Calculation of the gating charge for the Kv1.2 voltage-activated potassium channel

A Deep Learning Approach to Uncover Voltage-Gated Ion Channels' Intermediate States

Owing to recent advancements in cryo-electron microscopy, voltage-gated ion channels have gained a greater comprehension of their structural characteristics. However, a significant enigma remains unsolved for a large majority of these channels: their gating mechanism. This mechanism, which encompasses the conformational changes between open and closed states, is pivotal to their proper functioning. Beyond the binary states of open and closed, an ensemble of intermediate states defines the transition path in-between. Due to the lack of experimental data, one might resort to molecular dynamics simulations as an alternative to decipher these states and the transitions between them. However, the high-energy barriers and the colossal time scales involved hinder access to the latter. We present here an application of deep learning as a reliable pipeline for a comprehensive exploration of voltage-gated ion channel conformational rearrangements during gating. We showcase the pipeline performance specifically on the Kv1.2 voltage sensor domain and confront the results with existing data. We demonstrate how our physics-based deep learning approach contributes to the theoretical understanding of these channels and how it might provide further insights into the exploration of channelopathies.

Nernst Equilibrium, Rectification, and Saturation: Insights into Ion Channel Behavior

The dissipation of electrochemical gradients through ion channels plays a central role in biology. Herein we use voltage responsive kinetic models of ion channels to explore how electrical and chemical potentials differentially influence ion transport properties. These models demonstrate how electrically driven flux is greater than the Nernstian equivalent chemically driven flux, yet still perfectly cancels when the two gradients oppose each other. We find that the location and relative stability of ion binding sites dictates rectification properties by shifting the location of the most voltage sensitive transitions. However, these rectification properties invert when bulk concentrations increase relative to the binding site stabilities, moving the rate limiting steps from uptake into a relatively empty channel to release from an ion-blocked full channel. Additionally, the origin of channel saturation is shown to depend on the free energy of uptake relative to bulk concentrations. Collectively these insights provide framework for interpreting and predicting how channel properties manifest in electrochemical transport behavior.

In Silico Methods for the Discovery of Kv7.2/7.3 Channels Modulators: A Comprehensive Review

The growing interest in Kv7.2/7.3 agonists originates from the involvement of these channels in several brain hyperexcitability disorders. In particular, Kv7.2/7.3 mutants have been clearly associated with epileptic encephalopathies (DEEs) as well as with a spectrum of focal epilepsy disorders, often associated with developmental plateauing or regression. Nevertheless, there is a lack of available therapeutic options, considering that retigabine, the only molecule used in clinic as a broad-spectrum Kv7 agonist, has been withdrawn from the market in late 2016. This is why several efforts have been made both by both academia and industry in the search for suitable chemotypes acting as Kv7.2/7.3 agonists. In this context, in silico methods have played a major role, since the precise structures of different Kv7 homotetramers have been only recently disclosed. In the present review, the computational methods used for the design of Kv.7.2/7.3 small molecule agonists and the underlying medicinal chemistry are discussed in the context of their biological and structure-function properties.

Dynamics of activation in the voltage-sensing domain of Ciona intestinalis phosphatase Ci-VSP

The Ciona intestinalis voltage-sensing phosphatase (Ci-VSP) is a membrane protein containing a voltage-sensing domain (VSD) that is homologous to VSDs from voltage-gated ion channels responsible for cellular excitability. Previously published crystal structures of Ci-VSD in putative resting and active conformations suggested a helical-screw voltage sensing mechanism in which the S4 helix translocates and rotates to enable exchange of salt-bridge partners, but the microscopic details of the transition between the resting and active conformations remained unknown. Here, by combining extensive molecular dynamics simulations with a recently developed computational framework based on dynamical operators, we elucidate the microscopic mechanism of the resting-active transition at physiological membrane potential. Sparse regression reveals a small set of coordinates that distinguish intermediates that are hidden from electrophysiological measurements. The intermediates arise from a noncanonical helical-screw mechanism in which translocation, rotation, and side-chain movement of the S4 helix are only loosely coupled. These results provide insights into existing experimental and computational findings on voltage sensing and suggest ways of further probing its mechanism.

Anionic omega currents from single countercharge mutants in the voltage-sensing domain of Ci-VSP

The S4 segment of voltage-sensing domains (VSDs) directly responds to voltage changes by reorienting within the electric field as a permion. A narrow hydrophobic "gasket" or charge transfer center at the core of most VSDs focuses the electric field into a narrow region and catalyzes the sequential and reversible translocation of S4 positive gating charge residues across the electric field while preventing the permeation of physiological ions. Mutating specific S4 gating charges can cause ionic leak currents through the VSDs. These gating pores or omega currents play important pathophysiological roles in many diseases of excitability. Here, we show that mutating D129, a key countercharge residue in the Ciona intestinalis voltage-sensing phosphatase (Ci-VSP), leads to the generation of unique anionic omega currents. Neutralizing D129 causes a dramatic positive shift of activation, facilitates the formation of a continuous water path through the VSD, and creates a positive electrostatic potential landscape inside the VSD that contributes to its unique anionic selectivity. Increasing the population or dwell time of the conducting state by a high external pH or an engineered Cd2+ bridge markedly increases the current magnitude. Our findings uncover a new role of countercharge residues in the impermeable VSD of Ci-VSP and offer insights into mechanisms of the conduction of anionic omega currents linked to countercharge residue mutations.

Domain- and state-specific shape of the electric field tunes voltage sensing in voltage-gated sodium channels

The ability to sense transmembrane voltage underlies most physiological roles of voltage-gated sodium (Nav) channels. Whereas the key role of their voltage-sensing domains (VSDs) in channel activation is well established, the molecular underpinnings of voltage coupling remain incompletely understood. Voltage-dependent energetics of the activation process can be described in terms of the gating charge that is defined by coupling of charged residues to the external electric field. The shape of the electric field within VSDs is therefore crucial for the activation of voltage-gated ion channels. Here, we employed molecular dynamics simulations of cardiac Nav1.5 and bacterial NavAb, together with our recently developed tool g_elpot, to gain insights into the voltage-sensing mechanisms of Nav channels via high-resolution quantification of VSD electrostatics. In contrast to earlier low-resolution studies, we found that the electric field within VSDs of Nav channels has a complex isoform- and domain-specific shape, which prominently depends on the activation state of a VSD. Different VSDs vary not only in the length of the region where the electric field is focused but also differ in their overall electrostatics, with possible implications in the diverse ion selectivity of their gating pores. Due to state-dependent field reshaping, not only translocated basic but also relatively immobile acidic residues contribute significantly to the gating charge. In the case of NavAb, we found that the transition between structurally resolved activated and resting states results in a gating charge of 8e, which is noticeably lower than experimental estimates. Based on the analysis of VSD electrostatics in the two activation states, we propose that the VSD likely adopts a deeper resting state upon hyperpolarization. In conclusion, our results provide an atomic-level description of the gating charge, demonstrate diversity in VSD electrostatics, and reveal the importance of electric-field reshaping for voltage sensing in Nav channels.

The voltage-sensing domain of a hERG1 mutant is a cation-selective channel

A cationic leak current known as an "omega current" may arise from mutations of the first charged residue in the S4 of the voltage sensor domains of sodium and potassium voltage-gated channels. The voltage-sensing domains (VSDs) in these mutated channels act as pores allowing nonspecific passage of cations, such as Li+, K+, Cs+, and guanidinium. Interestingly, no omega currents have been previously detected in the nonswapped voltage-gated potassium channels such as the human-ether-a-go-go-related (hERG1), hyperpolarization-activated cyclic nucleotide-gated, and ether-a-go-go channels. In this work, we discovered a novel omega current by mutating the first charged residue of the S4 of the hERG1, K525 to serine. To characterize this omega current, we used various probes, including the hERG1 pore domain blocker, dofetilide, to show that the omega current does not require cation flux via the canonical pore domain. In addition, the omega flux does not cross the conventional selectivity filter. We also show that the mutated channel (K525S hERG1) conducts guanidinium. These data are indicative of the formation of an omega current channel within the VSD. Using molecular dynamics simulations with replica-exchange umbrella sampling simulations of the wild-type hERG1 and the K525S hERG1, we explored the molecular underpinnings governing the cation flow in the VSD of the mutant. We also show that the wild-type hERG1 may form water crevices supported by the biophysical surface accessibility data. Overall, our multidisciplinary study demonstrates that the VSD of hERG1 may act as a cation-selective channel wherein a mutation of the first charged residue in the S4 generates an omega current. Our simulation uncovers the atomistic underpinning of this mechanism.

Mechanism of voltage gating in the voltage-sensing phosphatase Ci-VSP

Conformational changes in voltage-sensing domains (VSDs) are driven by the transmembrane electric field acting on the protein charges. Yet, the overall energetics and detailed mechanism of this process are not fully understood. Here, we determined free energy and displacement charge landscapes as well as the major conformations visited during a complete functional gating cycle in the isolated VSD of the phosphatase Ci-VSP (Ci-VSD) comprising four transmembrane helices (segments S1 to S4). Molecular dynamics simulations highlight the extent of S4 movements. In addition to the crystallographically determined activated “Up” and resting “Down” states, the simulations predict two Ci-VSD conformations: a deeper resting state (“down-minus”) and an extended activated (“up-plus”) state. These additional conformations were experimentally probed via systematic cysteine mutagenesis with metal-ion bridges and the engineering of proton conducting mutants at hyperpolarizing voltages. The present results show that these four states are visited sequentially in a stepwise manner during voltage activation, each step translocating one arginine or the equivalent of ∼1 e 0 across the membrane electric field, yielding a transfer of ∼3 e 0 charges in total for the complete process.

The 70-year search for the voltage sensing mechanism of ion channels

This retrospective on the voltage‐sensing mechanisms and gating models of ion channels begins in 1952 with the charged gating particles postulated by Hodgkin and Huxley, viewed as charges moving across the membrane and controlling its permeability to Na⁺ and K⁺ ions. Hodgkin and Huxley postulated that their movement should generate small and fast capacitive currents, which were recorded 20 years later as gating currents. In the early 1980s, several voltage‐dependent channels were cloned and found to share a common architecture: four homologous domains or subunits, each displaying six transmembrane α‐helical segments, with the fourth segment (S4) displaying four to seven positive charges invariably separated by two non‐charged residues. This immediately suggested that this segment was serving as the voltage sensor of the channel (the molecular counterpart of the charged gating particle postulated by Hodgkin and Huxley) and led to the development of the sliding helix model. Twenty years later, the X‐ray crystallographic structures of many voltage‐dependent channels allowed investigation of their gating by molecular dynamics. Further understanding of how channels gate will benefit greatly from the acquisition of high‐resolution structures of each of their relevant functional or structural states. This will allow the application of molecular dynamics and other approaches. It will also be key to investigate the energetics of channel gating, permitting an understanding of the physical and molecular determinants of gating. The use of multiscale hierarchical approaches might finally prove to be a rewarding strategy to overcome the limits of the various single approaches to the study of channel gating.

Nanosecond Pulsed Electric Field (nsPEF): Opening the Biotechnological Pandora’s Box

Nanosecond Pulsed Electric Field (nsPEF) is an electrostimulation technique first developed in 1995; nsPEF requires the delivery of a series of pulses of high electric fields in the order of nanoseconds into biological tissues or cells. They primary effects in cells is the formation of membrane nanopores and the activation of ionic channels, leading to an incremental increase in cytoplasmic Ca2+ concentration, which triggers a signaling cascade producing a variety of effects: from apoptosis up to cell differentiation and proliferation. Further, nsPEF may affect organelles, making nsPEF a unique tool to manipulate and study cells. This technique is exploited in a broad spectrum of applications, such as: sterilization in the food industry, seed germination, anti-parasitic effects, wound healing, increased immune response, activation of neurons and myocites, cell proliferation, cellular phenotype manipulation, modulation of gene expression, and as a novel cancer treatment. This review thoroughly explores both nsPEF’s history and applications, with emphasis on the cellular effects from a biophysics perspective, highlighting the role of ionic channels as a mechanistic driver of the increase in cytoplasmic Ca2+ concentration.

Molecular Insights Into Binding and Activation of the Human KCNQ2 Channel by Retigabine

Voltage-gated potassium channels of the Kv7.x family are involved in a plethora of biological processes across many tissues in animals, and their misfunctioning could lead to several pathologies ranging from diseases caused by neuronal hyperexcitability, such as epilepsy, or traumatic injuries and painful diabetic neuropathy to autoimmune disorders. Among the members of this family, the Kv7.2 channel can form hetero-tetramers together with Kv7.3, forming the so-called M-channels, which are primary regulators of intrinsic electrical properties of neurons and of their responsiveness to synaptic inputs. Here, prompted by the similarity between the M-current and that in Kv7.2 alone, we perform a computational-based characterization of this channel in its different conformational states and in complex with the modulator retigabine. After validation of the structural models of the channel by comparison with experimental data, we investigate the effect of retigabine binding on the two extreme states of Kv7.2 (resting-closed and activated-open). Our results suggest that binding, so far structurally characterized only in the intermediate activated-closed state, is possible also in the other two functional states. Moreover, we show that some effects of this binding, such as increased flexibility of voltage sensing domains and propensity of the pore for open conformations, are virtually independent on the conformational state of the protein. Overall, our results provide new structural and dynamic insights into the functioning and the modulation of Kv7.2 and related channels.

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.

The conformational cycle of prestin underlies outer-hair cell electromotility

The voltage-dependent motor protein prestin (also known as SLC26A5) is responsible for the electromotive behaviour of outer-hair cells and underlies the cochlear amplifier1. Knockout or impairment of prestin causes severe hearing loss2-5. Despite the key role of prestin in hearing, the mechanism by which mammalian prestin senses voltage and transduces it into cellular-scale movements (electromotility) is poorly understood. Here we determined the structure of dolphin prestin in six distinct states using single-particle cryo-electron microscopy. Our structural and functional data suggest that prestin adopts a unique and complex set of states, tunable by the identity of bound anions (Cl- or SO42-). Salicylate, a drug that can cause reversible hearing loss, competes for the anion-binding site of prestin, and inhibits its function by immobilizing prestin in a new conformation. Our data suggest that the bound anion together with its coordinating charged residues and helical dipole act as a dynamic voltage sensor. An analysis of all of the anion-dependent conformations reveals how structural rearrangements in the voltage sensor are coupled to conformational transitions at the protein-membrane interface, suggesting a previously undescribed mechanism of area expansion. Visualization of the electromotility cycle of prestin distinguishes the protein from the closely related SLC26 anion transporters, highlighting the basis for evolutionary specialization of the mammalian cochlear amplifier at a high resolution.

A second S4 movement opens hyperpolarization-activated HCN channels

Rhythmic activity in pacemaker cells, as in the sino-atrial node in the heart, depends on the activation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels. As in depolarization-activated K⁺ channels, the fourth transmembrane segment S4 functions as the voltage sensor in hyperpolarization-activated HCN channels. But how the inward movement of S4 in HCN channels at hyperpolarized voltages couples to channel opening is not understood. Using voltage clamp fluorometry, we found here that S4 in HCN channels moves in two steps in response to hyperpolarizations and that the second S4 step correlates with gate opening. We found a mutation in sea urchin HCN channels that separate the two S4 steps in voltage dependence. The E356A mutation in S4 shifts the main S4 movement to positive voltages, but channel opening remains at negative voltages. In addition, E356A reveals a second S4 movement at negative voltages that correlates with gate opening. Cysteine accessibility and molecular models suggest that the second S4 movement opens up an intracellular crevice between S4 and S5 that would allow radial movement of the intracellular ends of S5 and S6 to open HCN channels.

Structural Mechanism of ω-Currents in a Mutated Kv7.2 Voltage Sensor Domain from Molecular Dynamics Simulations

Activation of voltage-gated ion channels is regulated by conformational changes of the voltage sensor domains (VSDs), four water- and ion-impermeable modules peripheral to the central, permeable pore domain. Anomalous currents, defined as ω-currents, have been recorded in response to mutations of residues on the VSD S4 helix and associated with ion fluxes through the VSDs. In humans, gene defects in the potassium channel Kv7.2 result in a broad range of epileptic disorders, from benign neonatal seizures to severe epileptic encephalopathies. Experimental evidence suggests that the R207Q mutation in S4, associated with peripheral nerve hyperexcitability, induces ω-currents at depolarized potentials, but the fine structural details are still elusive. In this work, we use atom-detailed molecular dynamics simulations and a refined model structure of the Kv7.2 VSD in the active conformation in a membrane/water environment to study the effect of R207Q and four additional mutations of proven clinical importance. Our results demonstrate that the R207Q mutant shows the most pronounced increase of hydration in the internal VSD cavity, a feature favoring the occurrence of ω-currents. Free energy and kinetics calculations of sodium permeation through the native and mutated VSD indicate as more favorable the formation of a cationic current in the latter. Overall, our simulations establish a mechanistic linkage between genetic variations and their physiological outcome, by providing a computational description that includes both thermodynamic and kinetic features of ion permeation associated with ω-currents.

Electromechanical coupling in the hyperpolarization-activated K+ channel KAT1

Voltage-gated potassium (K_v) channels orchestrate electrical signaling and control cell volume by gating in response to either membrane depolarization or hyperpolarization. Yet, while all voltage-sensing domains transduce transmembrane electric field changes by a common mechanism involving the outward or inward translocation of gating charges^1–3, the general determinants of channel gating polarity remain poorly understood⁴. Here, we suggest a molecular mechanism for electromechanical coupling and gating polarity in non-domain-swapped K_v channels based on the cryo-EM structure of KAT1, the hyperpolarization-activated K_v channel from Arabidopsis thaliana. KAT1 displays a depolarized voltage sensor, which interacts with a closed pore domain directly via two interfaces and indirectly via an intercalated phospholipid. Functional evaluation of KAT1 structure-guided mutants at the sensor-pore interfaces suggests a mechanism in which direct interaction between the sensor and C-linker hairpin in the adjacent pore subunit is the primary determinant of gating polarity. We suggest that a ~5–7 Å inward motion of the S4 sensor helix can underlie a direct-coupling mechanism, driving a conformational reorientation of the C-linker and ultimately opening the activation gate formed by the S6 intracellular bundle. This direct-coupling mechanism contrasts with allosteric mechanisms proposed for hyperpolarization-activated cyclic nucleotide-gated (HCN) channels⁵, and may represent an unexpected link between depolarization and hyperpolarization-activated channels.

Roles for Countercharge in the Voltage Sensor Domain of Ion Channels

Voltage-gated ion channels share a common structure typified by peripheral, voltage sensor domains. Their S4 segments respond to alteration in membrane potential with translocation coupled to ion permeation through a central pore domain. The mechanisms of gating in these channels have been intensely studied using pioneering methods such as measurement of charge displacement across a membrane, sequencing of genes coding for voltage-gated ion channels, and the development of all-atom molecular dynamics simulations using structural information from prokaryotic and eukaryotic channel proteins. One aspect of this work has been the description of the role of conserved negative countercharges in S1, S2, and S3 transmembrane segments to promote sequential salt-bridge formation with positively charged residues in S4 segments. These interactions facilitate S4 translocation through the lipid bilayer. In this review, we describe functional and computational work investigating the role of these countercharges in S4 translocation, voltage sensor domain hydration, and in diseases resulting from countercharge mutations.

Molecular Insights from Conformational Ensembles via Machine Learning

Biomolecular simulations are intrinsically high dimensional and generate noisy data sets of ever-increasing size. Extracting important features from the data is crucial for understanding the biophysical properties of molecular processes, but remains a big challenge. Machine learning (ML) provides powerful dimensionality reduction tools. However, such methods are often criticized as resembling black boxes with limited human-interpretable insight. We use methods from supervised and unsupervised ML to efficiently create interpretable maps of important features from molecular simulations. We benchmark the performance of several methods, including neural networks, random forests, and principal component analysis, using a toy model with properties reminiscent of macromolecular behavior. We then analyze three diverse biological processes: conformational changes within the soluble protein calmodulin, ligand binding to a G protein-coupled receptor, and activation of an ion channel voltage-sensor domain, unraveling features critical for signal transduction, ligand binding, and voltage sensing. This work demonstrates the usefulness of ML in understanding biomolecular states and demystifying complex simulations.

Voltage-dependent gating in K channels: experimental results and quantitative models

Voltage-dependent K channels open and close in response to voltage changes across the cell membrane. This voltage dependence was postulated to depend on the presence of charged particles moving through the membrane in response to voltage changes. Recording of gating currents originating from the movement of these particles fully confirmed this hypothesis, and gave substantial experimental clues useful for the detailed understanding of the process. In the absence of structural information, the voltage-dependent gating was initially investigated using discrete Markov models, an approach only capable of providing a kinetic and thermodynamic comprehension of the process. The elucidation of the crystal structure of the first voltage-dependent channel brought in a dramatic change of pace in the understanding of channel gating, and in modeling the underlying processes. It was now possible to construct quantitative models using molecular dynamics, where all the interactions of each individual atom with the surroundings were taken into account, and its motion predicted by Newton's laws. Unfortunately, this modeling is computationally very demanding, and in spite of the advances in simulation procedures and computer technology, it is still limited in its predictive ability. To overcome these limitations, several groups have developed more macroscopic voltage gating models. Their approaches understandably require a number of approximations, which must however be physically well justified. One of these models, based on the description of the voltage sensor as a Brownian particle, that we have recently developed, is able to simultaneously describe the behavior of a single voltage sensor and to predict the macroscopic gating current originating from a population of sensors. The basics of this model are here described, and a typical application using the Kv1.2/2.1 chimera channel structure is also presented.

Simulation of Gating Currents of the Shaker K Channel Using a Brownian Model of the Voltage Sensor

The physical mechanism underlying the voltage-dependent gating of K channels is usually addressed theoretically using molecular dynamics simulations. However, besides being computationally very expensive, this approach is presently unable to fully predict the behavior of fundamental variables of channel gating such as the macroscopic gating current, and hence, it is presently unable to validate the model. To fill this gap, here we propose a voltage-gating model that treats the S4 segment as a Brownian particle moving through a gating channel pore and adjacent internal and external vestibules. In our model, charges on the S4 segment are screened by charged residues localized on neighboring segments of the channel protein and by ions present in the vestibules, whose dynamics are assessed using a flux conservation equation. The electrostatic voltage spatial profile is consistently assessed by applying the Poisson equation to all the charges present in the system. The treatment of the S4 segment as a Brownian particle allows description of the dynamics of a single S4 segment using the Langevin stochastic differential equation or the behavior of a population of S4 segments-useful for assessing the macroscopic gating current-using the Fokker-Planck equation. The proposed model confirms the gating charge transfer hypothesis with the movement of the S4 segment among five different stable positions where the gating charges interact in succession with the negatively charged residues on the channel protein. This behavior produces macroscopic gating currents quite similar to those experimentally found.

Voltage-Dependent Profile Structures of a Kv-Channel via Time-Resolved Neutron Interferometry

Available experimental techniques cannot determine high-resolution three-dimensional structures of membrane proteins under a transmembrane voltage. Hence, the mechanism by which voltage-gated cation channels couple conformational changes within the four voltage sensor domains, in response to either depolarizing or polarizing transmembrane voltages, to opening or closing of the pore domain's ion channel remains unresolved. Single-membrane specimens, composed of a phospholipid bilayer containing a vectorially oriented voltage-gated K+ channel protein at high in-plane density tethered to the surface of an inorganic multilayer substrate, were developed to allow the application of transmembrane voltages in an electrochemical cell. Time-resolved neutron reflectivity experiments, enhanced by interferometry enabled by the multilayer substrate, were employed to provide directly the low-resolution profile structures of the membrane containing the vectorially oriented voltage-gated K+ channel for the activated, open and deactivated, closed states of the channel under depolarizing and hyperpolarizing transmembrane voltages applied cyclically. The profile structures of these single membranes were dominated by the voltage-gated K+ channel protein because of the high in-plane density. Importantly, the use of neutrons allowed the determination of the voltage-dependent changes in both the profile structure of the membrane and the distribution of water within the profile structure. These two key experimental results were then compared to those predicted by three computational modeling approaches for the activated, open and deactivated, closed states of three different voltage-gated K+ channels in hydrated phospholipid bilayer membrane environments. Of the three modeling approaches investigated, only one state-of-the-art molecular dynamics simulation that directly predicted the response of a voltage-gated K+ channel within a phospholipid bilayer membrane to applied transmembrane voltages by utilizing very long trajectories was found to be in agreement with the two key experimental results provided by the time-resolved neutron interferometry experiments.

Role of individual S4 segments in gating of Cav3.1 T-type calcium channel by voltage

Contributions of voltage sensing S4 segments in domains I – IV of Ca_V3.1 channel to channel activation were analyzed. Neutralization of the uppermost charge in individual S4 segments by exchange of arginine for cysteine was employed. Mutant channels with single exchange in domains I – IV, in two adjacent domains, and in all four domains were constructed and expressed in HEK 293 cells. Changes in maximal gating charge Q_max and the relation between Q_max and maximal conductance G_max were evaluated. Q_max was the most affected by single mutation in domain I and by double mutations in domains I + II and I + IV. The ratio G_max/Q_max proportional to opening probability of the channel was significantly decreased by the mutation in domain III and increased by mutations in domains I and II. In channels containing double mutations G_max/Q_max ratio increased significantly when the mutation in domain I was included. Mutations in domains II and III zeroed each other. Mutation in domain IV prevented the decrease caused by the mutation in domain III. Neither ion current nor gating current was observed when channels with quadruple mutations were expressed. Immunocytochemistry analysis did not reveal the presence of channel protein in the cell membrane. Likely, quadruple mutation results in a structural change that affects the channel’s trafficking mechanism. Altogether, S4 segments in domains I-IV of the Ca_V3.1 channel unequally contribute to channel gating by voltage. We suggest the most important role of the voltage sensor in the domain I and lesser roles of voltage sensors in domains II and III.

Challenges and advances in atomistic simulations of potassium and sodium ion channel gating and permeation

Ion channels are implicated in many essential physiological events such as electrical signal propagation and cellular communication. The advent of K⁺ and Na⁺ ion channel structure determination has facilitated numerous investigations of molecular determinants of their behaviour. At the same time, rapid development of computer hardware and molecular simulation methodologies has made computational studies of large biological molecules in all-atom representation tractable. The concurrent evolution of experimental structural biology with biomolecular computer modelling has yielded mechanistic details of fundamental processes unavailable through experiments alone, such as ion conduction and ion channel gating. This review is a short survey of the atomistic computational investigations of K⁺ and Na⁺ ion channels, focusing on KcsA and several voltage-gated channels from the K_V and Na_V families, which have garnered many successes and engendered several long-standing controversies regarding the nature of their structure-function relationship. We review the latest advancements and challenges facing the field of molecular modelling and simulation regarding the structural and energetic determinants of ion channel function and their agreement with experimental observations.

Continuum Gating Current Models Computed with Consistent Interactions

The action potential of nerve and muscle is produced by voltage-sensitive channels that include a specialized device to sense voltage. The voltage sensor depends on the movement of charges in the changing electric field as suggested by Hodgkin and Huxley. Gating currents of the voltage sensor are now known to depend on the movements of positively charged arginines through the hydrophobic plug of a voltage sensor domain. Transient movements of these permanently charged arginines, caused by the change of transmembrane potential V, further drag the S4 segment and induce opening/closing of the ion conduction pore by moving the S4-S5 linker. This moving permanent charge induces capacitive current flow everywhere. Everything interacts with everything else in the voltage sensor and protein, and so it must also happen in its mathematical model. A Poisson-Nernst-Planck (PNP)-steric model of arginines and a mechanical model for the S4 segment are combined using energy variational methods in which all densities and movements of charge satisfy conservation laws, which are expressed as partial differential equations in space and time. The model computes gating current flowing in the baths produced by arginines moving in the voltage sensor. The model also captures the capacitive pile up of ions in the vestibules that link the bulk solution to the hydrophobic plug. Our model reproduces the signature properties of gating current: 1) equality of ON and OFF charge Q in integrals of gating current, 2) saturating voltage dependence in the Q(charge)-voltage curve, and 3) many (but not all) details of the shape of gating current as a function of voltage. Our results agree qualitatively with experiments and can be improved by adding more details of the structure and its correlated movements. The proposed continuum model is a promising tool to explore the dynamics and mechanism of the voltage sensor.

Main-chain mutagenesis reveals intrahelical coupling in an ion channel voltage-sensor

Membrane proteins are universal signal decoders. The helical transmembrane segments of these proteins play central roles in sensory transduction, yet the mechanistic contributions of secondary structure remain unresolved. To investigate the role of main-chain hydrogen bonding on transmembrane function, we encoded amide-to-ester substitutions at sites throughout the S4 voltage-sensing segment of Shaker potassium channels, a region that undergoes rapid, voltage-driven movement during channel gating. Functional measurements of ester-harboring channels highlight a transitional region between α-helical and 3₁₀ segments where hydrogen bond removal is particularly disruptive to voltage-gating. Simulations of an active voltage sensor reveal that this region features a dynamic hydrogen bonding pattern and that its helical structure is reliant upon amide support. Overall, the data highlight the specialized role of main-chain chemistry in the mechanism of voltage-sensing; other catalytic transmembrane segments may enlist similar strategies in signal transduction mechanisms.

The helical transmembrane segments of membrane proteins play central roles in sensory transduction but the mechanistic basis for their function remains unresolved. Here the authors identify regions in the S4 voltage-sensing segment of Shaker potassium channels where local helical structure is reliant upon backbone amide support.

Phosphatidylinositol 4,5-bisphosphate (PIP2) regulates KCNQ3 K+ channels by interacting with four cytoplasmic channel domains

Phosphatidylinositol 4,5-bisphosphate (PIP₂) in the plasma membrane regulates the function of many ion channels, including M-type (potassium voltage-gated channel subfamily Q member (KCNQ), K_v7) K⁺ channels; however, the molecular mechanisms involved remain unclear. To this end, we here focused on the KCNQ3 subtype that has the highest apparent affinity for PIP₂ and performed extensive mutagenesis in regions suggested to be involved in PIP₂ interactions among the KCNQ family. Using perforated patch-clamp recordings of heterologously transfected tissue culture cells, total internal reflection fluorescence microscopy, and the zebrafish (Danio rerio) voltage-sensitive phosphatase to deplete PIP₂ as a probe, we found that PIP₂ regulates KCNQ3 channels through four different domains: 1) the A-B helix linker that we previously identified as important for both KCNQ2 and KCNQ3, 2) the junction between S6 and the A helix, 3) the S2-S3 linker, and 4) the S4-S5 linker. We also found that the apparent strength of PIP₂ interactions within any of these domains was not coupled to the voltage dependence of channel activation. Extensive homology modeling and docking simulations with the WT or mutant KCNQ3 channels and PIP₂ were consistent with the experimental data. Our results indicate that PIP₂ modulates KCNQ3 channel function by interacting synergistically with a minimum of four cytoplasmic domains.

Determining the molecular basis of voltage sensitivity in membrane proteins

The identification of voltage-sensing elements in membrane proteins is challenging due to the diversity of voltage-sensing mechanisms. Kasimova et al. present a computational approach to predict the elements involved in voltage sensing, which they validate using voltage-gated ion channels.

Voltage-sensitive membrane proteins are united by their ability to transform changes in membrane potential into mechanical work. They are responsible for a spectrum of physiological processes in living organisms, including electrical signaling and cell-cycle progression. Although the mechanism of voltage-sensing has been well characterized for some membrane proteins, including voltage-gated ion channels, even the location of the voltage-sensing elements remains unknown for others. Moreover, the detection of these elements by using experimental techniques is challenging because of the diversity of membrane proteins. Here, we provide a computational approach to predict voltage-sensing elements in any membrane protein, independent of its structure or function. It relies on an estimation of the propensity of a protein to respond to changes in membrane potential. We first show that this property correlates well with voltage sensitivity by applying our approach to a set of voltage-sensitive and voltage-insensitive membrane proteins. We further show that it correctly identifies authentic voltage-sensitive residues in the voltage-sensor domain of voltage-gated ion channels. Finally, we investigate six membrane proteins for which the voltage-sensing elements have not yet been characterized and identify residues and ions that might be involved in the response to voltage. The suggested approach is fast and simple and enables a characterization of voltage sensitivity that goes beyond mere identification of charges. We anticipate that its application before mutagenesis experiments will significantly reduce the number of potential voltage-sensitive elements to be tested.

Voltage and pH sensing by the voltage-gated proton channel, HV1

Voltage-gated proton channels are unique ion channels, membrane proteins that allow protons but no other ions to cross cell membranes. They are found in diverse species, from unicellular marine life to humans. In all cells, their function requires that they open and conduct current only under certain conditions, typically when the electrochemical gradient for protons is outwards. Consequently, these proteins behave like rectifiers, conducting protons out of cells. Their activity has electrical consequences and also changes the pH on both sides of the membrane. Here we summarize what is known about the way these proteins sense the membrane potential and the pH inside and outside the cell. Currently, it is hypothesized that membrane potential is sensed by permanently charged arginines (with very high pKa) within the protein, which results in parts of the protein moving to produce a conduction pathway. The mechanism of pH sensing appears to involve titratable side chains of particular amino acids. For this purpose their pKa needs to be within the operational pH range. We propose a 'counter-charge' model for pH sensing in which electrostatic interactions within the protein are selectively disrupted by protonation of internally or externally accessible groups.

Gating Pore Currents in Sodium Channels

Voltage-gated sodium channels belong to the superfamily of voltage-gated cation channels. Their structure is based on domains comprising a voltage sensor domain (S1-S4 segments) and a pore domain (S5-S6 segments). Mutations in positively charged residues of the S4 segments may allow protons or cations to pass directly through the gating pore constriction of the voltage sensor domain; these anomalous currents are referred to as gating pore or omega (ω) currents. In the skeletal muscle disorder hypokalemic periodic paralysis, and in arrhythmic dilated cardiomyopathy, inherited mutations of S4 arginine residues promote omega currents that have been shown to be a contributing factor in the pathogenesis of these sodium channel disorders. Characterization of gating pore currents in these channelopathies and with artificial mutations has been possible by measuring the voltage-dependence and selectivity of these leak currents. The basis of gating pore currents and the structural basis of S4 movement through the gating pore has also been studied extensively with molecular dynamics. These simulations have provided valuable insight into the nature of S4 translocation and the physical basis for the effects of mutations that promote permeation of protons or cations through the gating pore.

Conformational landscapes of membrane proteins delineated by enhanced sampling molecular dynamics simulations

The expansion of computational power, better parameterization of force fields, and the development of novel algorithms to enhance the sampling of the free energy landscapes of proteins have allowed molecular dynamics (MD) simulations to become an indispensable tool to understand the function of biomolecules. The temporal and spatial resolution of MD simulations allows for the study of a vast number of processes of interest. Here, we review the computational efforts to uncover the conformational free energy landscapes of a subset of membrane proteins: ion channels, transporters and G-protein coupled receptors. We focus on the various enhanced sampling techniques used to study these questions, how the conclusions come together to build a coherent picture, and the relationship between simulation outcomes and experimental observables.

Gating of Connexin Channels by transjunctional-voltage: Conformations and models of open and closed states

Voltage is an important physiologic regulator of channels formed by the connexin gene family. Connexins are unique among ion channels in that both plasma membrane inserted hemichannels (undocked hemichannels) and intercellular channels (aggregates of which form gap junctions) have important physiological roles. The hemichannel is the fundamental unit of gap junction voltage-gating. Each hemichannel displays two distinct voltage-gating mechanisms that are primarily sensitive to a voltage gradient formed along the length of the channel pore (the transjunctional voltage) rather than sensitivity to the absolute membrane potential (V_m or V_i-o). These transjunctional voltage dependent processes have been termed V_j- or fast-gating and loop- or slow-gating. Understanding the mechanism of voltage-gating, defined as the sequence of voltage-driven transitions that connect open and closed states, first and foremost requires atomic resolution models of the end states. Although ion channels formed by connexins were among the first to be characterized structurally by electron microscopy and x-ray diffraction in the early 1980's, subsequent progress has been slow. Much of the current understanding of the structure-function relations of connexin channels is based on two crystal structures of Cx26 gap junction channels. Refinement of crystal structure by all-atom molecular dynamics and incorporation of charge changing protein modifications has resulted in an atomic model of the open state that arguably corresponds to the physiologic open state. Obtaining validated atomic models of voltage-dependent closed states is more challenging, as there are currently no methods to solve protein structure while a stable voltage gradient is applied across the length of an oriented channel. It is widely believed that the best approach to solve the atomic structure of a voltage-gated closed ion channel is to apply different but complementary experimental and computational methods and to use the resulting information to derive a consensus atomic structure that is then subjected to rigorous validation. In this paper, we summarize our efforts to obtain and validate atomic models of the open and voltage-driven closed states of undocked connexin hemichannels. This article is part of a Special Issue entitled: Gap Junction Proteins edited by Jean Claude Herve.

Gating Charge Calculations by Computational Electrophysiology Simulations

Electrical cell signaling requires adjustment of ion channel, receptor, or transporter function in response to changes in membrane potential. For the majority of such membrane proteins, the molecular details of voltage sensing remain insufficiently understood. Here, we present a molecular dynamics simulation-based method to determine the underlying charge movement across the membrane-the gating charge-by measuring electrical capacitor properties of membrane-embedded proteins. We illustrate the approach by calculating the charge transfer upon membrane insertion of the HIV gp41 fusion peptide, and validate the method on two prototypical voltage-dependent proteins, the Kv1.2 K⁺ channel and the voltage sensor of the Ciona intestinalis voltage-sensitive phosphatase, against experimental data. We then use the gating charge analysis to study how the T1 domain modifies voltage sensing in Kv1.2 channels and to investigate the voltage dependence of the initial binding of two Na⁺ ions in Na⁺-coupled glutamate transporters. Our simulation approach quantifies various mechanisms of voltage sensing, enables direct comparison with experiments, and supports mechanistic interpretation of voltage sensitivity by fractional amino acid contributions.

Structural Insights into the Atomistic Mechanisms of Action of Small Molecule Inhibitors Targeting the KCa3.1 Channel Pore

The intermediate-conductance Ca2+-activated K+ channel (KCa3.1) constitutes an attractive pharmacological target for immunosuppression, fibroproliferative disorders, atherosclerosis, and stroke. However, there currently is no available crystal structure of this medically relevant channel that could be used for structure-assisted drug design. Using the Rosetta molecular modeling suite we generated a molecular model of the KCa3.1 pore and tested the model by first confirming previously mapped binding sites and visualizing the mechanism of TRAM-34 (1-[(2-chlorophenyl)diphenylmethyl]-1H-pyrazole), senicapoc (2,2-bis-(4-fluorophenyl)-2-phenylacetamide), and NS6180 (4-[[3-(trifluoromethyl)phenyl]methyl]-2H-1,4-benzothiazin-3(4H)-one) inhibition at the atomistic level. All three compounds block ion conduction directly by fully or partially occupying the site that would normally be occupied by K+ before it enters the selectivity filter. We then challenged the model to predict the receptor sites and mechanisms of action of the dihydropyridine nifedipine and an isosteric 4-phenyl-pyran. Rosetta predicted receptor sites for nifedipine in the fenestration region and for the 4-phenyl-pyran in the pore lumen, which could both be confirmed by site-directed mutagenesis and electrophysiology. While nifedipine is thus not a pore blocker and might be stabilizing the channel in a nonconducting conformation or interfere with gating, the 4-phenyl-pyran was found to be a classical pore blocker that directly inhibits ion conduction similar to the triarylmethanes TRAM-34 and senicapoc. The Rosetta KCa3.1 pore model explains the mechanism of action of several KCa3.1 blockers at the molecular level and could be used for structure-assisted drug design.

Small molecule modulation of voltage gated sodium channels

Voltage gated sodium channels are fundamental players in animals physiology. By triggering the depolarization of the lipid membrane they enable generation and propagation of the action potential. The involvement of these channels in numerous pathological conditions makes them relevant target for pharmaceutical intervention. Therefore, modulation of sodium conductance via small molecule binding constitutes a promising strategy to treat a large variety of diseases. However, this approach entails significant challenges: voltage gated sodium channels are complex nanomachines and the details of their workings have only recently started to become clear. Here we review - with emphasis on the computational studies - some of the major milestones in the long-standing search of a quantitative microscopic description of the molecular mechanism and modulation of voltage-gated sodium channels.

Efficient internalization of TAT peptide in zwitterionic DOPC phospholipid membrane revealed by neutron diffraction

The aim of this study is to investigate the interactions between TAT peptides and a neutral DOPC bilayer by using neutron lamellar diffraction. The distribution of TAT peptides and the perturbation of water distribution across the DOPC bilayer were revealed. When compared to our previous study on an anionic DOPC/DOPS bilayer (X. Chen et al., Biochim Biophys Acta. 2013. 1828 (8), 1982-1988), a much deeper insertion of TAT peptides was found in the hydrophobic core of DOPC bilayer at a depth of 6.0Å from the center of the bilayer, a position close to the double bond of fatty acyl chain. We conclude that the electrostatic attractions between the positively charged TAT peptides and the negatively charged headgroups of phospholipid are not essential for the direct translocation. Furthermore, the interactions of TAT peptides with the DOPC bilayer were found to vary in a concentration-dependent manner. A limited number of peptides first associate with the phosphate moieties on the lipid headgroups by using the guanidinium ions pairing. Then the energetically favorable water defect structures are adopted to maintain the arginine residues hydrated by drawing water molecules and lipid headgroups into the bilayer core. Such bilayer deformations consequently lead to the deep intercalation of TAT peptides into the bilayer core. Once a threshold concentration of TAT peptide in the bilayer is reached, a significant rearrangement of bilayer will happen and steady-state water pores will form.

Atomistic Modeling of Ion Conduction through the Voltage-Sensing Domain of the Shaker K+ Ion Channel

Voltage-sensing domains (VSDs) sense changes in the membrane electrostatic potential and, through conformational changes, regulate a specific function. The VSDs of wild-type voltage-dependent K⁺, Na⁺, and Ca²⁺ channels do not conduct ions, but they can become ion-permeable through pathological mutations in the VSD. Relatively little is known about the underlying mechanisms of conduction through VSDs. The most detailed studies have been performed on Shaker K⁺ channel variants in which ion conduction through the VSD is manifested in electrophysiology experiments as a voltage-dependent inward current, the so-called omega current, which appears when the VSDs are in their resting state conformation. Only monovalent cations appear to permeate the Shaker VSD via a pathway that is believed to be, at least in part, the same as that followed by the S4 basic side chains during voltage-dependent activation. We performed μs-time scale atomistic molecular dynamics simulations of a cation-conducting variant of the Shaker VSD under applied electric fields in an experimentally validated resting-state conformation, embedded in a lipid bilayer surrounded by solutions containing guanidinium chloride or potassium chloride. Our simulations provide insights into the Shaker VSD permeation pathway, the protein-ion interactions that control permeation kinetics, and the mechanism of voltage-dependent activation of voltage-gated ion channels.

Functional diversity of potassium channel voltage-sensing domains

Voltage-gated potassium channels or Kv's are membrane proteins with fundamental physiological roles. They are composed of 2 main functional protein domains, the pore domain, which regulates ion permeation, and the voltage-sensing domain, which is in charge of sensing voltage and undergoing a conformational change that is later transduced into pore opening. The voltage-sensing domain or VSD is a highly conserved structural motif found in all voltage-gated ion channels and can also exist as an independent feature, giving rise to voltage sensitive enzymes and also sustaining proton fluxes in proton-permeable channels. In spite of the structural conservation of VSDs in potassium channels, there are several differences in the details of VSD function found across variants of Kvs. These differences are mainly reflected in variations in the electrostatic energy needed to open different potassium channels. In turn, the differences in detailed VSD functioning among voltage-gated potassium channels might have physiological consequences that have not been explored and which might reflect evolutionary adaptations to the different roles played by Kv channels in cell physiology.

A Microscopic Capacitor Model of Voltage Coupling in Membrane Proteins: Gating Charge Fluctuations in Ci-VSD

The voltage sensitivity of membrane proteins is reflected in the response of the voltage sensing domains (VSDs) to the changes in membrane potential. This response is implicated in the displacement of positively charged residues, associated with the conformational changes of VSDs. The displaced charges generate nonlinear (i.e., voltage-dependent) capacitance current called the gating current (and its corresponding gating charge), which is a key experimental quantity that characterizes voltage activation in VSMP. However, the relevant theoretical/computational approaches, aimed to correlate the structural information on VSMP to electrophysiological measurements, have been rather limited, posing a broad challenge in computer simulations of VSMP. Concomitant with the development of our coarse-graining (CG) model of voltage coupling, we apply our theoretical framework for the treatments of voltage effects in membrane proteins to modeling the VSMP activation, taking the VSDs (Ci-VSD) derived from the Ciona intestinalis voltage sensitive phosphatase (Ci-VSP) as a model system. Our CG model reproduces the observed gating charge of Ci-VSD activation in several different perspectives. In particular, a new closed-form expression of the gating charge is evaluated in both nonequilibrium and equilibrium ways, while considering the fluctuation-dissipation relation that connects a nonequilibrium measurement of the gating charge to an equilibrium measurement of charge fluctuations (i.e., the voltage-independent linear component of membrane capacitance). In turn, the expression uncovers a novel link that connects an equilibrium measurement of the voltage-independent linear capacitance to a nonequilibrium measurement of the voltage-dependent nonlinear capacitance (whose integral over voltage is equal to the gating charge). In addition, our CG model yields capacitor-like voltage dependent free energy parabolas, resulting in the free energy difference and the free energy barrier for the Ci-VSD activation at "zero" (depolarization) membrane potential. Significantly, the resultant voltage dependent energetics enables a direct evaluation of capacitance-voltage relationship (C-V curve) as well as charge-voltage relationship (Q-V curve) that is in a good agreement with the observed measurement of Ci-VSD voltage activation. Importantly, an extension of our kinetic/thermodynamic model of voltage dependent activation in VSMP allows for novel derivations of voltage-dependent rate constants, whose parameters are expressed by the intrinsic properties of VSMP. These novel closed-form expressions offer a physicochemical foundation for the semiempirical Eyring-type voltage dependent rate equations that have been the cornerstone for the phenomenological (kinetic) descriptions of gating and membrane currents in the mechanistic study of ion channels and transporters. Our extended theoretical framework developed in the present study has potential implications on the roles played by gating charge fluctuations for the spike generations in nerve cells within the framework of the Hodgkin-Huxley-type model.

Structural Refinement of Proteins by Restrained Molecular Dynamics Simulations with Non-interacting Molecular Fragments

The knowledge of multiple conformational states is a prerequisite to understand the function of membrane transport proteins. Unfortunately, the determination of detailed atomic structures for all these functionally important conformational states with conventional high-resolution approaches is often difficult and unsuccessful. In some cases, biophysical and biochemical approaches can provide important complementary structural information that can be exploited with the help of advanced computational methods to derive structural models of specific conformational states. In particular, functional and spectroscopic measurements in combination with site-directed mutations constitute one important source of information to obtain these mixed-resolution structural models. A very common problem with this strategy, however, is the difficulty to simultaneously integrate all the information from multiple independent experiments involving different mutations or chemical labels to derive a unique structural model consistent with the data. To resolve this issue, a novel restrained molecular dynamics structural refinement method is developed to simultaneously incorporate multiple experimentally determined constraints (e.g., engineered metal bridges or spin-labels), each treated as an individual molecular fragment with all atomic details. The internal structure of each of the molecular fragments is treated realistically, while there is no interaction between different molecular fragments to avoid unphysical steric clashes. The information from all the molecular fragments is exploited simultaneously to constrain the backbone to refine a three-dimensional model of the conformational state of the protein. The method is illustrated by refining the structure of the voltage-sensing domain (VSD) of the Kv1.2 potassium channel in the resting state and by exploring the distance histograms between spin-labels attached to T4 lysozyme. The resulting VSD structures are in good agreement with the consensus model of the resting state VSD and the spin-spin distance histograms from ESR/DEER experiments on T4 lysozyme are accurately reproduced.

Knowledge of multiple conformational states of membrane transport proteins is a prerequisite to understand their function. However, the determination of atomic structures for all these states with conventional high-resolution approaches can be very challenging due to inherent difficulties in high yield purification of functional membrane transport proteins. Various complementary structural information of proteins in their native states can be obtained by a variety of biophysical and biochemical methods with site-directed mutations. Here, a novel restrained molecular dynamics structural refinement method is developed to help derive a structural model that is consistent with experimental data by incorporating all the experimental constraints simultaneously through the use of non-interacting all-atom molecular fragments. The method can be easily and effectively extended to incorporate many kinds of structural constraints from a variety of biophysical and biochemical experiments, and should be very useful in generating and refining models of proteins in specific functional states.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

A general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two "equilibrium" (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments.

A Structural Model of the Human α7 Nicotinic Receptor in an Open Conformation

Nicotinic acetylcholine receptors (nAchRs) are ligand-gated ion channels that regulate chemical transmission at the neuromuscular junction. Structural information is available at low resolution from open and closed forms of an eukaryotic receptor, and at high resolution from other members of the same structural family, two prokaryotic orthologs and an eukaryotic GluCl channel. Structures of human channels however are still lacking. Homology modeling and Molecular Dynamics simulations are valuable tools to predict structures of unknown proteins, however, for the case of human nAchRs, they have been unsuccessful in providing a stable open structure so far. This is due to different problems with the template structures: on one side the homology with prokaryotic species is too low, while on the other the open eukaryotic GluCl proved itself unstable in several MD studies and collapsed to a dehydrated, non-conductive conformation, even when bound to an agonist. Aim of this work is to obtain, by a mixing of state-of-the-art homology and simulation techniques, a plausible prediction of the structure (still unknown) of the open state of human α7 nAChR complexed with epibatidine, from which it is possible to start structural and functional test studies. To prevent channel closure we employ a restraint that keeps the transmembrane pore open, and obtain in this way a stable, hydrated conformation. To further validate this conformation, we run four long, unbiased simulations starting from configurations chosen at random along the restrained trajectory. The channel remains stable and hydrated over the whole runs. This allows to assess the stability of the putative open conformation over a cumulative time of 1 μs, 800 ns of which are of unbiased simulation. Mostly based on the analysis of pore hydration and size, we suggest that the obtained structure has reasonable chances to be (at least one of the possible) structures of the channel in the open conformation.

Molecular pathophysiology and pharmacology of the voltage-sensing module of neuronal ion channels

Voltage-gated ion channels (VGICs) are membrane proteins that switch from a closed to open state in response to changes in membrane potential, thus enabling ion fluxes across the cell membranes. The mechanism that regulate the structural rearrangements occurring in VGICs in response to changes in membrane potential still remains one of the most challenging topic of modern biophysics. Na⁺, Ca²⁺ and K⁺ voltage-gated channels are structurally formed by the assembly of four similar domains, each comprising six transmembrane segments. Each domain can be divided into two main regions: the Pore Module (PM) and the Voltage-Sensing Module (VSM). The PM (helices S₅ and S₆ and intervening linker) is responsible for gate opening and ion selectivity; by contrast, the VSM, comprising the first four transmembrane helices (S₁–S₄), undergoes the first conformational changes in response to membrane voltage variations. In particular, the S₄ segment of each domain, which contains several positively charged residues interspersed with hydrophobic amino acids, is located within the membrane electric field and plays an essential role in voltage sensing. In neurons, specific gating properties of each channel subtype underlie a variety of biological events, ranging from the generation and propagation of electrical impulses, to the secretion of neurotransmitters and to the regulation of gene expression. Given the important functional role played by the VSM in neuronal VGICs, it is not surprising that various VSM mutations affecting the gating process of these channels are responsible for human diseases, and that compounds acting on the VSM have emerged as important investigational tools with great therapeutic potential. In the present review we will briefly describe the most recent discoveries concerning how the VSM exerts its function, how genetically inherited diseases caused by mutations occurring in the VSM affects gating in VGICs, and how several classes of drugs and toxins selectively target the VSM.

Domain and interdomain energetics underlying gating in Shaker-type Kv channels

To understand gating events with a time-base many orders-of-magnitude slower than that of atomic motion in voltage-gated ion channels such as the Shaker-type KV channels, a multiscale physical model is constructed from the experimentally well-characterized voltage-sensor (VS) domains coupled to a hydrophobic gate. The four VS domains are described by a continuum electrostatic model under voltage-clamp conditions, the control of ion flow by the gate domain is described by a vapor-lock mechanism, and the simple coupling principle is informed by known experimental results and trial-and-error. The configurational energy computed for each element is used to produce a total Hamiltonian that is a function of applied voltage, VS positions, and gate radius. We compute statistical-mechanical expectation values of macroscopic laboratory observables. This approach stands in contrast with molecular-dynamic models which are challenged by increasing scale, and kinetic models which assume a probability distribution rather than derive it from the underlying physics. This generic model predicts well the Shaker charge/voltage and conductance/voltage relations; the tight constraints underlying these results allow us to quantitatively assess the underlying physical mechanisms. The total electrical work picked up by the VS domains is an order-of-magnitude larger than the work required to actuate the gate itself, suggesting an energetic basis for the evolutionary flexibility of the voltage-gating mechanism. The cooperative slide-and-interlock behavior of the VS domains described by the VS-gate coupling relation leads to the experimentally observed bistable gating. This engineering approach should prove useful in the investigation of various elements underlying gating characteristics and degraded behavior due to mutation.

ATP synthase

Oxygenic photosynthesis is the principal converter of sunlight into chemical energy. Cyanobacteria and plants provide aerobic life with oxygen, food, fuel, fibers, and platform chemicals. Four multisubunit membrane proteins are involved: photosystem I (PSI), photosystem II (PSII), cytochrome b6f (cyt b6f), and ATP synthase (FOF1). ATP synthase is likewise a key enzyme of cell respiration. Over three billion years, the basic machinery of oxygenic photosynthesis and respiration has been perfected to minimize wasteful reactions. The proton-driven ATP synthase is embedded in a proton tight-coupling membrane. It is composed of two rotary motors/generators, FO and F1, which do not slip against each other. The proton-driven FO and the ATP-synthesizing F1 are coupled via elastic torque transmission. Elastic transmission decouples the two motors in kinetic detail but keeps them perfectly coupled in thermodynamic equilibrium and (time-averaged) under steady turnover. Elastic transmission enables operation with different gear ratios in different organisms.

Voltage-dependent gating and gating charge measurements in the Kv1.2 potassium channel

Kv1.2’s gating charge is less than Shaker’s, and the specific contributions of charged S4 residues differ, suggesting that the electric field distribution in the Kv1.2 voltage-sensing domain is different than Shaker’s.

Much has been learned about the voltage sensors of ion channels since the x-ray structure of the mammalian voltage-gated potassium channel Kv1.2 was published in 2005. High resolution structural data of a Kv channel enabled the structural interpretation of numerous electrophysiological findings collected in various ion channels, most notably Shaker, and permitted the development of meticulous computational simulations of the activation mechanism. The fundamental premise for the structural interpretation of functional measurements from Shaker is that this channel and Kv1.2 have the same characteristics, such that correlation of data from both channels would be a trivial task. We tested these assumptions by measuring Kv1.2 voltage-dependent gating and charge per channel. We found that the Kv1.2 gating charge is near 10 elementary charges (e_o), ∼25% less than the well-established 13–14 e_o in Shaker. Next, we neutralized positive residues in the Kv1.2 S4 transmembrane segment to investigate the cause of the reduction of the gating charge and found that, whereas replacing R1 with glutamine decreased voltage sensitivity to ∼50% of the wild-type channel value, mutation of the subsequent arginines had a much smaller effect. These data are in marked contrast to the effects of charge neutralization in Shaker, where removal of the first four basic residues reduces the gating charge by roughly the same amount. In light of these differences, we propose that the voltage-sensing domains (VSDs) of Kv1.2 and Shaker might undergo the same physical movement, but the septum that separates the aqueous crevices in the VSD of Kv1.2 might be thicker than Shaker’s, accounting for the smaller Kv1.2 gating charge.