Dynamics of K+ ion conduction through Kv1.2

Do selectivity filter carbonyls in K+ channels flip away from the pore? Two-dimensional infrared spectroscopy study

Molecular dynamics simulations revealed that the carbonyls of the Val residue in the conserved selectivity filter sequence TVGTG of potassium ion channels can flip away from the pore to form hydrogen bonds with the network of water molecules residing behind the selectivity filter. Such a configuration has been proposed to be relevant for C-type inactivation. Experimentally, X-ray crystallography of the KcsA channel admits the possibility that the Val carbonyls can flip, but it cannot decisively confirm the existence of such a configuration. In this study, we combined molecular dynamics simulations and line shape theory to design two-dimensional infrared spectroscopy experiments that can corroborate the existence of the selectivity filter configuration with flipped Val carbonyls. This ability to distinguish between flipped and unflipped carbonyls is based on the varying strength of the electric field inside and outside the pore, which is directly linked to carbonyl stretching frequencies that can be resolved using infrared spectroscopy.

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.

Computational study of ion permeation through claudin-4 paracellular channels

Claudins (Cldns) form a large family of protein homologs that are essential for the assembly of paracellular tight junctions (TJs), where they form channels or barriers with tissue-specific selectivity for permeants. In contrast to several family members whose physiological role has been identified, the function of claudin 4 (Cldn4) remains elusive, despite experimental evidence suggesting that it can form anion-selective TJ channels in the renal epithelium. Computational approaches have recently been employed to elucidate the molecular basis of Cldns' function, and hence could help in clarifying the role of Cldn4. In this work, we use structural modeling and all-atom molecular dynamics simulations to transfer two previously introduced structural models of Cldn-based paracellular complexes to Cldn4 to reproduce a paracellular anion channel. Free energy calculations for ionic transport through the pores allow us to establish the thermodynamic properties driving the ion-selectivity of the structures. While one model shows a cavity permeable to chloride and repulsive to cations, the other forms barrier to the passage of all the major physiological ions. Furthermore, our results confirm the charge selectivity role of the residue Lys65 in the first extracellular loop of the protein, rationalizing Cldn4 control of paracellular permeability.

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.

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.

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.

Comparison of K+ Channel Families

K⁺ channels enable potassium to flow across the membrane with great selectivity. There are four K⁺ channel families: voltage-gated K (K_v), calcium-activated (K_Ca), inwardly rectifying K (K_ir), and two-pore domain potassium (K_2P) channels. All four K⁺ channels are formed by subunits assembling into a classic tetrameric (4x1P = 4P for the K_v, K_Ca, and K_ir channels) or tetramer-like (2x2P = 4P for the K_2P channels) architecture. These subunits can either be the same (homomers) or different (heteromers), conferring great diversity to these channels. They share a highly conserved selectivity filter within the pore but show different gating mechanisms adapted for their function. K⁺ channels play essential roles in controlling neuronal excitability by shaping action potentials, influencing the resting membrane potential, and responding to diverse physicochemical stimuli, such as a voltage change (K_v), intracellular calcium oscillations (K_Ca), cellular mediators (K_ir), or temperature (K_2P).

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.

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.

Conduction through a narrow inward-rectifier K+ channel pore

G-protein–gated inwardly rectifying potassium channels are important mediators of inhibitory neurotransmission. Based on microsecond-scale molecular dynamics simulations, Bernsteiner et al. propose novel gating details that may enable K⁺ flux via a direct knock-on mechanism.

Inwardly rectifying potassium (Kir) channels play a key role in controlling membrane potentials in excitable and unexcitable cells, thereby regulating a plethora of physiological processes. G-protein–gated Kir channels control heart rate and neuronal excitability via small hyperpolarizing outward K⁺ currents near the resting membrane potential. Despite recent breakthroughs in x-ray crystallography and cryo-EM, the gating and conduction mechanisms of these channels are poorly understood. MD simulations have provided unprecedented details concerning the gating and conduction mechanisms of voltage-gated K⁺ and Na⁺ channels. Here, we use multi-microsecond–timescale MD simulations based on the crystal structures of GIRK2 (Kir3.2) bound to phosphatidylinositol-4,5-bisphosphate to provide detailed insights into the channel’s gating dynamics, including insights into the behavior of the G-loop gate. The simulations also elucidate the elementary steps that underlie the movement of K⁺ ions through an inward-rectifier K⁺ channel under an applied electric field. Our simulations suggest that K⁺ permeation might occur via direct knock-on, similar to the mechanism recently shown for K_v channels.

Lipid molecules can induce an opening of membrane-facing tunnels in cytochrome P450 1A2

Cytochrome P450 1A2 (P450 1A2, CYP1A2) is a membrane-bound enzyme that oxidizes a broad range of hydrophobic substrates. The structure and dynamics of both the catalytic and trans-membrane (TM) domains of this enzyme in the membrane/water environment were investigated using a multiscale computational approach, including coarse-grained and all-atom molecular dynamics. Starting from the spontaneous self-assembly of the system containing the TM or soluble domain immersed in randomized dilauroyl phosphatidylcholine (DLPC)/water mixture into their respective membrane-bound forms, we reconstituted the membrane-bound structure of the full-length P450 1A2. This structure includes a TM helix that spans the membrane, while being connected to the catalytic domain by a short flexible loop. Furthermore, in this model, the upper part of the TM helix interacts directly with a conserved and highly hydrophobic N-terminal proline-rich segment of the catalytic domain; this segment and the FG loop are immersed in the membrane, whereas the remaining portion of the catalytic domain remains exposed to aqueous solution. The shallow membrane immersion of the catalytic domain induces a depression in the opposite intact layer of the phospholipids. This structural effect may help in stabilizing the position of the TM helix directly beneath the catalytic domain. The partial immersion of the catalytic domain also allows for the enzyme substrates to enter the active site from either aqueous solution or phospholipid environment via several solvent- and membrane-facing tunnels in the full-length P450 1A2. The calculated tunnel dynamics indicated that the opening probability of the membrane-facing tunnels is significantly enhanced when a DLPC molecule spontaneously penetrates into the membrane-facing tunnel 2d. The energetics of the lipid penetration process were assessed by the linear interaction energy (LIE) approximation, and found to be thermodynamically feasible.

Validity of the Electrodiffusion Model for Calculating Conductance of Simple Ion Channels

We examine the validity and utility of the electrodiffusion (ED) equation, i.e., the generalized Nernst-Planck equation, to characterize, in combination with molecular dynamics, the electrophysiological behavior of simple ion channels. As models, we consider three systems-two naturally occurring channels formed by α-helical bundles of peptaibols, trichotoxin, and alamethicin, and a synthetic, hexameric channel, formed by a peptide that contains only leucine and serine. All these channels mediate transport of potassium and chloride ions. Starting with equilibrium properties, such as the potential of mean force experienced by an ion traversing the channel and diffusivity, obtained from molecular dynamics simulations, the ED equation can be used to determine the full current-voltage dependence with modest or no additional effort. The potential of mean force can be obtained not only from equilibrium simulations, but also, with comparable accuracy, from nonequilibrium simulations at a single voltage. The main assumptions underlying the ED equation appear to hold well for the channels and voltages studied here. To expand the utility of the ED equation, we examine what are the necessary and sufficient conditions for Ohmic and nonrectifying behavior and relate deviations from this behavior to the shape of the ionic potential of mean force.

IBiSA_Tools: A Computational Toolkit for Ion-Binding State Analysis in Molecular Dynamics Trajectories of Ion Channels

Ion conduction mechanisms of ion channels are a long-standing conundrum. Although the molecular dynamics (MD) method has been extensively used to simulate ion conduction dynamics at the atomic level, analysis and interpretation of MD results are not straightforward due to complexity of the dynamics. In our previous reports, we proposed an analytical method called ion-binding state analysis to scrutinize and summarize ion conduction mechanisms by taking advantage of a variety of analytical protocols, e.g., the complex network analysis, sequence alignment, and hierarchical clustering. This approach effectively revealed the ion conduction mechanisms and their dependence on the conditions, i.e., ion concentration and membrane voltage. Here, we present an easy-to-use computational toolkit for ion-binding state analysis, called IBiSA_tools. This toolkit consists of a C++ program and a series of Python and R scripts. From the trajectory file of MD simulations and a structure file, users can generate several images and statistics of ion conduction processes. A complex network named ion-binding state graph is generated in a standard graph format (graph modeling language; GML), which can be visualized by standard network analyzers such as Cytoscape. As a tutorial, a trajectory of a 50 ns MD simulation of the Kv1.2 channel is also distributed with the toolkit. Users can trace the entire process of ion-binding state analysis step by step. The novel method for analysis of ion conduction mechanisms of ion channels can be easily used by means of IBiSA_tools. This software is distributed under an open source license at the following URL: http://www.ritsumei.ac.jp/~ktkshr/ibisa_tools/

Multi scale modeling of 2450MHz electric field effects on microtubule mechanical properties

Microtubule (MT) rigidity and response to 2450MHz electric fields were investigated, via multi scale modeling approach. For this purpose, six systems were designed and simulated to consider all types of feasible interactions between α and β monomers in MT, by using all atom molecular dynamics method. Subsequently, coarse grain modeling was used to design different lengths of MT. Investigation of effects of external 2450MHz electric field on MT showed MT less rigidity in the presence of such field, which may perturb its functions. Moreover, an additional computational setup was designed to study effects of 2450MHz field on MT response to AFM tip. It was found, more tip velocity led to MT faster transformation and less time was required to change MT elastic response to plastic one, applying constant radius. Moreover it was observed smaller tip caused to increase required time to change MT elastic response to plastic one, considering constant velocity. Furthermore, exposing MT to 2450MHz field led to no significant changes in MT response to AFM tip, but quick change in MT elastic response to plastic one.

Bias-Exchange Metadynamics Simulations: An Efficient Strategy for the Analysis of Conduction and Selectivity in Ion Channels

Conduction through ion channels possesses two interesting features: (i) different ionic species are selected with high-selectivity and (ii) ions travel across the channel with rates approaching free-diffusion. Molecular dynamics simulations have the potential to reveal how these processes take place at the atomic level. However, analysis of conduction and selectivity at atomistic detail is still hampered by the short time scales accessible by computer simulations. Several algorithms have been developed to "accelerate" sampling along the slow degrees of freedom of the process under study and thus to probe longer time scales. In these algorithms, the slow degrees of freedom need to be defined in advance, which is a well-known shortcoming. In the particular case of ion conduction, preliminary assumptions about the number and type of ions participating in the permeation process need to be made. In this study, a novel approach for the analysis of conduction and selectivity based on bias-exchange metadynamics simulations was tested. This approach was compared with umbrella sampling simulations, using a model of a Na(+)-selective channel. Analogous conclusions resulted from both techniques, but the computational cost of bias-exchange simulations was lower. In addition, with bias-exchange metadynamics it was possible to calculate free energy profiles in the presence of a variable number and type of permeating ions. This approach might facilitate the definition of the set of collective variables required to analyze conduction and selectivity in ion channels.

Functional and Modeling Studies of the Transmembrane Region of the TRPM8 Channel

Members of the transient receptor potential (TRP) ion channel family act as polymodal cellular sensors, which aid in regulating Ca(2+) homeostasis. Within the TRP family, TRPM8 is the cold receptor that forms a nonselective homotetrameric cation channel. In the absence of TRPM8 crystal structure, little is known about the relationship between structure and function. Inferences of TRPM8 structure have come from mutagenesis experiments coupled to electrophysiology, mainly regarding the fourth transmembrane helix (S4), which constitutes a moderate voltage-sensing domain, and about cold sensor and phosphatidylinositol 4,5-bisphosphate binding sites, which are both located in the C-terminus of TRPM8. In this study, we use a combination of molecular modeling and experimental techniques to examine the structure of the TRPM8 transmembrane and pore helix region including the conducting conformation of the selectivity filter. The model is consistent with a large amount of functional data and was further tested by mutagenesis. We present structural insight into the role of residues involved in intra- and intersubunit interactions and their link with the channel activity, sensitivity to icilin, menthol and cold, and impact on channel oligomerization.

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.

The effects of external electric fields of 900 MHz and 2450 MHz frequencies onαβ-tubulin dimer stabilized by paclitaxel: Molecular dynamics approach

Using molecular dynamics simulation method, the effects of external electric fields of 900[Formula: see text]MHz and 2450 frequencies on [Formula: see text]-tubulin dimer stabilized by paclitaxel, have been modeled. Due to this purpose, two systems, (A) [Formula: see text]-tubulin dimer and (B) [Formula: see text]-tubulin dimer stabilized by paclitaxel, were exposed to an external electric field of 0.01[Formula: see text]V/nm with frequency values of 900[Formula: see text]MHz and 2450[Formula: see text]MHz. It was found that application of these fields, which are in the range of cell phone and microwave frequencies, increased the flexibility of each system. Since paclitaxel, as chemotherapy drug, is used to increase the rigidity of dimer, application of such fields may disturb the effect of paclitaxel on the dimer. Consequently, negative side effects on the chemotherapy process may be observed.

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.

Computational studies of transport in ion channels using metadynamics

Molecular dynamics simulations have played a fundamental role in numerous fields of science by providing insights into the structure and dynamics of complex systems at the atomistic level. However, exhaustive sampling by standard molecular dynamics is in most cases computationally prohibitive, and the time scales accessible remain significantly shorter than many biological processes of interest. In particular, in the study of ion channels, realistic models to describe permeation and gating require accounting for large numbers of particles and accurate interaction potentials, which severely limits the length of the simulations. To overcome such limitations, several advanced methods have been proposed among which is metadynamics. In this algorithm, an external bias potential to accelerate sampling along selected collective variables is introduced. This bias potential discourages visiting regions of the configurational space already explored. In addition, the bias potential provides an estimate of the free energy as a function of the collective variables chosen once the simulation has converged. In this review, recent contributions of metadynamics to the field of ion channels are discussed, including how metadynamics has been used to search for transition states, predict permeation pathways, treat conformational flexibility that underlies the coupling between gating and permeation, or compute free energy of permeation profiles. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

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.

Water molecules response to an external GHz electric field in KcsA potassium channel: A molecular modeling approach

KcsA potassium channel is a membrane protein that allows the passage of potassium ions and water molecules across the cellular membrane. Using molecular dynamics (MD) simulation method, the effect of an applied GHz oscillating electric field of strength 0.004 V/nm on the dynamics of K + and water molecules in a KcsA channel was modeled. It was found that the application of GHz range electric field caused a change in the potential energy profile of the water molecules in the filter sites, causing an increase in the delay time of the water molecules in these sites. Therefore, exposing the channel to the GHz fields can perturb the dynamics of the water molecules in the filter, and consequently, the channel operation may be disturbed. Furthermore, the results show that the applied field has no major effects on the dipole orientation of water molecules in the channel.

Influence of GHz electric fields on the mechanical properties of a microtubule

The effects of external GHz electric fields on the mechanical properties of a microtubule (MT) have been modeled through the application of a molecular dynamics simulation method. To explore the properties of the MT, two different systems each consisting of a pair of dimers were exposed to an 0.03 V/nm electric field with a frequency ranging between 1 to 10 GHz. It was found that the Young's modulus of each system, which is related to the flexibility of the MT, was lower at some frequencies and higher at others in comparison with normal biological conditions. Hence, the application of such an electric field with a frequency in this range may affect MT function, which could have positive or negative effects on cell health. Positive effects include its potential use in cancer treatment, where the application of such a field could lead to a decrease in MT rigidity, similar to the effect of Taxol on MTs. Negative effects include unwanted changes to the mechanical properties of MTs (e.g., disturbing the cell division process and in turn increasing the risk of cancer) upon the application of such a field.

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.

Electric Field Effect on Phospholipid Monolayers at an Aqueous-Organic Liquid-Liquid Interface

The electric potential difference across cell membranes, known as the membrane potential, plays an important role in the activation of many biological processes. To investigate the effect of the membrane potential on the molecular ordering of lipids within a biomimetic membrane, a self-assembled monolayer of 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (SOPC) lipids at an electrified 1,2-dichloroethane/water interface is studied with X-ray reflectivity and interfacial tension. Measurements over a range of electric potential differences, -150 to +130 mV, that encompass the range of typical biomembrane potentials demonstrate a nearly constant and stable structure whose lipid interfacial density is comparable to that found in other biomimetic membrane systems. Measurements at higher positive potentials, up to 330 mV, illustrate a monotonic decrease in the lipid interfacial density and accompanying variations in the interfacial configuration of the lipid. Molecular dynamics simulations, designed to mimic the experimental conditions, show that the measured changes in lipid configuration are due primarily to the variation in area per lipid with increasing applied electric field. Rotation of the SOPC dipole moment by the torque from the applied electric field appears to be negligible, except at the highest measured potentials. The simulations confirm in atomistic detail the measured potential-dependent characteristics of SOPC monolayers. Our hybrid study sheds light on phospholipid monolayer stability under different membrane potentials, which is important for understanding membrane processes. This study also illustrates the use of X-ray surface scattering to probe the ordering of surfactant monolayers at an electrified aqueous-organic liquid-liquid interface.

External electric field effects on the mechanical properties of the αβ-tubulin dimer of microtubules: a molecular dynamics study

The mechanical properties of the αβ-tubulin dimer of microtubules was modeled by using the molecular dynamics (MD) simulation method. The effect on the mechanical properties of the dimer of the existence and nonexistence of an applied electric field, either constant or periodic, was studied. Since there are charged or polar groups in the dimer structure, the electric field can interact with the dimer. The elastic constant and Young's modulus of the dimer were decreased when the dimer was exposed to a constant electric field of 0.03 V/nm. Furthermore, applying an oscillating electric field in the 1 GHz range to the dimer increased the elastic constant and Young's modulus of the dimer. These parameters were related to dimer rigidity and, consequently, in this frequency range, the application of electric fields may affect the function of microtubules.

Molecular dynamics simulations of membrane proteins under asymmetric ionic concentrations

A computational method is developed to allow molecular dynamics simulations of biomembrane systems under realistic ionic gradients and asymmetric salt concentrations while maintaining the conventional periodic boundary conditions required to minimize finite-size effects in an all-atom explicit solvent representation. The method, which consists of introducing a nonperiodic energy step acting on the ionic species at the edge of the simulation cell, is first tested with illustrative applications to a simple membrane slab model and a phospholipid membrane bilayer. The nonperiodic energy-step method is then used to calculate the reversal potential of the bacterial porin OmpF, a large cation-specific β-barrel channel, by simulating the I-V curve under an asymmetric 10:1 KCl concentration gradient. The calculated reversal potential of 28.6 mV is found to be in excellent agreement with the values of 26–27 mV measured from lipid bilayer experiments, thereby demonstrating that the method allows realistic simulations of nonequilibrium membrane transport with quantitative accuracy. As a final example, the pore domain of Kv1.2, a highly selective voltage-activated K⁺ channel, is simulated in a lipid bilayer under conditions that recreate, for the first time, the physiological K⁺ and Na⁺ concentration gradients and the electrostatic potential difference of living cells.

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.

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.

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.

Collective diffusion model for ion conduction through microscopic channels

Ion conduction through microscopic channels is of central importance in both biology and nanotechnology. To better understand the current-voltage (I-V) dependence of ion channels, here we describe and prove a collective diffusion model that quantitatively relates the spontaneous ion permeation at equilibrium to the stationary ionic fluxes driven by small voltages. The model makes it possible to determine the channel conductance in the linear I-V range from equilibrium simulations without the application of a voltage. To validate the theory, we perform molecular-dynamics simulations on two channels-a conical-shaped nanopore and the transmembrane pore of an α-hemolysin-under both equilibrium and nonequilibrium conditions. The simulations reveal substantial couplings between the motions of cations and anions, which are effectively captured by the collective coordinate in the model. Although the two channels exhibit very different linear ranges in the I-V curves, in both cases the channel conductance at small voltages is in reasonable agreement with the prediction from the equilibrium simulation. The simulations also suggest that channel charges, rather than geometric asymmetry, play a more prominent role in current rectification.

Ion concentration-dependent ion conduction mechanism of a voltage-sensitive potassium channel

Voltage-sensitive potassium ion channels are essential for life, but the molecular basis of their ion conduction is not well understood. In particular, the impact of ion concentration on ion conduction has not been fully studied. We performed several micro-second molecular dynamics simulations of the pore domain of the Kv1.2 potassium channel in KCl solution at four different ion concentrations, and scrutinized each of the conduction events, based on graphical representations of the simulation trajectories. As a result, we observed that the conduction mechanism switched with different ion concentrations: at high ion concentrations, potassium conduction occurred by Hodgkin and Keynes' knock-on mechanism, where the association of an incoming ion with the channel is tightly coupled with the dissociation of an outgoing ion, in a one-step manner. On the other hand, at low ion concentrations, ions mainly permeated by a two-step association/dissociation mechanism, in which the association and dissociation of ions were not coupled, and occurred in two distinct steps. We also found that this switch was triggered by the facilitated association of an ion from the intracellular side within the channel pore and by the delayed dissociation of the outermost ion, as the ion concentration increased.

Multiscale molecular dynamics simulations of membrane proteins

The time and length scales accessible by biomolecular simulations continue to increase. This is in part due to improvements in algorithms and computing performance, but is also the result of the emergence of coarse-grained (CG) potentials, which complement and extend the information obtainable from fully detailed models. CG methods have already proven successful for a range of applications that benefit from the ability to rapidly simulate spontaneous self-assembly within a lipid membrane environment, including the insertion and/or oligomerization of a range of "toy models," transmembrane peptides, and single- and multi-domain proteins. While these simplified approaches sacrifice atomistic level detail, it is now straightforward to "reverse map" from CG to atomistic descriptions, providing a strategy to assemble membrane proteins within a lipid environment, prior to all-atom simulation. Moreover, recent developments have been made in "dual resolution" techniques, allowing different molecules in the system to be modeled with atomistic or CG resolution simultaneously.

Nonselective conduction in a mutated NaK channel with three cation-binding sites

The NaK channel is a cation-selective protein with similar permeability for K(+) and Na(+) ions. Crystallographic structures are available for the wild-type and mutated NaK channels with different numbers of cation-binding sites. We have performed a comparison between the potentials of mean force governing the translocation of K(+) ions and mixtures of one Na(+) and three K(+) ions in a mutated NaK channel with only three cation-binding sites (NaK-CNG). Since NaK-CNG is not selective for K(+) over Na(+), analysis of its multi-ion potential energy surfaces can provide clues about how selectivity originates. Comparison of the potentials of mean force of NaK-CNG and K(+)-selective channels yields observations that strongly suggest that the number of contiguous ion binding sites in a single-file mechanism is the key determinant of the channel's selectivity properties, as already proposed by experimental studies. We conclude that the presence of four binding sites in K(+)-selective channels is essential for highly selective and efficient permeation of K(+) ions, and that a key difference between K(+)-selective and nonselective channels is the absence/presence of a binding site for Na(+) ions at the boundary between S2 and S3 in the context of multi-ion permeation events.

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 investigation of the ω-current in the Kv1.2 voltage sensor domains

Voltage sensor domains (VSD) are transmembrane proteins that respond to changes in membrane voltage and modulate the activity of ion channels, enzymes, or in the case of proton channels allow permeation of protons across the cell membrane. VSDs consist of four transmembrane segments, S1-S4, forming an antiparallel helical bundle. The S4 segment contains several positively charged residues, mainly arginines, located at every third position along the helix. In the voltage-gated Shaker K(+) channel, the mutation of the first arginine of S4 to a smaller uncharged amino acid allows permeation of cations through the VSD. These currents, known as ω-currents, pass through the VSD and are distinct from K(+) currents passing through the main ion conduction pore. Here we report molecular dynamics simulations of the ω-current in the resting-state conformation for Kv1.2 and for four of its mutants. The four tested mutants exhibit various degrees of conductivity for K(+) and Cl(-) ions, with a slight selectivity for K(+) over Cl(-). Analysis of the ion permeation pathway, in the case of a highly conductive mutant, reveals a negatively charged constriction region near the center of the membrane that might act as a selectivity filter to prevent permeation of anions through the pore. The residues R1 in S4 and E1 in S2 are located at the narrowest region of the ω-pore for the resting state conformation of the VSD, in agreement with experiments showing that the largest increase in current is produced by the double mutation E1D and R1S.

Permeation and block of the Kv1.2 channel examined using brownian and molecular dynamics

Using both Brownian and molecular dynamics, we replicate many of the salient features of Kv1.2, including the current-voltage-concentration profiles and the binding affinity and binding mechanisms of charybdotoxin, a scorpion venom. We also elucidate how structural differences in the inner vestibule can give rise to significant differences in its permeation characteristics. Current-voltage-concentration profiles are constructed using Brownian dynamics simulations, based on the crystal structure 2A79. The results are compatible with experimental data, showing similar conductance, rectification, and saturation with current. Unlike KcsA, for example, the inner pore of Kv1.2 is mainly hydrophobic and neutral, and to explore the consequences of this, we investigate the effect of mutating neutral proline residues at the mouth of the inner vestibule to charged aspartate residues. We find an increased conductance, less inward rectification, and quicker saturation of the current-voltage profile. Our simulations use modifications to our Brownian dynamics program that extend the range of channels that can be usefully modeled. Using molecular dynamics, we investigate the binding of the charybdotoxin scorpion venom to the outer vestibule of the channel. A potential of mean force is derived using umbrella sampling, giving a dissociation constant within a factor of ∼2 to experimentally derived constants. The residues involved in the toxin binding are in agreement with experimental mutagenesis studies. We thus show that the experimental observations on the voltage-gated channel, including the toxin-channel interaction, can reliably be replicated by using the two widely used computational tools.