard-knock mechanism have lower frequencies, homogeneous 2D lineshapes, and multiple peaks. In contrast, ion configurations of the soft-knock model produce 2D IR spectra with a single peak at a higher frequency and inhomogeneous lineshape. We conclude that under equilibrium conditions, in the absence of transmembrane voltage, both water and K+ ions occupy the selectivity filter of the KcsA channel in the closed conductive state. The ion configuration is central to the mechanism of ion transport through potassium channels.

Permeability enhancement of Kv1.2 potassium channel by a terahertz electromagnetic field

As biomolecules vibrate and rotate in the terahertz band, the biological effects of terahertz electromagnetic fields have drawn considerable attention from the physiological and medical communities. Ion channels are the basis of biological electrical signals, so studying the effect of terahertz electromagnetic fields on ion channels is significant. In this paper, the effect of a terahertz electromagnetic field with three different frequencies, 6, 15, and 25 THz, on the Kv1.2 potassium ion channel was investigated by molecular dynamics simulations. The results show that an electromagnetic field with a 15 THz frequency can significantly enhance the permeability of the Kv1.2 potassium ion channel, which is 1.7 times higher than without an applied electric field. By analyzing the behavior of water molecules, it is found that the electromagnetic field with the 15 THz frequency shortens the duration of frozen and relaxation processes when potassium ions pass through the channel, increases the proportion of the direct knock-on mode, and, thus, enhances the permeability of the Kv1.2 potassium ion channel.

Mechanism of external K+ sensitivity of KCNQ1 channels

KCNQ1 voltage-gated K+ channels are involved in a wide variety of fundamental physiological processes and exhibit the unique feature of being markedly inhibited by external K+. Despite the potential role of this regulatory mechanism in distinct physiological and pathological processes, its exact underpinnings are not well understood. In this study, using extensive mutagenesis, molecular dynamics simulations, and single-channel recordings, we delineate the molecular mechanism of KCNQ1 modulation by external K+. First, we demonstrate the involvement of the selectivity filter in the external K+ sensitivity of the channel. Then, we show that external K+ binds to the vacant outermost ion coordination site of the selectivity filter inducing a diminution in the unitary conductance of the channel. The larger reduction in the unitary conductance compared to whole-cell currents suggests an additional modulatory effect of external K+ on the channel. Further, we show that the external K+ sensitivity of the heteromeric KCNQ1/KCNE complexes depends on the type of associated KCNE subunits.

Bio-membranes: Picosecond to second dynamics and plasticity as deciphered by solid state NMR

Since the first membrane models in the 1970s, the concept of biological membranes has evolved considerably. The membrane is now seen as a very complex mixture whose dynamic behavior is even more complex. Solid-state NMR is well suited for such studies as it can probe the movements of the membrane from picoseconds to seconds. Two NMR observables can be used: motionally averaged spectra and relaxation times. They bring information on order parameters, phase transitions, correlation times, activation energies and membrane elasticity. Spectra are used to determine the nature of the membrane phase. The order parameters can be measured directly from spectra that are dominated by quadrupolar, dipolar and chemical shielding magnetic interactions and allow describing the lipid membrane as being very rigid at the glycerol and chain level and very fluid at its center and surface. Correlation times and activation energies can be measured for intramolecular motions (pico to nanoseconds), molecular motions (nano to 100 ns) and collective modes of membrane deformation (microseconds). Sterols modulate membrane phases, order parameters, correlation times and membrane elasticity. In general terms, sterols tend to act to reduce the impact of environmental changes on molecular order and dynamics. They can be described as regulators of membrane dynamics by keeping them in a state of dynamics that changes very little when the temperature or other factors change. The presence of such large-scale membrane dynamics is proposed as a means of adapting to evolutionary constraints.

Current Trends and Changes in Use of Membrane Molecular Dynamics Simulations within Academia and the Pharmaceutical Industry

There has been an almost exponential increase in the use of molecular dynamics simulations in basic research and industry over the last 5 years, with almost a doubling in the number of publications each year. Many of these are focused on neurological membranes, and biological membranes in general, applied to the medical industry. A smaller portion have utilized membrane simulations to answer more basic questions related to the function of specific proteins, chemicals or biological processes. This review covers some newer studies, alongside studies from the last two decades, to determine changes in the field. Some of these are basic, while others are more profound, such as multi-component embedded membrane machinery. It is clear that many facets of the discipline remain the same, while the focus on and uses of the technology are broadening in scope and utilization as a general research tool. Analysis of recent literature provides an overview of the current methodologies, covers some of the recent trends or advances and tries to make predictions of the overall path membrane molecular dynamics will follow in the coming years. In general, the overview presented is geared towards the general scientific community, who may wish to introduce the use of these methodologies in light of these changes, making molecular dynamic simulations more feasible for general scientific or medical research.

Structure and Computational Electrophysiology of Ac-LS3, a Synthetic Ion Channel

Computer simulations are reported on Ac-LS3, a synthetic ion channel, containing 21 residues with a Leu-Ser-Ser-Leu-Leu-Ser-Leu heptad repeat, which forms ions channels upon application of voltage. A hexameric, coiled-coil bundle initially positioned perpendicular to the membrane settled into a stable, tilted structure after 1.5 μs, most likely to improve contacts between the non-polar exterior of the channel and the hydrophobic core of the membrane. Once tilted, the bundle remained in this state during subsequent simulations of nearly 10 μs at voltages ranging from 200 to -100 mV. In contrast, attempts to identify a stable pentameric structure failed, thus supporting the hypothesis that the channel is a hexamer. Results at 100 mV were used to reconstruct the free energy profiles for K⁺ and Cl^- in the channel. This was done by way of several methods in which results of molecular dynamics (MD) simulations were combined with the electrodiffusion model. Two of them developed recently do not require knowledge of the diffusivity. Instead, they utilize one-sided density profiles and committor probabilities. The consistency between different methods is very good, supporting the utility of the newly developed methods for reconstructing free energies of ions in channels. The flux of K⁺, which accounts for most of the current through the channel, calculated directly from MD matches well the total measured current. However, the current of Cl^- is somewhat overestimated, possibly due to a slightly unbalanced force field involving chloride. The current-voltage dependence was also reconstructed by way of a recently developed, efficient method that requires simulations only at a single voltage, yielding good agreement with the experiment. Taken together, the results demonstrate that computational electrophysiology has become a reliable tool for studying how channels mediate ion transport through membranes.

Simulation and Machine Learning Methods for Ion-Channel Structure Determination, Mechanistic Studies and Drug Design

Ion channels are expressed in almost all living cells, controlling the in-and-out communications, making them ideal drug targets, especially for central nervous system diseases. However, owing to their dynamic nature and the presence of a membrane environment, ion channels remain difficult targets for the past decades. Recent advancement in cryo-electron microscopy and computational methods has shed light on this issue. An explosion in high-resolution ion channel structures paved way for structure-based rational drug design and the state-of-the-art simulation and machine learning techniques dramatically improved the efficiency and effectiveness of computer-aided drug design. Here we present an overview of how simulation and machine learning-based methods fundamentally changed the ion channel-related drug design at different levels, as well as the emerging trends in the field.

P-Loop Channels: Experimental Structures, and Physics-Based and Neural Networks-Based Models

The superfamily of P-loop channels includes potassium, sodium, and calcium channels, as well as TRP channels and ionotropic glutamate receptors. A rapidly increasing number of crystal and cryo-EM structures have revealed conserved and variable elements of the channel structures. Intriguing differences are seen in transmembrane helices of channels, which may include π-helical bulges. The bulges reorient residues in the helices and thus strongly affect their intersegment contacts and patterns of ligand-sensing residues. Comparison of the experimental structures suggests that some π-bulges are dynamic: they may appear and disappear upon channel gating and ligand binding. The AlphaFold2 models represent a recent breakthrough in the computational prediction of protein structures. We compared some crystal and cryo-EM structures of P-loop channels with respective AlphaFold2 models. Folding of the regions, which are resolved experimentally, is generally similar to that predicted in the AlphaFold2 models. The models also reproduce some subtle but significant differences between various P-loop channels. However, patterns of π-bulges do not necessarily coincide in the experimental and AlphaFold2 structures. Given the importance of dynamic π-bulges, further studies involving experimental and theoretical approaches are necessary to understand the cause of the discrepancy.

Computational methods and theory for ion channel research

Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.

Ion Selectivity in the ENaC/DEG Family: A Systematic Review with Supporting Analysis

The Epithelial Sodium Channel/Degenerin (ENaC/DEG) family is a superfamily of sodium-selective channels that play diverse and important physiological roles in a wide variety of animal species. Despite their differences, they share a high homology in the pore region in which the ion discrimination takes place. Although ion selectivity has been studied for decades, the mechanisms underlying this selectivity for trimeric channels, and particularly for the ENaC/DEG family, are still poorly understood. This systematic review follows PRISMA guidelines and aims to determine the main components that govern ion selectivity in the ENaC/DEG family. In total, 27 papers from three online databases were included according to specific exclusion and inclusion criteria. It was found that the G/SxS selectivity filter (glycine/serine, non-conserved residue, serine) and other well conserved residues play a crucial role in ion selectivity. Depending on the ion type, residues with different properties are involved in ion permeability. For lithium against sodium, aromatic residues upstream of the selectivity filter seem to be important, whereas for sodium against potassium, negatively charged residues downstream of the selectivity filter seem to be important. This review provides new perspectives for further studies to unravel the mechanisms of ion selectivity.

Sodium Ions Do Not Stabilize the Selectivity Filter of a Potassium Channel

Ion conduction is an essential function for electrical activity in all organisms. The non-selective ion channel NaK was previously shown to adopt two stable conformations of the selectivity filter. Here, we present solid-state NMR measurements of NaK demonstrating a population shift between these conformations induced by changing the ions in the sample while the overall structure of NaK is not affected. We show that two K⁺-selective mutants (NaK2K and NaK2K-Y66F) suffer a complete loss of selectivity filter stability under Na⁺ conditions, but do not collapse into a defined structure. Widespread chemical shift perturbations are seen between the Na⁺ and K⁺ states of the K⁺-selective mutants in the region of the pore helix indicating structural changes. We conclude that the stronger link between the selectivity filter and the pore helix in the K⁺-selective mutants, compared to the non-selective wild-type NaK channel, reduces the ion-dependent conformational flexibility of the selectivity filter.

Electrophysiological Properties from Computations at a Single Voltage: Testing Theory with Stochastic Simulations

We use stochastic simulations to investigate the performance of two recently developed methods for calculating the free energy profiles of ion channels and their electrophysiological properties, such as current–voltage dependence and reversal potential, from molecular dynamics simulations at a single applied voltage. These methods require neither knowledge of the diffusivity nor simulations at multiple voltages, which greatly reduces the computational effort required to probe the electrophysiological properties of ion channels. They can be used to determine the free energy profiles from either forward or backward one-sided properties of ions in the channel, such as ion fluxes, density profiles, committor probabilities, or from their two-sided combination. By generating large sets of stochastic trajectories, which are individually designed to mimic the molecular dynamics crossing statistics of models of channels of trichotoxin, p7 from hepatitis C and a bacterial homolog of the pentameric ligand-gated ion channel, GLIC, we find that the free energy profiles obtained from stochastic simulations corresponding to molecular dynamics simulations of even a modest length are burdened with statistical errors of only 0.3 kcal/mol. Even with many crossing events, applying two-sided formulas substantially reduces statistical errors compared to one-sided formulas. With a properly chosen reference voltage, the current–voltage curves can be reproduced with good accuracy from simulations at a single voltage in a range extending for over 200 mV. If possible, the reference voltages should be chosen not simply to drive a large current in one direction, but to observe crossing events in both directions.

The Persistent Question of Potassium Channel Permeation Mechanisms

Potassium channels play critical roles in many physiological processes, providing a selective permeation route for K⁺ ions in and out of a cell, by employing a carefully designed selectivity filter, evolutionarily conserved from viruses to mammals. The structure of the selectivity filter was determined at atomic resolution by x-ray crystallography, showing a tight coordination of desolvated K⁺ ions by the channel. However, the molecular mechanism of K⁺ ions permeation through potassium channels remains unclear, with structural, functional and computational studies often providing conflicting data and interpretations. In this review, we will present the proposed mechanisms, discuss their origins, and will critically assess them against all available data. General properties shared by all potassium channels are introduced first, followed by the introduction of two main mechanisms of ion permeation: soft and direct knock-on. Then, we will discuss critical computational and experimental studies that shaped the field. We will especially focus on molecular dynamics (MD) simulations, that provided mechanistic and energetic aspects of K⁺ permeation, but at the same time created long-standing controversies. Further challenges and possible solutions are presented as well.

Unraveling of a Strongly Correlated Dynamical Network of Residues Controlling the Permeation of Potassium in KcsA Ion Channel

The complicated patterns of the single-channel currents in potassium ion channel KcsA are governed by the structural variability of the selectivity filter. A comparative analysis of the dynamics of the wild type KcsA channel and several of its mutants showing different conducting patterns was performed. A strongly correlated dynamical network of interacting residues is found to play a key role in regulating the state of the wild type channel. The network is centered on the aspartate D80 which plays the role of a hub by strong interacting via hydrogen bonds with residues E71, R64, R89, and W67. Residue D80 also affects the selectivity filter via its backbones. This network further compromises ions and water molecules located inside the channel that results in the mutual influence: the permeation depends on the configuration of residues in the network, and the dynamics of network's residues depends on locations of ions and water molecules inside the selectivity filter. Some features of the network provide a further understanding of experimental results describing the KcsA activity. In particular, the necessity of anionic lipids to be present for functioning the channel is explained by the interaction between the lipids and the arginine residues R64 and R89 that prevents destabilizing the structure of the selectivity filter.

High-Resolution Structures of K+ Channels

Potassium channels are present in every living cell and essential to setting up a stable, non-zero transmembrane electrostatic potential which manifests the off-equilibrium livelihood of the cell. They are involved in other cellular activities and regulation, such as the controlled release of hormones, the activation of T-cells for immune response, the firing of action potential in muscle cells and neurons, etc. Pharmacological reagents targeting potassium channels are important for treating various human diseases linked to dysfunction of the channels. High-resolution structures of these channels are very useful tools for delineating the detailed chemical basis underlying channel functions and for structure-based design and optimization of their pharmacological and pharmaceutical agents. Structural studies of potassium channels have revolutionized biophysical understandings of key concepts in the field - ion selectivity, conduction, channel gating, and modulation, making them multi-modality targets of pharmacological regulation. In this chapter, I will select a few high-resolution structures to illustrate key structural insights, proposed allostery behind channel functions, disagreements still open to debate, and channel-lipid interactions and co-evolution. The known structural consensus allows the inference of conserved molecular mechanisms shared among subfamilies of K⁺ channels and makes it possible to develop channel-specific pharmaceutical agents.

Conduction and Gating Properties of the TRAAK Channel from Molecular Dynamics Simulations with Different Force Fields

In recent years, the K2P family of potassium channels has been the subject of intense research activity. Owing to the complex function and regulation of this family of ion channels, it is common practice to complement experimental findings with the atomistic description provided by computational approaches such as molecular dynamics (MD) simulations, especially, in light of the unprecedented timescales accessible at present. However, despite recent substantial improvements, the accuracy of MD simulations is still undermined by the intrinsic limitations of force fields. Here, we systematically assessed the performance of the most popular force fields employed to study ion channels at timescales that are orders of magnitude greater than the ones accessible when these energy functions were first developed. Using 32 μs of trajectories, we investigated the dynamics of a member of the K2P ion channel family, the TRAAK channel, using two established force fields in simulations of biological systems: AMBER and CHARMM. We found that while results are comparable on the nanosecond timescales, significant inconsistencies arise at microsecond timescales.

Modulation of Function, Structure and Clustering of K+ Channels by Lipids: Lessons Learnt from KcsA

KcsA, a prokaryote tetrameric potassium channel, was the first ion channel ever to be structurally solved at high resolution. This, along with the ease of its expression and purification, made KcsA an experimental system of choice to study structure–function relationships in ion channels. In fact, much of our current understanding on how the different channel families operate arises from earlier KcsA information. Being an integral membrane protein, KcsA is also an excellent model to study how lipid–protein and protein–protein interactions within membranes, modulate its activity and structure. In regard to the later, a variety of equilibrium and non-equilibrium methods have been used in a truly multidisciplinary effort to study the effects of lipids on the KcsA channel. Remarkably, both experimental and “in silico” data point to the relevance of specific lipid binding to two key arginine residues. These residues are at non-annular lipid binding sites on the protein and act as a common element to trigger many of the lipid effects on this channel. Thus, processes as different as the inactivation of channel currents or the assembly of clusters from individual KcsA channels, depend upon such lipid binding.

Queueing arrival and release mechanism for K+ permeation through a potassium channel

The mechanism underlying ion permeation through potassium channels still remains controversial. K+ ions permeate across a narrow selectivity filter (SF) in a single file. Conventional scenarios assume that K+ ions are tightly bound in the SF, and, thus, they are displaced from their energy well by ion-ion repulsion with an incoming ion. This tight coupling between entering and exiting ions has been called the "knock-on" mechanism. However, this paradigm is contradicted by experimental data measuring the water-ion flux coupling ratio, demonstrating fewer ion occupancies. Here, the results of molecular dynamics simulations of permeation through the KcsA potassium channel revealed an alternative mechanism. In the aligned ions in the SF (an ion queue), the outermost K+ was readily and spontaneously released toward the extracellular space, and the affinity of the relevant ion was ~ 50 mM. Based on this low-affinity regime, a simple queueing mechanism described by loose coupling of entering and exiting ions is proposed.

Perturbations of Native Membrane Protein Structure in Alkyl Phosphocholine Detergents: A Critical Assessment of NMR and Biophysical Studies

Membrane proteins perform a host of vital cellular functions. Deciphering the molecular mechanisms whereby they fulfill these functions requires detailed biophysical and structural investigations. Detergents have proven pivotal to extract the protein from its native surroundings. Yet, they provide a milieu that departs significantly from that of the biological membrane, to the extent that the structure, the dynamics, and the interactions of membrane proteins in detergents may considerably vary, as compared to the native environment. Understanding the impact of detergents on membrane proteins is, therefore, crucial to assess the biological relevance of results obtained in detergents. Here, we review the strengths and weaknesses of alkyl phosphocholines (or foscholines), the most widely used detergent in solution-NMR studies of membrane proteins. While this class of detergents is often successful for membrane protein solubilization, a growing list of examples points to destabilizing and denaturing properties, in particular for α-helical membrane proteins. Our comprehensive analysis stresses the importance of stringent controls when working with this class of detergents and when analyzing the structure and dynamics of membrane proteins in alkyl phosphocholine detergents.

H. R, Thamleena A. H, Joseph A, Ben A, V. U. K. Roles of different amino-acid residues towards binding and selective transport of K+ through KcsA K+-ion channel

Each amino acid in the selectivity filter plays a distinct role towards binding and transport of K⁺ ion through KcsA.

Permeating disciplines: Overcoming barriers between molecular simulations and classical structure-function approaches in biological ion transport

Ion translocation across biological barriers is a fundamental requirement for life. In many cases, controlling this process-for example with neuroactive drugs-demands an understanding of rapid and reversible structural changes in membrane-embedded proteins, including ion channels and transporters. Classical approaches to electrophysiology and structural biology have provided valuable insights into several such proteins over macroscopic, often discontinuous scales of space and time. Integrating these observations into meaningful mechanistic models now relies increasingly on computational methods, particularly molecular dynamics simulations, while surfacing important challenges in data management and conceptual alignment. Here, we seek to provide contemporary context, concrete examples, and a look to the future for bridging disciplinary gaps in biological ion transport. This article is part of a Special Issue entitled: Beyond the Structure-Function Horizon of Membrane Proteins edited by Ute Hellmich, Rupak Doshi and Benjamin McIlwain.

Validating a Coarse-Grained Voltage Activation Model by Comparing Its Performance to the Results of Monte Carlo Simulations

Simulating the nature of voltage-activated systems is a problem of major current interest, ranging from the action of voltage-gated ion channels to energy storage batteries. However, fully microscopic converging molecular simulations of external voltage effects present a major challenge, and macroscopic models are associated with major uncertainties about the dielectric treatment and the underlying physical basis. Recently we developed a coarse-grained (CG) model that represents explicitly the electrodes, the electrolytes, and the membrane/protein system. The CG model provides a semimacroscopic way of capturing the microscopic physics of voltage-activated systems. Our method was originally validated by reproducing macroscopic and analytical results for key test cases and then used in modeling voltage-activated ion channels and related problems. In this work, we further establish the reliability of the CG voltage model by comparing it to the results of Monte Carlo (MC) simulations with a microscopic electrolyte model. The comparison explores different aspects of membrane, electrolyte, and electrode systems ranging from the Gouy-Chapman model to the determination of the electrolyte charge distribution in the solution between two electrodes (without and with a separating membrane), as well as the evaluation of gating charges. Overall the agreement is very impressive. This provides confidence in the CG model and also shows that the MC model can be used in realistic simulation of voltage activation of membrane proteins with sufficient computer time.

Theoretical approaches for dynamical ordering of biomolecular systems

BACKGROUND

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

SCOPE OF REVIEW

We review the framework of quantum mechanical/molecular mechanical (QM/MM) calculations, AA MD simulations, CG modeling, and integral equation theories. Applications of these methods to the dynamical ordering of biomolecular systems are also exemplified.

MAJOR CONCLUSIONS

The QM/MM calculation enables the study of chemical reactions. The AA MD simulation, which omits the QM calculation, can follow longer time-scale phenomena. By reducing the number of degrees of freedom and the computational cost, CG modeling can follow much longer time-scale phenomena than AA modeling. Integral equation theories for liquids elucidate the liquid structure, for example, whether the liquid follows a radial distribution function.

GENERAL SIGNIFICANCE

These theoretical approaches can analyze the dynamic behaviors of biomolecular systems. They also provide useful tools for exploring the dynamic ordering systems of biomolecules, such as self-assembly. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Ion channels and ion selectivity

Specific macromolecular transport systems, ion channels and pumps, provide the pathways to facilitate and control the passage of ions across the lipid membrane. Ion channels provide energetically favourable passage for ions to diffuse rapidly and passively according to their electrochemical potential. Selective ion channels are essential for the excitability of biological membranes: the action potential is a transient phenomenon that reflects the rapid opening and closing of voltage-dependent Na⁺-selective and K⁺-selective channels. One of the most critical functional aspects of K⁺ channels is their ability to remain highly selective for K⁺ over Na⁺ while allowing high-throughput ion conduction at a rate close to the diffusion limit. Permeation through the K⁺ channel selectivity filter is believed to proceed as a 'knockon' mechanism, in which 2-3 K⁺ ions interspersed by water molecules move in a single file. Permeation through the comparatively wider and less selective Na⁺ channels also proceeds via a loosely coupled knockon mechanism, although the ions do not need to be fully dehydrated. While simple structural concepts are often invoked to rationalize the mechanism of ion selectivity, a deeper analysis shows that subtle effects play an important role in these flexible dynamical structures.

Pore size matters for potassium channel conductance

Ion channels are membrane proteins that mediate efficient ion transport across the hydrophobic core of cell membranes, an unlikely process in their absence. K⁺ channels discriminate K⁺ over cations with similar radii with extraordinary selectivity and display a wide diversity of ion transport rates, covering differences of two orders of magnitude in unitary conductance. The pore domains of large- and small-conductance K⁺ channels share a general architectural design comprising a conserved narrow selectivity filter, which forms intimate interactions with permeant ions, flanked by two wider vestibules toward the internal and external openings. In large-conductance K⁺ channels, the inner vestibule is wide, whereas in small-conductance channels it is narrow. Here we raise the idea that the physical dimensions of the hydrophobic internal vestibule limit ion transport in K⁺ channels, accounting for their diversity in unitary conductance.

Multi-ion free energy landscapes underscore the microscopic mechanism of ion selectivity in the KcsA channel

Potassium (K(+)) channels are transmembrane proteins that passively and selectively allow K(+) ions to flow through them, after opening in response to an external stimulus. One of the most critical functional aspects of their function is their ability to remain very selective for K(+) over Na(+) while allowing high-throughput ion conduction at a rate close to the diffusion limit. Classically, it is assumed that the free energy difference between K(+) and Na(+) in the pore relative to the bulk solution is the critical quantity at the origin of selectivity. This is the thermodynamic view of ion selectivity. An alternative view assumes that kinetic factors play the dominant role. Recent results from a number of studies have also highlighted the great importance of the multi-ion single file on the selectivity of K(+) channels. The data indicate that having multiple K(+) ions bound simultaneously is required for selective K(+) conduction, and that a reduction in the number of bound K(+) ions destroys the multi-ion selectivity mechanism utilized by K(+) channels. In the present study, multi-ion potential of mean force molecular dynamics computations are carried out to clarify the mechanism of ion selectivity in the KcsA channel. The computations show that the multi-ion character of the permeation process is a critical element for establishing the selective ion conductivity through K(+)-channels. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Voltage-Gated Sodium Channels: Mechanistic Insights From Atomistic Molecular Dynamics Simulations

The permeation of ions and other molecules across biological membranes is an inherent requirement of all cellular organisms. Ion channels, in particular, are responsible for the conduction of charged species, hence modulating the propagation of electrical signals. Despite the universal physiological implications of this property, the molecular functioning of ion channels remains ambiguous. The combination of atomistic structural data with computational methodologies, such as molecular dynamics (MD) simulations, is now considered routine to investigate structure-function relationships in biological systems. A fuller understanding of conduction, selectivity, and gating, therefore, is steadily emerging due to the applicability of these techniques to ion channels. However, because their structure is known at atomic resolution, studies have consistently been biased toward K(+) channels, thus the molecular determinants of ionic selectivity, activation, and drug blockage in Na(+) channels are often overlooked. The recent increase of available crystallographic data has eminently encouraged the investigation of voltage-gated sodium (NaV) channels via computational methods. Here, we present an overview of simulation studies that have contributed to our understanding of key principles that underlie ionic conduction and selectivity in Na(+) channels, in comparison to the K(+) channel analogs.

Ion Concentration- and Voltage-Dependent Push and Pull Mechanisms of Potassium Channel Ion Conduction

The mechanism of ion conduction by potassium channels is one of the central issues in physiology. In particular, it is still unclear how the ion concentration and the membrane voltage drive ion conduction. We have investigated the dynamics of the ion conduction processes in the Kv1.2 pore domain, by molecular dynamics (MD) simulations with several different voltages and ion concentrations. By focusing on the detailed ion movements through the pore including selectivity filter (SF) and cavity, we found two major conduction mechanisms, called the III-IV-III and III-II-III mechanisms, and the balance between the ion concentration and the voltage determines the mechanism preference. In the III-IV-III mechanism, the outermost ion in the pore is pushed out by a new ion coming from the intracellular fluid, and four-ion states were transiently observed. In the III-II-III mechanism, the outermost ion is pulled out first, without pushing by incoming ions. Increases in the ion concentration and voltage accelerated ion conductions, but their mechanisms were different. The increase in the ion concentrations facilitated the III-IV-III conductions, while the higher voltages increased the III-II-III conductions, indicating that the pore domain of potassium channels permeates ions by using two different driving forces: a push by intracellular ions and a pull by voltage.

Simulations of outer membrane channels and their permeability

Channels in the outer membrane of Gram-negative bacteria provide essential pathways for the controlled and unidirectional transport of ions, nutrients and metabolites into the cell. At the same time the outer membrane serves as a physical barrier for the penetration of noxious substances such as antibiotics into the bacteria. Most antibiotics have to pass through these membrane channels to either reach cytoplasmic bound targets or to further cross the hydrophobic inner membrane. Considering the pharmaceutical significance of antibiotics, understanding the functional role and mechanism of these channels is of fundamental importance in developing strategies to design new drugs with enhanced permeation abilities. Due to the biological complexity of membrane channels and experimental limitations, computer simulations have proven to be a powerful tool to investigate the structure, dynamics and interactions of membrane channels. Considerable progress has been made in computer simulations of membrane channels during the last decade. The goal of this review is to provide an overview of the computational techniques and their roles in modeling the transport across outer membrane channels. A special emphasis is put on all-atom molecular dynamics simulations employed to better understand the transport of molecules. Moreover, recent molecular simulations of ion, substrate and antibiotics translocation through membrane pores are briefly summarized. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Biased Molecular Simulations for Free-Energy Mapping: A Comparison on the KcsA Channel as a Test Case

The calculation of free-energy landscapes in proteins is a challenge for modern numerical simulations. As to the case of potassium ion channels is concerned, it is particularly interesting because of the nanometric dimensions of the selectivity filter, where the complex electrostatics is highly relevant. The present study aims at comparing three different techniques used to bias molecular dynamics simulations, namely Umbrella Sampling, Steered Molecular Dynamics, and Metadynamics, never applied all together in the past to the same channel protein. Our test case is represented by potassium ions permeating the selectivity filter of the KcsA channel.

Unraveling the mechanism of selective ion transport in hydrophobic subnanometer channels

Recently reported synthetic organic nanopore (SONP) can mimic a key feature of natural ion channels, i.e., selective ion transport. However, the physical mechanism underlying the K(+)/Na(+) selectivity for the SONPs is dramatically different from that of natural ion channels. To achieve a better understanding of the selective ion transport in hydrophobic subnanometer channels in general and SONPs in particular, we perform a series of ab initio molecular dynamics simulations to investigate the diffusivity of aqua Na(+) and K(+) ions in two prototype hydrophobic nanochannels: (i) an SONP with radius of 3.2 Å, and (ii) single-walled carbon nanotubes (CNTs) with radii of 3-5 Å (these radii are comparable to those of the biological potassium K(+) channels). We find that the hydration shell of aqua Na(+) ion is smaller than that of aqua K(+) ion but notably more structured and less yielding. The aqua ions do not lower the diffusivity of water molecules in CNTs, but in SONP the diffusivity of aqua ions (Na(+) in particular) is strongly suppressed due to the rugged inner surface. Moreover, the aqua Na(+) ion requires higher formation energy than aqua K(+) ion in the hydrophobic nanochannels. As such, we find that the ion (K(+) vs. Na(+)) selectivity of the (8, 8) CNT is ∼20× higher than that of SONP. Hence, the (8, 8) CNT is likely the most efficient artificial K(+) channel due in part to its special interior environment in which Na(+) can be fully solvated, whereas K(+) cannot. This work provides deeper insights into the physical chemistry behind selective ion transport in nanochannels.

Visualizing KcsA conformational changes upon ion binding by infrared spectroscopy and atomistic modeling

The effect of ion binding in the selectivity filter of the potassium channel KcsA is investigated by combining amide I Fourier-transform infrared spectroscopy with structure-based spectral modeling. Experimental difference IR spectra between K(+)-bound KcsA and Na(+)-bound KcsA are in good qualitative agreement with spectra modeled from structural ensembles generated from molecular dynamics simulations. The molecular origins of the vibrational modes contributing to differences in these spectra are determined not only from structural differences in the selectivity filter but also from the pore helices surrounding this region. Furthermore, the coordination of K(+) or Na(+) to carbonyls in the selectivity filter effectively decouples the vibrations of those carbonyls from the rest of the protein, creating local probes of the electrostatic environment. The results suggest that it is necessary to include the influence of the surrounding helices in discussing selectivity and transport in KcsA and, on a more general level, that IR spectroscopy offers a nonperturbative route to studying the structure and dynamics of ion channels.

Computational modeling of membrane proteins

The determination of membrane protein (MP) structures has always trailed that of soluble proteins due to difficulties in their overexpression, reconstitution into membrane mimetics, and subsequent structure determination. The percentage of MP structures in the protein databank (PDB) has been at a constant 1-2% for the last decade. In contrast, over half of all drugs target MPs, only highlighting how little we understand about drug-specific effects in the human body. To reduce this gap, researchers have attempted to predict structural features of MPs even before the first structure was experimentally elucidated. In this review, we present current computational methods to predict MP structure, starting with secondary structure prediction, prediction of trans-membrane spans, and topology. Even though these methods generate reliable predictions, challenges such as predicting kinks or precise beginnings and ends of secondary structure elements are still waiting to be addressed. We describe recent developments in the prediction of 3D structures of both α-helical MPs as well as β-barrels using comparative modeling techniques, de novo methods, and molecular dynamics (MD) simulations. The increase of MP structures has (1) facilitated comparative modeling due to availability of more and better templates, and (2) improved the statistics for knowledge-based scoring functions. Moreover, de novo methods have benefited from the use of correlated mutations as restraints. Finally, we outline current advances that will likely shape the field in the forthcoming decade.

Conformational dynamics of shaker-type Kv1.1 ion channel in open, closed, and two mutated states

The dynamic properties of shaker-type Kv1.1 ion channel in its open, closed, & two mutated (E325D & V408A) states embedded in DPPC membrane have been investigated using all-atom force field-based MD simulation. Here, we represent the detailed channel stability, gating environment of charge-carrying residues, salt bridge interaction among the voltage-sensing domains (VSDs), movement of S4 helix, and ion conduction of pore. At positive potential, the S4 helix undergoes lateral fluctuations in accordance with their gating motions found in every model. During transition from closed to active state conformation, charged residues of S4 move "up" across the membrane with an average tilt angle difference of 24°, which is more consistent with the paddle model of channel gating. The E325D mutation at C-terminal end of S4-S5 helical linker leads the channel to a rapid activated state by pushing the gating charge residues upward beside the VSDs resulting in more prominent tilt of S4. Similarly in V408A mutant model, disruption of hydrophobic gate at S6 C-terminal end takes place, which causes the violation of channel-active conformation by bringing the C-terminal end of S4 to its corresponding resting state. The ion permeation is observed only in open-state conformation.

Ion permeation in K⁺ channels occurs by direct Coulomb knock-on

Potassium channels selectively conduct K(+) ions across cellular membranes with extraordinary efficiency. Their selectivity filter exhibits four binding sites with approximately equal electron density in crystal structures with high K(+) concentrations, previously thought to reflect a superposition of alternating ion- and water-occupied states. Consequently, cotranslocation of ions with water has become a widely accepted ion conduction mechanism for potassium channels. By analyzing more than 1300 permeation events from molecular dynamics simulations at physiological voltages, we observed instead that permeation occurs via ion-ion contacts between neighboring K(+) ions. Coulomb repulsion between adjacent ions is found to be the key to high-efficiency K(+) conduction. Crystallographic data are consistent with directly neighboring K(+) ions in the selectivity filter, and our model offers an intuitive explanation for the high throughput rates of K(+) channels.

All-atom molecular dynamics simulation of a photosystem i/detergent complex

All-atom molecular dynamics (MD) simulation was used to investigate the solution structure and dynamics of the photosynthetic pigment-protein complex photosystem I (PSI) from Thermosynechococcus elongatus embedded in a toroidal belt of n-dodecyl-β-d-maltoside (DDM) detergent. Evaluation of root-mean-square deviations (RMSDs) relative to the known crystal structure show that the protein complex surrounded by DDM molecules is stable during the 200 ns simulation time, and root-mean-square fluctuation (RMSF) analysis indicates that regions of high local mobility correspond to solvent-exposed regions such as turns in the transmembrane α-helices and flexible loops on the stromal and lumenal faces. Comparing the protein-detergent complex to a pure detergent micelle, the detergent surrounding the PSI trimer is found to be less densely packed but with more ordered detergent tails, contrary to what is seen in most lipid bilayer models. We also investigated any functional implications for the observed conformational dynamics and protein-detergent interactions, discovering interesting structural changes in the psaL subunits associated with maintaining the trimeric structure of the protein. Importantly, we find that the docking of soluble electron mediators such as cytochrome c6 and ferredoxin to PSI is not significantly impacted by the solubilization of PSI in detergent.

K(+) and Na(+) conduction in selective and nonselective ion channels via molecular dynamics simulations

Generations of scientists have been captivated by ion channels and how they control the workings of the cell by admitting ions from one side of the cell membrane to the other. Elucidating the molecular determinants of ion conduction and selectivity are two of the most fundamental issues in the field of biophysics. Combined with ongoing progress in structural studies, modeling and simulation have been an integral part of the development of the field. As of this writing, the relentless growth in computational power, the development of new algorithms to tackle the so-called rare events, improved force-field parameters, and the concomitant increasing availability of membrane protein structures, allow simulations to contribute even further, providing more-complete models of ion conduction and selectivity in ion channels. In this report, we give an overview of the recent progress made by simulation studies on the understanding of ion permeation in selective and nonselective ion channels.

Potassium ions in the cavity of a KcsA channel model

The high rate of ion flux and selectivity of potassium channels has been attributed to the conformation and dynamics of the ions in the filter which connects the channel cavity and the extracellular environment. The cavity serves as the reservoir for potassium ions diffusing from the intracellular medium. The cavity is believed to decrease the dielectric barrier for the ions to enter the filter. We study here the equilibrium and dynamic properties of potassium ions entering the water-filled cavity of a KcsA channel model. Atomistic molecular dynamics simulations that are supplemented by electrostatic calculations reveal the important role of water molecules and the partially charged protein helices at the bottom of the cavity in overcoming the energy barrier and stabilizing the potassium ion in the cavity. We further show that the average time for a potassium ion to enter the cavity is much shorter than the conduction rate of a potassium passing through the filter, and this time duration is insensitive over a wide range of the membrane potential. The conclusions drawn from the study of the channel model are applicable in generalized contexts, including the entry of ions in artificial ion channels and other confined geometries.

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.

A computational study of barium blockades in the KcsA potassium channel based on multi-ion potential of mean force calculations and free energy perturbation

Electrophysiological studies have established that the permeation of Ba(2+) ions through the KcsA K(+)-channel is impeded by the presence of K(+) ions in the external solution, while no effect is observed for external Na(+) ions. This Ba(2+) "lock-in" effect suggests that at least one of the external binding sites of the KcsA channel is thermodynamically selective for K(+). We used molecular dynamics simulations to interpret these lock-in experiments in the context of the crystallographic structure of KcsA. Assuming that the Ba(2+) is bound in site S(2) in the dominant blocked state, we examine the conditions that could impede its translocation and cause the observed "lock-in" effect. Although the binding of a K(+) ion to site S(1) when site S(2) is occupied by Ba(2+) is prohibitively high in energy (>10 kcal/mol), binding to site S0 appears to be more plausible (ΔG > 4 kcal/mol). The 2D potential of mean force (PMF) for the simultaneous translocation of Ba(2+) from site S(2) to site S(1) and of a K(+) ion on the extracellular side shows a barrier that is consistent with the concept of external lock-in. The barrier opposing the movement of Ba(2+) is very high when a cation is in site S(0), and considerably smaller when the site is unoccupied. Furthermore, free energy perturbation calculations show that site S(0) is selective for K(+) by 1.8 kcal/mol when S(2) is occupied by Ba(2+). However, the same site S(0) is nonselective when site S(2) is occupied by K(+), which shows that the presence of Ba(2+) affects the selectivity of the pore. A theoretical framework within classical rate theory is presented to incorporate the concentration dependence of the external ions on the lock-in effect.

Probing the energy landscape of activation gating of the bacterial potassium channel KcsA

The bacterial potassium channel KcsA, which has been crystallized in several conformations, offers an ideal model to investigate activation gating of ion channels. In this study, essential dynamics simulations are applied to obtain insights into the transition pathways and the energy profile of KcsA pore gating. In agreement with previous hypotheses, our simulations reveal a two phasic activation gating process. In the first phase, local structural rearrangements in TM2 are observed leading to an intermediate channel conformation, followed by large structural rearrangements leading to full opening of KcsA. Conformational changes of a highly conserved phenylalanine, F114, at the bundle crossing region are crucial for the transition from a closed to an intermediate state. 3.9 µs umbrella sampling calculations reveal that there are two well-defined energy barriers dividing closed, intermediate, and open channel states. In agreement with mutational studies, the closed state was found to be energetically more favorable compared to the open state. Further, the simulations provide new insights into the dynamical coupling effects of F103 between the activation gate and the selectivity filter. Investigations on individual subunits support cooperativity of subunits during activation gating.