Free-energy landscape of ion-channel voltage-sensor-domain activation

Dual mechanisms contribute to enhanced voltage dependence of an electric fish potassium channel

The voltage dependence of different voltage-gated potassium channels, described by the voltage at which half of the channels are open (V1/2), varies over a range of 80 mV and is influenced by factors such as the number of positive gating charges and the identity of the hydrophobic amino acids in the channel's voltage sensor (S4). Here we explore by experimental manipulations and molecular dynamics simulation the contributions of two derived features of an electric fish potassium channel (Kv1.7a) that is among the most voltage-sensitive Shaker family potassium channels known. These are a patch of four contiguous negatively charged glutamates in the S3-S4 extracellular loop and a glutamate in the S3b helix. We find that these negative charges affect V1/2 by separate, complementary mechanisms. In the closed state, the S3-S4 linker negative patch reduces the membrane surface charge biasing the channel to enter the open state while, upon opening, the negative amino acid in the S3b helix faces the second (R2) gating charge of the voltage sensor electrostatically biasing the channel to remain in the open state. This work highlights two evolutionary novelties that illustrate the potential influence of negatively charged amino acids in extracellular loops and adjacent helices to voltage dependence.

Effective data-driven collective variables for free energy calculations from metadynamics of paths

A variety of enhanced sampling (ES) methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is crucially dependent on the ability of the chosen CVs to capture the relevant slow degrees of freedom of the system. For complex processes, finding such CVs is the real challenge. Machine learning (ML) CVs offer, in principle, a solution to handle this problem. However, these methods rely on the availability of high-quality datasets-ideally incorporating information about physical pathways and transition states-which are difficult to access, therefore greatly limiting their domain of application. Here, we demonstrate how these datasets can be generated by means of ES simulations in trajectory space via the metadynamics of paths algorithm. The approach is expected to provide a general and efficient way to generate efficient ML-based CVs for the fast prediction of free energy landscapes in ES simulations. We demonstrate our approach with two numerical examples, a 2D model potential and the isomerization of alanine dipeptide, using deep targeted discriminant analysis as our ML-based CV of choice.

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.

Modulation of the IKS channel by PIP2 requires two binding sites per monomer

The phosphatidyl-inositol-4,5-bisphosphate (PIP₂) lipid has been shown to be crucial for the coupling between the voltage sensor and the pore of the potassium voltage-gated K_V7 channel family, especially the K_V7.1 channel. Expressed in the myocardium membrane, K_V7.1 forms a complex with KCNE1 auxiliary subunits to generate the I_KS current. Here we present molecular models of the transmembrane region of this complex in its three known states, namely the Resting/Closed (RC), the Intermediate/Closed (IC), and the Activated/Open (AO), robustness of which is assessed by agreement with a range of biophysical data. Molecular Dynamics (MD) simulations of these models embedded in a lipid bilayer including phosphatidyl-inositol-4,5-bisphosphate (PIP₂) lipids show that in presence of KCNE1, two PIP₂ lipids are necessary to stabilize each state. The simulations also show that KCNE1 interacts with both PIP₂ binding sites, forming a tourniquet around the pore and preventing its opening. The present investigation provides therefore key molecular elements that govern the role of PIP₂ in KCNE1 modulation of I_KS channels, possibly a common mechanism by which auxiliary KCNE subunits might modulate a variety of other ion channels.

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.

Hijacking of Cellular Functions by Severe Acute Respiratory Syndrome Coronavirus-2. Permeabilization and Polarization of the Host Lipid Membrane by Viroporins

Like all viral infections, SARS-CoV-2 acts at multiple levels, hijacking fundamental cellular functions and assuring its replication and immune system evasion. In particular, the viral 3' Open Reading Frame (ORF3a) codes for a hydrophobic protein, which embeds in the cellular membrane, where it acts as an ion viroporin and is related to strong inflammatory response. Here we report equilibrium and enhanced sampling molecular dynamic simulation of the SARS-CoV-2 ORF3a in a model lipid bilayer, showing how the protein permeabilizes the lipid membrane, via the formation of a water channel, which in turn assures ion transport. We report the free energy profile for both K+ and Cl- transfer from the cytosol to the extracellular domain. The important role of ORF3a in the viral cycle and its high conservation among coronaviruses may also make it a target of choice for future antiviral development, further justifying the elucidation of its mechanism at the atomistic level.

Enhanced sampling without borders: on global biasing functions and how to reweight them

Molecular dynamics (MD) simulations are a powerful tool to follow the time evolution of biomolecular motions in atomistic resolution. However, the high computational demand of these simulations limits the timescales of motions that can be observed. To resolve this issue, so called enhanced sampling techniques are developed, which extend conventional MD algorithms to speed up the simulation process. Here, we focus on techniques that apply global biasing functions. We provide a broad overview of established enhanced sampling methods and promising new advances. As the ultimate goal is to retrieve unbiased information from biased ensembles, we also discuss benefits and limitations of common reweighting schemes. In addition to concisely summarizing critical assumptions and implications, we highlight the general application opportunities as well as uncertainties of global enhanced sampling.

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.

Predicting Ion Channel Conductance via Dissipation-Corrected Targeted Molecular Dynamics and Langevin Equation Simulations

Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, here we applied dissipation-corrected targeted molecular dynamics in combination with Langevin equation simulations to potassium diffusion through the gramicidin A channel as a test system. Performing a nonequilibrium principal component analysis on backbone dihedral angles, we find coupled protein-ion dynamics to occur during ion transfer. The dissipation-corrected free energy profiles correspond well to predictions from other biased simulation methods. The incorporation of an external electric field in Langevin simulations enables the prediction of macroscopic observables in the form of I-V characteristics.

Polyamine blockade and binding energetics in the MthK potassium channel

Polyamines such as spermidine and spermine are found in nearly all cells, at concentrations ranging up to 0.5 mM. These cations are endogenous regulators of cellular K⁺ efflux, binding tightly in the pores of inwardly rectifying K⁺ (K_ir) channels in a voltage-dependent manner. Although the voltage dependence of K_ir channel polyamine blockade is thought to arise at least partially from the energetically coupled movements of polyamine and K⁺ ions through the pore, the nature of physical interactions between these molecules is unclear. Here we analyze the polyamine-blocking mechanism in the model K⁺ channel MthK, using a combination of electrophysiology and computation. Spermidine (SPD³⁺) and spermine (SPM⁴⁺) each blocked current through MthK channels in a voltage-dependent manner, and blockade by these polyamines was described by a three-state kinetic scheme over a wide range of polyamine concentrations. In the context of the scheme, both SPD³⁺ and SPM⁴⁺ access a blocking site with similar effective gating valences (0.84 ± 0.03 e₀ for SPD³⁺ and 0.99 ± 0.04 e₀ for SPM⁴⁺), whereas SPM⁴⁺ binds in the blocked state with an ∼20-fold higher affinity than SPD³⁺ (K_d = 28.1 ± 3.1 µM for SPD³⁺ and 1.28 ± 0.20 µM for SPM⁴⁺), consistent with a free energy difference of 1.8 kcal/mol. Molecular simulations of the MthK pore in complex with either SPD³⁺ or SPM⁴⁺ are consistent with the leading amine interacting with the hydroxyl groups of T59, at the selectivity filter threshold, with access to this site governed by outward movement of K⁺ ions. These coupled movements can account for a large fraction of the voltage dependence of blockade. In contrast, differences in binding energetics between SPD³⁺ and SPM⁴⁺ may arise from distinct electrostatic interactions between the polyamines and carboxylate oxygens on the side chains of E92 and E96, located in the pore-lining helix.

A novel theoretical framework reveals more than one voltage-sensing pathway in the lateral membrane of outer hair cells

Outer hair cell (OHC) electromotility amplifies acoustic vibrations throughout the frequency range of hearing. Electromotility requires that the lateral membrane protein prestin undergo a conformational change upon changes in the membrane potential to produce an associated displacement charge. The magnitude of the charge displaced and the mid-reaction potential (when one half of the charge is displaced) reflects whether the cells will produce sufficient gain at the resting membrane potential to boost sound in vivo. Voltage clamp measurements performed under near-identical conditions ex vivo show the charge density and mid-reaction potential are not always the same, confounding interpretation of the results. We compare the displacement charge measurements in OHCs from rodents with a theory shown to exhibit good agreement with in silico simulations of voltage-sensing reactions in membranes. This model equates the charge density to the potential difference between two pseudo-equilibrium states of the sensors when they are in a stable conformation and not contributing to the displacement current. The model predicts this potential difference to be one half of its value midway into the reaction, when one equilibrium conformation transforms to the other pseudo-state. In agreement with the model, we find the measured mid-reaction potential to increase as the charge density decreases to exhibit a negative slope of ∼1/2. This relationship suggests that the prestin sensors exhibit more than one stable hyperpolarized state and that voltage sensing occurs by more than one pathway. We determine the electric parameters for prestin sensors and use the analytical expressions of the theory to estimate the energy barriers for the two voltage-dependent pathways. This analysis explains the experimental results, supports the theoretical approach, and suggests that voltage sensing occurs by more than one pathway to enable amplification throughout the frequency range of hearing.

Improved Hodgkin-Huxley type model for neural action potentials

The simple Goldman-Hodgkin-Katz model for resting-state membrane potentials has been generalized to provide a new nonlinear theoretical model for action potentials in perfused axons. Our minimalistic model appeals naturally to physically based electrodiffusion principles to describe electric-current densities inside sodium and potassium-ion channels whereas the 1952 Hodgkin-Huxley model describes such current densities in an ad hoc way. Although the two models share similar schemes for the kinetics of ion-channel gating, our relaxation times for channel gating are simpler, being independent of membrane potential. Like the theoretical model of Hodgkin and Huxley, based primarily on experimental data at [Formula: see text], our dynamical system behaves as a 4-dimensional resonator exhibiting subthreshold oscillations. Although our present analysis refers to experiments at [Formula: see text], re-parameterizations of this model should permit consideration of action potentials at alternative temperatures. The predicted speed of propagating action potentials in giant axons of squid at [Formula: see text] is in excellent agreement with the Hodgkin-Huxley experimental value at [Formula: see text]. In cases where our model predictions differ from those of the Hodgkin-Huxley model, new experiments will be required to determine which model is more accurate.

Structure and Sequence-based Computational Approaches to Allosteric Signal Transduction: Application to Electromechanical Coupling in Voltage-gated Ion Channels

Allosteric signaling underlies the function of many biomolecules, including membrane proteins such as ion channels. Experimental methods have enabled specific quantitative insights into the coupling between the voltage sensing domain (VSD) and the pore gate of voltage-gated ion channels, located tens of Ångström apart from one another, as well as pinpointed specific residues and domains that participate in electromechanical signal transmission. Nevertheless, an overall atomic-level resolution picture is difficult to obtain from these methods alone. Today, thanks to the cryo-EM resolution revolution, we have access to high resolution structures of many different voltage-gated ion channels in various conformational states, putting a quantitative description of the processes at the basis of these changes within our close reach. Here, we review computational methods that build on structures to detect and characterize allosteric signaling and pathways. We then examine what has been learned so far about electromechanical coupling between VSD and pore using such methods. While no general theory of electromechanical coupling in voltage-gated ion channels integrating results from all these methods is available yet, we outline the types of insights that could be achieved in the near future using the methods that have not yet been put to use in this field of application.

Voltage-Dependent Transport of Neutral Solutes through Nanopores: A Molecular View

The permeation of (neutral) molecules through nanopores in the presence of external voltages depends on several factors including pore electrostatics, electrophoretic force, and electro-osmotic drag. In earlier single-channel electrophysiology experiments, voltage-dependent asymmetric transport of neutral α-cyclodextrin (α-CD) molecules through the biological nanopore ΔCymA was observed. The voltage-dependent ion-associated flow of water, the so-called electro-osmotic flow, has been suggested to be the key factor behind the observed asymmetric behavior. The influence of pore electrostatics and electrophoretic force and their interplay with the electro-osmotic drag with varying buffers and voltages has not yet been analyzed at the molecular level. Hence, the detailed physical mechanism behind this intriguing permeation process is in part still unclear. In the present study, we have performed 36 μs all-atom free energy calculations by combining applied-field molecular dynamics simulations with metadynamics techniques. The influence of several ionic conditions as well as external voltages on the permeation of α-CD molecules across the ΔCymA pore has been investigated. To decipher the thermodynamic and kinetic details, the lowest energy paths and the permeation times for α-CD translocation have been estimated. In the presence of KCl or MgCl₂ salts, the charge of the cations is found to control the direction and magnitude of the electro-osmotic flow, which in turn strongly affects α-CD permeation. Overall, the present findings significantly improve the fundamental understanding of the voltage-dependent transport of neutral solutes across nanopores.

Molecular Basis of SARS-CoV-2 Infection and Rational Design of Potential Antiviral Agents: Modeling and Simulation Approaches

The emergence in late 2019 of the coronavirus SARS-CoV-2 has resulted in the breakthrough of the COVID-19 pandemic that is presently affecting a growing number of countries. The development of the pandemic has also prompted an unprecedented effort of the scientific community to understand the molecular bases of the virus infection and to propose rational drug design strategies able to alleviate the serious COVID-19 morbidity. In this context, a strong synergy between the structural biophysics and molecular modeling and simulation communities has emerged, resolving at the atomistic level the crucial protein apparatus of the virus and revealing the dynamic aspects of key viral processes. In this Review, we focus on how in silico studies have contributed to the understanding of the SARS-CoV-2 infection mechanism and the proposal of novel and original agents to inhibit the viral key functioning. This Review deals with the SARS-CoV-2 spike protein, including the mode of action that this structural protein uses to entry human cells, as well as with nonstructural viral proteins, focusing the attention on the most studied proteases and also proposing alternative mechanisms involving some of its domains, such as the SARS unique domain. We demonstrate that molecular modeling and simulation represent an effective approach to gather information on key biological processes and thus guide rational molecular design strategies.

Modeling the Interactions Between Sodium Channels Provides Insight Into the Negative Dominance of Certain Channel Mutations

BACKGROUND

Nav1.5 cardiac Na+ channel mutations can cause arrhythmogenic syndromes. Some of these mutations exert a dominant negative effect on wild-type channels. Recent studies showed that Na+ channels can dimerize, allowing coupled gating. This leads to the hypothesis that allosteric interactions between Na+ channels modulate their function and that these interactions may contribute to the negative dominance of certain mutations.

METHODS

To investigate how allosteric interactions affect microscopic and macroscopic channel function, we developed a modeling paradigm in which Markovian models of two channels are combined. Allosteric interactions are incorporated by modifying the free energies of the composite states and/or barriers between states.

RESULTS

Simulations using two generic 2-state models (C-O, closed-open) revealed that increasing the free energy of the composite states CO/OC leads to coupled gating. Simulations using two 3-state models (closed-open-inactivated) revealed that coupled closings must also involve interactions between further composite states. Using two 6-state cardiac Na+ channel models, we replicated previous experimental results mainly by increasing the energies of the CO/OC states and lowering the energy barriers between the CO/OC and the CO/OO states. The channel model was then modified to simulate a negative dominant mutation (Nav1.5 p.L325R). Simulations of homodimers and heterodimers in the presence and absence of interactions showed that the interactions with the variant channel impair the opening of the wild-type channel and thus contribute to negative dominance.

CONCLUSION

Our new modeling framework recapitulates qualitatively previous experimental observations and helps identifying possible interaction mechanisms between ion channels.

The interplay of excitation and electroporation in nanosecond pulse stimulation

Conventional electric stimuli of micro- and millisecond duration excite or activate cells at voltages 10-100 times below the electroporation threshold. This ratio is remarkably different for nanosecond electric pulses (nsEP), which caused excitation and activation only at or above the electroporation threshold in diverse cell lines, primary cardiomyocytes, neurons, and chromaffin cells. Depolarization to the excitation threshold often results from (or is assisted by) the loss of the resting membrane potential due to ion leaks across the membrane permeabilized by nsEP. Slow membrane resealing and the build-up of electroporation damages prevent repetitive excitation by nsEP. However, peripheral nerves and muscles are exempt from this rule and withstand multiple cycles of excitation by nsEP without the loss of function or signs of electroporation. We show that the damage-free excitation by nsEP may be enabled by the membrane charging time constant sufficiently large to (1) cap the peak transmembrane voltage during nsEP below the electroporation threshold, and (2) extend the post-nsEP depolarization long enough to activate voltage-gated ion channels. The low excitatory efficacy of nsEP compared to longer pulses makes them advantageous for medical applications where the neuromuscular excitation is an unwanted side effect, such as electroporation-based cancer and tissue ablation.

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.

Cancellation of nerve excitation by the reversal of nanosecond stimulus polarity and its relevance to the gating time of sodium channels

The initiation of action potentials (APs) by membrane depolarization occurs after a brief vulnerability period, during which excitation can be abolished by the reversal of the stimulus polarity. This vulnerability period is determined by the time needed for gating of voltage-gated sodium channels (VGSC). We compared nerve excitation by ultra-short uni- and bipolar stimuli to define the time frame of bipolar cancellation and of AP initiation. Propagating APs in isolated frog sciatic nerve were elicited by cathodic pulses (200 ns-300 µs), followed by an anodic (canceling) pulse of the same duration after a 0-200-µs delay. We found that the earliest and the latest boundaries for opening the critical number of VGSC needed to initiate AP are, respectively, between 11 and 20 µs and between 100 and 200 µs after the onset of depolarization. Stronger depolarization accelerated AP initiation, apparently due to faster VGSC opening, but not beyond the 11-µs limit. Bipolar cancellation was augmented by reducing pulse duration, shortening the delay between pulses, decreasing the amplitude of the cathodic pulse, and increasing the amplitude of the anodic one. Some of these characteristics contrasted the bipolar cancellation of cell membrane electroporation (Pakhomov et al. in Bioelectrochemistry 122:123-133, 2018; Gianulis et al. in Bioelectrochemistry 119:10-19, 2017), suggesting different mechanisms. The ratio of nerve excitation thresholds for a unipolar cathodic pulse and a symmetrical bipolar pulse increased as a power function as the pulse duration decreased, in remarkable agreement with the predictions of SENN model of nerve excitation (Reilly and Diamant in Health Phys 83(3):356-365, 2002).

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

First-passage-time distribution in a moving parabolic potential with spatial roughness

In this paper, we investigate the first-passage-time distribution (FPTD) within a time-dependent parabolic potential in the presence of roughness with two methods: the Kramers theory and a nonsingular integral equation. By spatially averaging, the rough potential is equivalent to the combination of an effective smooth potential and an effective diffusion coefficient. Based on the Kramers theory, we first obtain Kramers approximations (KAs) of FPTD for both smooth and rough potentials. As expected, KA is valid only for high barriers and small external forces, and generally applicable for high barriers in rough potentials. To overcome the shortcoming of KA, a probability asymptotic approximation (PAA) based on an integral equation is proposed, which uses the transient probability density function (PDF) of the natural boundary conditions instead of the absorbing boundary conditions. We find that PAA fits very well even for large external forces. This enables us to analytically solve the FPTD for large external forces and low barriers as a strong extension to KA. In addition, we show that in the presence of a rough potential, the PAA of FPTD is in good agreement with numerical simulations for low barrier potentials. The PAA makes it possible to investigate the first-passage problem with ultrafast varying potentials and short exiting time. Thus, KA and PAA are complementary in determining the FPTD both for various barriers and external forces. Finally, the mean first-passage time (MFPT) is studied, which illustrates that the PAA of MFPT is effective almost in the whole range of external forces, while the KA of MFPT is valid only for small external forces.

Molecular mechanism of acetoacetyl-CoA enhanced kinetics for increased bioplastic production from Cupriavidus necator 428

Polyhydroxyalkanoates are gaining importance due to their biodegradable nature and close analogy to plastics. Polyhydroxybutyrate (PHB) is the most widely used bioplastic from polyalkanoate family, which is produced by a legion of bacterial species via phbCAB operon encoding β-ketothiolase (PhaA), NADPH-dependent acetoacetyl-coenzyme A (acetoacetyl-CoA) reductase (PhaB) and polyhydroxyalkanoate synthase (PhaC). Augmentation in the activity of these enzymes is promising for increased PHB production which is achieved by enzyme engineering strategies including non-structural and structural approaches. Our study is deployed on directed evolution-based experimentally reported mutants of PhaB enzyme with increased efficiency due to impact on critical structural factors. We have analyzed and compared the native PhaB with two of its variants Q47L and T173S in complex with their cofactor i.e. NADPH as well as the substrate i.e. acetoacetyl-CoA, via long range molecular dynamics simulations. Interaction profile, MMPBSA, essential dynamics, and free energy landscape analysis revealed that the enzyme efficiency is critically affected by cofactor interactions. It was also observed that mutants have higher equilibrium constant with lesser but optimal affinity for substrate and cofactor than the wild type, which might be the reason for increased efficiency of the mutants via enhanced substrate and cofactor exchange rate. Our study provides insights into the cofactor and substrate binding affinities to PhaB enzyme at atomistic level, which will facilitate designing of highly efficient PhaB enzymes for increased PHB production. Communicated by Ramaswamy H. Sarma.

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.

Replacing voltage sensor arginines with citrulline provides mechanistic insight into charge versus shape

Activation of voltage-gated channels results from the outward movement of arginine residues on the S4 segments. Infield et al. use in vivo nonsense suppression to replace Shaker's S4 arginine residues with citrulline and reveal that a positive charge is required on R4 for voltage-dependent deactivation.

Voltage-dependent activation of voltage-gated cation channels results from the outward movement of arginine-bearing helices within proteinaceous voltage sensors. The voltage-sensing residues in potassium channels have been extensively characterized, but current functional approaches do not allow a distinction between the electrostatic and steric contributions of the arginine side chain. Here we use chemical misacylation and in vivo nonsense suppression to encode citrulline, a neutral and nearly isosteric analogue of arginine, into the voltage sensor of the Shaker potassium channel. We functionally characterize the engineered channels and compare them with those bearing conventional mutations at the same positions. We observe effects on both voltage sensitivity and gating kinetics, enabling dissection of the roles of residue structure versus positive charge in channel function. In some positions, substitution with citrulline causes mild effects on channel activation compared with natural mutations. In contrast, substitution of the fourth S4 arginine with citrulline causes substantial changes in the conductance–voltage relationship and the kinetics of the channel, which suggests that a positive charge is required at this position for efficient voltage sensor deactivation and channel closure. The encoding of citrulline is expected to enable enhanced precision for the study of arginine residues located in crowded transmembrane environments in other membrane proteins. In addition, the method may facilitate the study of citrullination in vivo.

How to Connect Cardiac Excitation to the Atomic Interactions of Ion Channels

Many have worked to create cardiac action potential models that explicitly represent atomic-level details of ion channel structure. Such models have the potential to define new therapeutic directions and to show how nanoscale perturbations to channel function predispose patients to deadly cardiac arrhythmia. However, there have been significant experimental and theoretical barriers that have limited model usefulness. Recently, many of these barriers have come down, suggesting that considerable progress toward creating these long-sought models may be possible in the near term.

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

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

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.

Computational membrane biophysics: From ion channel interactions with drugs to cellular function

The rapid development of experimental and computational techniques has changed fundamentally our understanding of cellular-membrane transport. The advent of powerful computers and refined force-fields for proteins, ions, and lipids has expanded the applicability of Molecular Dynamics (MD) simulations. A myriad of cellular responses is modulated through the binding of endogenous and exogenous ligands (e.g. neurotransmitters and drugs, respectively) to ion channels. Deciphering the thermodynamics and kinetics of the ligand binding processes to these membrane proteins is at the heart of modern drug development. The ever-increasing computational power has already provided insightful data on the thermodynamics and kinetics of drug-target interactions, free energies of solvation, and partitioning into lipid bilayers for drugs. This review aims to provide a brief summary about modeling approaches to map out crucial binding pathways with intermediate conformations and free-energy surfaces for drug-ion channel binding mechanisms that are responsible for multiple effects on cellular functions. We will discuss post-processing analysis of simulation-generated data, which are then transformed to kinetic models to better understand the molecular underpinning of the experimental observables under the influence of drugs or mutations in ion channels. This review highlights crucial mathematical frameworks and perspectives on bridging different well-established computational techniques to connect the dynamics and timescales from all-atom MD and free energy simulations of ion channels to the physiology of action potentials in cellular models. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Roughness-enhanced transport in a tilted ratchet driven by Lévy noise

The enhanced transport of particles by roughness in a tilted rough ratchet potential subject to a Lévy noise is investigated in this paper. Due to the roughness, the transport process exhibits quite different properties compared to the smooth case. We find that the roughness on the potential wall functions like a ladder to provide the convenience for particles to climb up but hinder them to slide down. The mean first passage time from one well to its right adjacent well and the mean velocity are, respectively, calculated versus the roughness, the external force, and the Lévy stability index. Our results show that the roughness is able to induce an enhancement on the mean velocity of particles and accelerate the barrier crossing process. The general conditions require a small external force and a small Lévy stability index. We find that with increasing external forces, the enhancement areas of roughness and Lévy stability index both shrink. However, for the Lévy stability index within the enhancement area, its increase will enlarge the enhancement area of roughness. On the contrary, under the same conditions we observe that for a Gaussian noise the roughness always reduces the corresponding mean velocity which is very different from the case of Lévy noise.

Transports in a rough ratchet induced by Lévy noises

We study the transport of a particle subjected to a Lévy noise in a rough ratchet potential which is constructed by superimposing a fast oscillating trigonometric function on a common ratchet background. Due to the superposition of roughness, the transport process exhibits significantly different properties under the excitation of Lévy noises compared to smooth cases. The influence of the roughness on the directional motion is explored by calculating the mean velocities with respect to the Lévy stable index α and the spatial asymmetry parameter q of the ratchet. Variations in the splitting probability have been analyzed to illustrate how roughness affects the transport. In addition, we have examined the influences of roughness on the mean first passage time to know when it accelerates or slows down the first passage process. We find that the roughness can lead to a fast reduction of the absolute value of the mean velocity for small α, however the influence is small for large α. We have illustrated that the ladder-like roughness on the potential wall increases the possibility for particles to cross the gentle side of the ratchet, which results in an increase of the splitting probability to right for the right-skewed ratchet potential. Although the roughness increases the corresponding probability, it does not accelerate the mean first passage process to the right adjacent well. Our results show that the influences of roughness on the mean first passage time are sensitive to the combination of q and α. Hence, the proper q and α can speed up the passage process, otherwise it will slow down it.

Characterization of Ciprofloxacin Permeation Pathways across the Porin OmpC Using Metadynamics and a String Method

The rapid spreading of antimicrobial resistance in Gram-negative bacteria has become a major threat for humans as well as animals. As one of the main factors involved, the permeability of the outer membrane has attracted a great deal of attention recently. However, the knowledge regarding the translocation mechanisms for most available antibiotics is so far rather limited. Here, a theoretical study concerning the diffusion route of ciprofloxacin across the outer membrane porin OmpC from E. coli is presented. To this end, we establish a protocol to characterize meaningful permeation pathways by combining metadynamics with the zero-temperature string method. It was found that the lowest-energy pathway requires a reorientation of ciprofloxacin in the extracellular side of the porin before reaching the constriction region with its carboxyl group ahead. Several affinity sites have been identified, and their metastability has been evaluated using unbiased simulations. Such a detailed understanding is potentially very helpful in guiding the development of next generation antibiotics.

Modelling the interactions between animal venom peptides and membrane proteins

The active components of animal venoms are mostly peptide toxins, which typically target ion channels and receptors of both the central and peripheral nervous system, interfering with action potential conduction and/or synaptic transmission. The high degree of sequence conservation of their molecular targets makes a range of these toxins active at human receptors. The high selectivity and potency displayed by some of these toxins have prompted their use as pharmacological tools as well as drugs or drug leads. Molecular modelling has played an essential role in increasing our molecular-level understanding of the activity and specificity of animal toxins, as well as engineering them for biotechnological and pharmaceutical applications. This review focuses on the biological insights gained from computational and experimental studies of animal venom toxins interacting with membranes and ion channels. A host of recent X-ray crystallography and electron-microscopy structures of the toxin targets has contributed to a dramatic increase in the accuracy of the molecular models of toxin binding modes greatly advancing this exciting field of study. This article is part of the Special Issue entitled 'Venom-derived Peptides as Pharmacological Tools.'

Simulating the Activation of Voltage Sensing Domain for a Voltage-Gated Sodium Channel Using Polarizable Force Field

Voltage-gated sodium (Na_V) channels play vital roles in the signal transduction of excitable cells. Upon activation of a Na_V channel, the change of transmembrane voltage triggers conformational change of the voltage sensing domain, which then elicits opening of the pore domain and thus allows an influx of Na⁺ ions. Description of this process with atomistic details is in urgent demand. In this work, we simulated the partial activation process of the voltage sensing domain of a prokaryotic Na_V channel using a polarizable force field. We not only observed the conformational change of the voltage sensing domain from resting to preactive state, but also rigorously estimated the free energy profile along the identified reaction pathway. Comparison with the control simulation using an additive force field indicates that voltage-gating thermodynamics of Na_V channels may be inaccurately described without considering the electrostatic polarization effect.

On the role of water density fluctuations in the inhibition of a proton channel

Hv1 is a transmembrane four-helix bundle that transports protons in a voltage-controlled manner. Its crucial role in many pathological conditions, including cancer and ischemic brain damage, makes Hv1 a promising drug target. Starting from the recently solved crystal structure of Hv1, we used structural modeling and molecular dynamics simulations to characterize the channel's most relevant conformations along the activation cycle. We then performed computational docking of known Hv1 inhibitors, 2-guanidinobenzimidazole (2GBI) and analogs. Although salt-bridge patterns and electrostatic potential profiles are well-defined and distinctive features of activated versus nonactivated states, the water distribution along the channel lumen is dynamic and reflects a conformational heterogeneity inherent to each state. In fact, pore waters assemble into intermittent hydrogen-bonded clusters that are replaced by the inhibitor moieties upon ligand binding. The entropic gain resulting from releasing these conformationally restrained waters to the bulk solvent is likely a major contributor to the binding free energy. Accordingly, we mapped the water density fluctuations inside the pore of the channel and identified the regions of maximum fluctuation within putative binding sites. Two sites appear as outstanding: One is the already known binding pocket of 2GBI, which is accessible to ligands from the intracellular side; the other is a site located at the exit of the proton permeation pathway. Our analysis of the waters confined in the hydrophobic cavities of Hv1 suggests a general strategy for drug discovery that can be applied to any ion channel.

Regulation of KCNQ/Kv7 family voltage-gated K+ channels by lipids

Many years of studies have established that lipids can impact membrane protein structure and function through bulk membrane effects, by direct but transient annular interactions with the bilayer-exposed surface of protein transmembrane domains, and by specific binding to protein sites. Here, we focus on how phosphatidylinositol 4,5-bisphosphate (PIP₂) and polyunsaturated fatty acids (PUFAs) impact ion channel function and how the structural details of the interactions of these lipids with ion channels are beginning to emerge. We focus on the Kv7 (KCNQ) subfamily of voltage-gated K⁺ channels, which are regulated by both PIP₂ and PUFAs and play a variety of important roles in human health and disease. This article is part of a Special Issue entitled: Lipid order/lipid defects and lipid-control of protein activity edited by Dirk Schneider.

Lévy-noise-induced transport in a rough triple-well potential

Rough energy landscape and noisy environment are two common features in many subjects, such as protein folding. Due to the wide findings of bursting or spiking phenomenon in biology science, small diffusions mixing large jumps are adopted to model the noisy environment that can be properly described by Lévy noise. We combine the Lévy noise with the rough energy landscape, modeled by a potential function superimposed by a fast oscillating function, and study the transport of a particle in a rough triple-well potential excited by Lévy noise, rather than only small perturbations. The probabilities of a particle staying in the middle well are considered under different amplitudes of roughness to find out how roughness affects the steady-state probability density function. Variations in the mean first passage time from the middle well to the right well have been investigated with respect to Lévy parameters and amplitudes of the roughness. In addition, we have examined the influences of roughness on the splitting probabilities of the first escape from the middle well. We uncover that the roughness can enhance significantly the first escape of a particle from the middle well, especially for different skewness parameters, but weak differences are found for stability index and noise intensity on the probabilities a particle staying in the middle well and splitting probability to the right.

Voltage-sensor conformation shapes the intra-membrane drug binding site that determines gambierol affinity in Kv channels

Marine ladder-shaped polyether toxins are implicated in neurological symptoms of fish-borne food poisonings. The toxin gambierol, produced by the marine dinoflagellate Gambierdiscus toxicus, belongs to the group of ladder-shaped polyether toxins and inhibits Kv3.1 channels with nanomolar affinity through a mechanism of gating modification. Binding determinants for gambierol localize at the lipid-exposed interface of the pore forming S5 and S6 segments, suggesting that gambierol binds outside of the permeation pathway. To explore a possible involvement of the voltage-sensing domain (VSD), we made different chimeric channels between Kv3.1 and Kv2.1, exchanging distinct parts of the gating machinery. Our results showed that neither the electro-mechanical coupling nor the S1-S3a region of the VSD affect gambierol sensitivity. In contrast, the S3b-S4 part of the VSD (paddle motif) decreased gambierol sensitivity in Kv3.1 more than 100-fold. Structure determination by homology modeling indicated that the position of the S3b-S4 paddle and its primary structure defines the shape and∖or the accessibility of the binding site for gambierol, explaining the observed differences in gambierol affinity between the channel chimeras. Furthermore, these findings explain the observed difference in gambierol affinity for the closed and open channel configurations of Kv3.1, opening new possibilities for exploring the VSDs as selectivity determinants in drug design.

The molecular mechanism of secondary sodium symporters elucidated through the lens of the computational microscope

Transport of molecules across cellular membranes is a key biological process for normal cell function. In this review we describe current state-of-the-art knowledge on molecular mechanism of secondary active transporters obtained by molecular simulations studies.

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.

Theoretical and simulation studies on voltage-gated sodium channels

Voltage-gated sodium (Na_v) channels are indispensable membrane elements for the generation and propagation of electric signals in excitable cells. The successes in the crystallographic studies on prokaryotic Na_v channels in recent years greatly promote the mechanistic investigation of these proteins and their eukaryotic counterparts. In this paper, we mainly review the progress in computational studies, especially the simulation studies, on these proteins in the past years.