Molecular dynamics simulations of membrane proteins under asymmetric ionic concentrations

Molecular permeation through large pore channels: computational approaches and insights

Computational methods such as molecular dynamics (MD) have illuminated how single-atom ions permeate membrane channels and how selectivity among them is achieved. Much less is understood about molecular permeation through eukaryotic channels that mediate the flux of small molecules (e.g. connexins, pannexins, LRRC8s, CALHMs). Here we describe computational methods that have been profitably employed to explore the movements of molecules through wide pores, revealing mechanistic insights, guiding experiments, and suggesting testable hypotheses. This review illustrates MD techniques such as voltage-driven flux, potential of mean force, and mean first-passage-time calculations, as applied to molecular permeation through wide pores. These techniques have enabled detailed and quantitative modeling of molecular interactions and movement of permeants at the atomic level. We highlight novel contributors to the transit of molecules through these wide pathways. In particular, the flexibility and anisotropic nature of permeant molecules, coupled with the dynamics of pore-lining residues, lead to bespoke permeation dynamics. As more eukaryotic large-pore channel structures and functional data become available, these insights and approaches will be important for understanding the physical principles underlying molecular permeation and as guides for experimental design.

Generating Concentration Gradients across Membranes for Molecular Dynamics Simulations of Periodic Systems

The plasma membrane forms the boundary between a living entity and its environment and acts as a barrier to permeation and flow of substances. Several computational means of calculating permeability have been implemented for molecular dynamics (MD) simulations-based approaches. Except for double bilayer systems, most permeability studies have been performed under equilibrium conditions, in large part due to the challenges associated with creating concentration gradients in simulations utilizing periodic boundary conditions. To enhance the scientific understanding of permeation and complement the existing computational means of characterizing membrane permeability, we developed a non-equilibrium method that enables the generation and maintenance of steady-state gradients in MD simulations. We utilize PBCs advantageously by imposing a directional bias to the motion of permeants so that their crossing of the boundary replenishes the gradient, like a previous study on ions. Under these conditions, a net flow of permeants across membranes may be observed to determine bulk permeability by a direct application of J=PΔc. In the present study, we explore the results of its application to an exemplary O2 and POPC bilayer system, demonstrating accurate and precise permeability measurements. In addition, we illustrate the impact of permeant concentration and the choice of thermostat on the permeability. Moreover, we demonstrate that energetics of permeation can be closely examined by the dissipation of the gradient across the membrane to gain nuanced insights into the thermodynamics of permeability.

Non-equilibrium molecular dynamics of steady-state fluid transport through a 2D membrane driven by a concentration gradient

We use a novel non-equilibrium algorithm to simulate steady-state fluid transport through a two-dimensional (2D) membrane due to a concentration gradient by molecular dynamics (MD) for the first time. We confirm that, as required by the Onsager reciprocal relations in the linear-response regime, the solution flux obtained using this algorithm agrees with the excess solute flux obtained from an established non-equilibrium MD algorithm for pressure-driven flow. In addition, we show that the concentration-gradient-driven solution flux in this regime is quantified far more efficiently by explicitly applying a transmembrane concentration difference using our algorithm than by applying Onsager reciprocity to pressure-driven flow. The simulated fluid fluxes are captured with reasonable quantitative accuracy by our previously derived continuum theory of concentration-gradient-driven fluid transport through a 2D membrane [D. J. Rankin, L. Bocquet, and D. M. Huang, J. Chem. Phys. 151, 044705 (2019)] for a wide range of solution and membrane parameters, even though the simulated pore sizes are only several times the size of the fluid particles. The simulations deviate from the theory for strong solute-membrane interactions relative to thermal energy, for which the theoretical approximations breakdown. Our findings will be beneficial for a molecular-level understanding of fluid transport driven by concentration gradients through membranes made from 2D materials, which have diverse applications in energy harvesting, molecular separations, and biosensing.

Molecular dynamics analyses of CLDN15 pore size and charge selectivity

The Claudin-15 (CLDN15) channel is important for nutrient, electrolyte, and water transport in the gastrointestinal tract. We used cell culture studies and molecular dynamics simulations to elucidate its structure and permeability mechanisms. We provide a model that underscores the crucial role of the D55 residue in the CLDN15 selectivity filter, which interacts with permeating cations. Our studies demonstrated the mechanisms whereby the size and charge of the D55 residue influence paracellular permeability. By altering D55 to larger, negatively charged glutamic acid (E) or similarly sized neutral asparagine (N), we observed changes in pore size and selectivity, respectively. D55E mutation decreased pore size, favoring small ion permeability without affecting charge selectivity, while D55N mutation led to reduced charge selectivity without markedly altering size selectivity. These findings shed light on the complex interplay of size and charge selectivity of CLDN15 channels. This knowledge can inform the development of strategies to modulate the function of CLDN15 and similar channels, which has implications for tight junction modulation in health and disease.

Molecular dynamics simulation of phosphatidylcholine membrane in low ionic strengths of sodium chloride

The one-microsecond molecular dynamics simulations of a membrane-protein complex investigate the influence of the aqueous sodium chloride solutions on the structure and dynamics of a palmitoyl-oleoyl-phosphatidylcholine bilayer membrane. The simulations were performed on five different concentrations (40, 150, 200, 300, and 400 mM) in addition to a salt-free system by using the charmm36 force field for all atoms. Four biophysical parameters, (membrane thicknesses of annular and bulk lipids, and the area per lipid of both leaflets), were computed separately. Nevertheless, the area per lipid was expressed by using the Voronoi algorithm. All time-independent analyses were carried out for the last 400 ns trajectories. Different concentrations revealed dissimilar membrane dynamics before equilibration. The biophysical properties of the membrane (thickness, area-per-lipid, and order parameter) have non-significant changes with increasing ionic strength, however, the 150 mM system had exceptional behavior. Sodium cations were dynamically penetrating the membrane forming weak coordinate bonds with single or multiple lipids. Nevertheless, the binding constant was unaffected by the cation concentration. The electrostatic and Van der Waals energies of lipid-lipid interactions were influenced by the ionic strength. On the other hand, the Fast Fourier Transform was performed to figure out the dynamics at the membrane-protein interface. The nonbonding energies of membrane-protein interactions and order parameters explained the differences in the synchronization pattern. All results were consensus with experimental and theoretical works.Communicated by Ramaswamy H. Sarma.

Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux

Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.

Computational methods and theory for ion channel research

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

Capturing Membrane Phase Separation by Dual Resolution Molecular Dynamics Simulations

Understanding the lateral organization in plasma membranes remains an open problem and is of great interest to many researchers. Model membranes consisting of coexisting domains are commonly used as simplified models of plasma membranes. The coarse-grained (CG) Martini force field has successfully captured spontaneous separation of ternary membranes into a liquid-disordered and a liquid-ordered domain. With all-atom (AA) models, however, phase separation is much harder to achieve due to the slow underlying dynamics. To remedy this problem, here, we apply the virtual site (VS) hybrid method on a ternary membrane composed of saturated lipids, unsaturated lipids, and cholesterol to investigate the phase separation. The VS scheme couples the two membrane leaflets at CG and AA resolution. We found that the rapid phase separation reached by the CG leaflet can accelerate and guide this process in the AA leaflet.

Ion Conduction Mechanism as a Fingerprint of Potassium Channels

K⁺-channels are membrane proteins that regulate the selective conduction of potassium ions across cell membranes. Although the atomic mechanisms of K⁺ permeation have been extensively investigated, previous work focused on characterizing the selectivity and occupancy of the binding sites, the role of water molecules in the conduction process, or the identification of the minimum energy pathways enabling permeation. Here, we exploit molecular dynamics simulations and the analytical power of Markov state models to perform a comparative study of ion conduction in three distinct channel models. Significant differences emerged in terms of permeation mechanisms and binding site occupancy by potassium ions and/or water molecules from 100 μs cumulative trajectories. We found that, at odds with the current paradigm, each system displays a characteristic permeation mechanism, and thus, there is not a unique way by which potassium ions move through K⁺-channels. The high functional diversity of K⁺-channels can be attributed in part to the differences in conduction features that have emerged from this work. This study provides crucial information and further inspiration for wet-lab chemists designing new synthetic strategies to produce versatile artificial ion channels that emulate membrane transport for their applications in diagnosis, sensors, the next generation of water treatment technologies, etc., as the ability of synthetic channels to transport molecular ions across a bilayer in a controlled way is usually governed through the choice of metal ions, their oxidation states, or their coordination geometries.

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

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

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

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

Identification of inhibitor binding hotspots in Acinetobacter baumannii β-ketoacyl acyl carrier protein synthase III using molecular dynamics simulation

Acinetobacter baumannii is a gram-negative bacterium that is rapidly developing drug resistance due to the abuse of antibiotics. The emergence of multidrug-resistant A. baumannii has greatly contributed to the urgency of developing new antibiotics. Previously, we had discovered two potent inhibitors of A. baumannii β-ketoacyl acyl carrier protein synthase III (abKAS III), YKab-4 and YKab-6, which showed potent activity against A. baumannii. In addition, we have reported the crystal structure of abKAS III. In the present study, we investigated the binding between abKAS III and its inhibitors by docking simulation. Molecular dynamics (MD) simulations were performed using docked inhibitor models to identify the hotspot residues related to inhibitor binding. The binding free energies estimated using the MD simulations suggest that residues I198 and F260 of abKAS III serve as the inhibitor binding hotspots. I198, found to be responsible for mediating hydrophobic interactions with inhibitors, had the strongest residual binding energy among all abKAS III residues. We modeled glutamine substitutions of residues I198 and F260 and estimated the relative binding energies of the I198Q and F260Q variants. The results confirmed that I198 and F260 are the key inhibitor binding residues. The roles of the key residues in inhibitor binding, i.e. F260 in the α9 helix and the I198 in the β6β7 loop region, were investigated using principal component analysis (PCA). PCA revealed the structural changes resulting from the abKAS III I198Q and F260Q mutations and described the essential dynamics of the α9 helix. In addition, the results suggest that the β6β7 loop region may act as a gate keeper for ligand binding. Hydrophobic interactions involving I198 and F260 in abKAS III appear to be essential for the binding of the inhibitors YKab-4 and YKab-6. In conclusion, this study provides valuable information for the rational design of antibiotics via the inhibition of abKAS III.

Dual Resolution Membrane Simulations Using Virtual Sites

All-atomistic (AA) and coarse-grain (CG) simulations have been successfully applied to investigate a broad range of biomolecular processes. However, the accessible time and length scales of AA simulation are limited and the specific molecular details of CG simulation are simplified. Here, we propose a virtual site (VS) based hybrid scheme that can concurrently couple AA and CG resolutions in a single membrane simulation, mitigating the shortcomings of either representation. With some adjustments to make the AA and CG force fields compatible, we demonstrate that lipid bilayer properties are well kept in our hybrid approach. Our VS hybrid method was also applied to simulate a small lipid vesicle, with the inner leaflet and interior solvent represented in AA, and the outer leaflet together with exterior solvent at the CG level. Our multiscale method opens the way to investigate biomembrane properties at increased computational efficiency, in particular applications involving large solvent filled regions.

Large-Scale Conformational Changes and Protein Function: Breaking the in silico Barrier

Large-scale conformational changes are essential to link protein structures with their function at the cell and organism scale, but have been elusive both experimentally and computationally. Over the past few years developments in cryo-electron microscopy and crystallography techniques have started to reveal multiple snapshots of increasingly large and flexible systems, deemed impossible only short time ago. As structural information accumulates, theoretical methods become central to understand how different conformers interconvert to mediate biological function. Here we briefly survey current in silico methods to tackle large conformational changes, reviewing recent examples of cross-validation of experiments and computational predictions, which show how the integration of different scale simulations with biological information is already starting to break the barriers between the in silico, in vitro, and in vivo worlds, shedding new light onto complex biological problems inaccessible so far.

Atomistic modeling and molecular dynamics analysis of human CaV1.2 channel using external electric field and ion pulling simulations

BACKGROUND

Human Ca_V1.2 (hCav1.2), a calcium selective voltage-gated channel, plays important roles in normal cardiac and neuronal functions. Calcium influx and gating mechanisms leading to the activation of hCa_V1.2 are critical for its functionalities. Lack of an experimentally resolved structure of hCa_V1.2 remains a significant impediment in molecular-level understanding of this channel. This work focuses on building atomistic hCa_V1.2 model and studying calcium influx using computational approaches.

METHODS

We employed homology modeling and molecular dynamics (MD) to build the structure of hCa_V1.2. Subsequently, we employed steered molecular dynamics (SMD) to understand calcium ion permeation in hCa_V1.2.

RESULTS

We report a comprehensive three-dimensional model of a closed state hCa_V1.2 refined under physiological membrane-bound conditions using MD simulations. Our SMD simulations on the model revealed four important barriers for ion permeation: this includes three calcium binding sites formed by the EEEE- and TTTT- rings within the selectivity filter region and a large barrier rendered by the hydrophobic internal gate. Our results also revealed that the first hydration shell of calcium remained intact throughout the simulations, thus playing an important role in ion permeation in hCa_V1.2.

CONCLUSIONS

Our results have provided some important mechanistic insights into the structure, dynamics and ion permeation in hCa_V1.2. The significant barriers for ion permeation formed by the four phenylalanine residues at the internal gate region suggest that this site is important for channel activation.

Membrane Protein-Lipid Interactions Probed Using Mass Spectrometry

Membrane proteins that exist in lipid bilayers are not isolated molecular entities. The lipid molecules that surround them play crucial roles in maintaining their full structural and functional integrity. Research directed at investigating these critical lipid-protein interactions is developing rapidly. Advancements in both instrumentation and software, as well as in key biophysical and biochemical techniques, are accelerating the field. In this review, we provide a brief outline of structural techniques used to probe protein-lipid interactions and focus on the molecular aspects of these interactions obtained from native mass spectrometry (native MS). We highlight examples in which lipids have been shown to modulate membrane protein structure and show how native MS has emerged as a complementary technique to X-ray crystallography and cryo-electron microscopy. We conclude with a short perspective on future developments that aim to better understand protein-lipid interactions in the native environment.

Calculating Single-Channel Permeability and Conductance from Transition Paths

Permeability and conductance are the major transport properties of membrane channels, quantifying the rate of channel crossing by the solute. It is highly desirable to calculate these quantities in all-atom molecular dynamics simulations. When the solute crossing rate is low, however, direct methods would require prohibitively long simulations, and one thus typically adopts alternative strategies based on the free energy of single solute along the channel. Here we present a new method to calculate the crossing rate by initiating unbiased trajectories in which the solute is released at the free energy barrier. In this method, the total time the solute spends in the barrier region during a channel crossing (transition path) is used to determine the kinetic rate. Our method achieves a significantly higher statistical accuracy than the classical reactive flux method, especially for diffusive barrier crossing. Our test on ion permeation through a carbon nanotube verifies that the method correctly predicts the crossing rate and reproduces the spontaneous crossing events as in long equilibrium simulations. The rigorous and efficient method here will be valuable for quantitatively connecting simulations to experimental measurement of membrane channels.

Molecular Mechanism of Conductance Enhancement in Narrow Cation-Selective Membrane Channels

Membrane proteins known as ryanodine receptors (RyRs) display large conductance of ∼1 nS and nearly ideal charge selectivity. Both properties are inversely correlated in other large-conductance but nonselective biological nanopores (i.e., α-hemolysin) used as industrial biosensors. Although recent cryo-electron microscopy structures of RyR2 show similarities to K⁺- and Na⁺-selective channels, it remains unclear whether similar ion conduction mechanisms occur in RyR2. Here, we combine microseconds of all-atom molecular dynamics (MD) simulations with mutagenesis and electrophysiology experiments to investigate large K⁺ conductance and charge selectivity (cation vs anion) in an open-state structure of RyR2. Our results show that a water-mediated knock-on mechanism enhances the cation permeation. The polar Q4863 ring may function as a confinement zone amplifying charge selectivity, while the cytoplasmic vestibule can contribute to the efficiency of the cation attraction. We also provide direct evidence that the rings of acidic residues at the channel vestibules are critical for both conductance and charge discrimination in RyRs.

Molecular determination of claudin-15 organization and channel selectivity

Members of the claudin family form tight junctions between adjacent epithelial and endothelial cells. Samanta et al. build an atomic model of claudin-15 using molecular dynamics simulations and conclude that four claudin-15 molecules each contribute an aspartic acid residue to form a selectivity filter.

Tight junctions are macromolecular structures that traverse the space between adjacent cells in epithelia and endothelia. Members of the claudin family are known to determine tight junction permeability in a charge- and size-selective manner. Here, we use molecular dynamics simulations to build and refine an atomic model of claudin-15 channels and study its transport properties. Our simulations indicate that claudin-15 forms well-defined channels for ions and molecules and otherwise “seals” the paracellular space through hydrophobic interactions. Ionic currents, calculated from simulation trajectories of wild-type as well as mutant channels, reflect in vitro measurements. The simulations suggest that the selectivity filter is formed by a cage of four aspartic acid residues (D55), contributed by four claudin-15 molecules, which creates a negative electrostatic potential to favor cation flux over anion flux. Charge reversal or charge ablation mutations of D55 significantly reduce cation permeability in silico and in vitro, whereas mutations of other negatively charged pore amino acid residues have a significantly smaller impact on channel permeability and selectivity. The simulations also indicate that water and small ions can pass through the channel, but larger cations, such as tetramethylammonium, do not traverse the pore. Thus, our model provides an atomic view of claudin channels, their transport function, and a potential three-dimensional organization of its selectivity filter.

Ion-triggered selectivity in bacterial sodium channels

Since the availability of the first crystal structure of a bacterial Na⁺ channel in 2011, understanding selectivity across this family of membrane proteins has been the subject of intense research efforts. Initially, free energy calculations based on molecular dynamics simulations revealed that although sodium ions can easily permeate the channel with their first hydration shell almost intact, the selectivity filter is too narrow for efficient conduction of hydrated potassium ions. This steric view of selectivity was subsequently questioned by microsecond atomic trajectories, which proved that the selectivity filter appears to the permeating ions as a highly degenerate, liquid-like environment. Although this liquid-like environment looks optimal for rapid conduction of Na⁺, it seems incompatible with efficient discrimination between similar ion species, such as Na⁺ and K⁺, through steric effects. Here extensive molecular dynamics simulations, combined with Markov state model analyses, reveal that at positive membrane potentials, potassium ions trigger a conformational change of the selectivity toward a nonconductive metastable state. It is this transition of the selectivity filter, and not steric effects, that prevents the outward flux of K⁺ at positive membrane potentials. This description of selectivity, triggered by the nature of the permeating ions, might have implications on the current understanding of how ion channels, and in particular bacterial Na⁺ channels, operate at the atomic scale.

In silico assessment of the conduction mechanism of the Ryanodine Receptor 1 reveals previously unknown exit pathways

The ryanodine receptor 1 is a large calcium ion channel found in mammalian skeletal muscle. The ion channel gained a lot of attention recently, after multiple independent authors published near-atomic cryo electron microscopy data. Taking advantage of the unprecedented quality of structural data, we performed molecular dynamics simulations on the entire ion channel as well as on a reduced model. We calculated potentials of mean force for Ba2+, Ca2+, Mg2+, K+, Na+ and Cl- ions using umbrella sampling to identify the key residues involved in ion permeation. We found two main binding sites for the cations, whereas the channel is strongly repulsive for chloride ions. Furthermore, the data is consistent with the model that the receptor achieves its ion selectivity by over-affinity for divalent cations in a calcium-block-like fashion. We reproduced the experimental conductance for potassium ions in permeation simulations with applied voltage. The analysis of the permeation paths shows that ions exit the pore via multiple pathways, which we suggest to be related to the experimental observation of different subconducting states.

Ampicillin permeation across OmpF, the major outer-membrane channel in Escherichia coli

The outer cell wall of the Gram-negative bacteria is a crucial barrier for antibiotics to reach their target. Here, we show that the chemical stability of the widely used antibiotic ampicillin is a major factor in the permeation across OmpF to reach the target in the periplasm. Using planar lipid bilayers we investigated the interactions and permeation of OmpF with ampicillin, its basic pH-induced primary degradation product (penicilloic acid), and the chemically more stable benzylpenicillin. We found that the solute-induced ion current fluctuation is 10 times higher with penicilloic acid than with ampicillin. Furthermore, we also found that ampicillin can easily permeate through OmpF, at an ampicillin gradient of 10 μm and a conductance of G_amp ≅ 3.8 fS, with a flux rate of roughly 237 molecules/s of ampicillin at V_m = 10 mV. The structurally related benzylpenicillin yields a lower conductance of G_amp ≅ 2 fS, corresponding to a flux rate of ≈120 molecules/s. In contrast, the similar sized penicilloic acid was nearly unable to permeate through OmpF. MD calculations show that, besides their charge difference, the main differences between ampicillin and penicilloic acid are the shape of the molecules, and the strength and direction of the dipole vector. Our results show that OmpF can impose selective permeation on similar sized molecules based on their structure and their dipolar properties.

Exploring the Membrane Potential of Simple Dual-Membrane Systems as Models for Gap-Junction Channels

The conductance of ion channels can be modulated by a transmembrane potential difference, due to alterations on ion-mobility and also by changes in the pore structure. Despite the vast knowledge regarding the influence of voltage on transport properties of ion channels, little attention has been paid to describe, with atomic detail, the modulation of ionic transport in gap-junction channels (GJCs). Hence, molecular dynamics simulations were performed to explore the conductance of simple dual-membrane systems that account for the very basic features of GJCs. In doing so, we studied the influence of different charge distributions in the channel surface on these idealized systems under external electric fields, paying attention to the behavior of the electrostatic potential, ion density, ion currents, and equilibrium properties. Our results demonstrate that the incorporation of a charge distribution akin GJCs decreased anionic currents, favoring the transport of cationic species. Moreover, a thermodynamic characterization of ionic transport in these systems demonstrate the existence of a kinetic barrier that hinders anionic currents, reinforcing the role played by the internal arrangement of charges in GJCs. Overall, our results provide insights at the atomic scale on the effects of charge distributions over ionic transport, constituting a step forward into a better understanding of GJCs.

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

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

Simulating Current-Voltage Relationships for a Narrow Ion Channel Using the Weighted Ensemble Method

Ion channels are responsible for a myriad of fundamental biological processes via their role in controlling the flow of ions through water-filled membrane-spanning pores in response to environmental cues. Molecular simulation has played an important role in elucidating the mechanism of ion conduction, but connecting atomistically detailed structural models of the protein to electrophysiological measurements remains a broad challenge due to the computational cost of reaching the necessary time scales. Here, we introduce an enhanced sampling method for simulating the conduction properties of narrow ion channels using the Weighted ensemble (WE) sampling approach. We demonstrate the application of this method to calculate the current–voltage relationship as well as the nonequilibrium ion distribution at steady-state of a simple model ion channel. By direct comparisons with long brute force simulations, we show that the WE simulations rigorously reproduce the correct long-time scale kinetics of the system and are capable of determining these quantities using significantly less aggregate simulation time under conditions where permeation events are rare.

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

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

Multilevel summation method for electrostatic force evaluation

The multilevel summation method (MSM) offers an efficient algorithm utilizing convolution for evaluating long-range forces arising in molecular dynamics simulations. Shifting the balance of computation and communication, MSM provides key advantages over the ubiquitous particle–mesh Ewald (PME) method, offering better scaling on parallel computers and permitting more modeling flexibility, with support for periodic systems as does PME but also for semiperiodic and nonperiodic systems. The version of MSM available in the simulation program NAMD is described, and its performance and accuracy are compared with the PME method. The accuracy feasible for MSM in practical applications reproduces PME results for water property calculations of density, diffusion constant, dielectric constant, surface tension, radial distribution function, and distance-dependent Kirkwood factor, even though the numerical accuracy of PME is higher than that of MSM. Excellent agreement between MSM and PME is found also for interface potentials of air–water and membrane–water interfaces, where long-range Coulombic interactions are crucial. Applications demonstrate also the suitability of MSM for systems with semiperiodic and nonperiodic boundaries. For this purpose, simulations have been performed with periodic boundaries along directions parallel to a membrane surface but not along the surface normal, yielding membrane pore formation induced by an imbalance of charge across the membrane. Using a similar semiperiodic boundary condition, ion conduction through a graphene nanopore driven by an ion gradient has been simulated. Furthermore, proteins have been simulated inside a single spherical water droplet. Finally, parallel scalability results show the ability of MSM to outperform PME when scaling a system of modest size (less than 100 K atoms) to over a thousand processors, demonstrating the suitability of MSM for large-scale parallel simulation.

Computational studies of transport in ion channels using metadynamics

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

Insights into the function of ion channels by computational electrophysiology simulations

Ion channels are of universal importance for all cell types and play key roles in cellular physiology and pathology. Increased insight into their functional mechanisms is crucial to enable drug design on this important class of membrane proteins, and to enhance our understanding of some of the fundamental features of cells. This review presents the concepts behind the recently developed simulation protocol Computational Electrophysiology (CompEL), which facilitates the atomistic simulation of ion channels in action. In addition, the review provides guidelines for its application in conjunction with the molecular dynamics software package GROMACS. We first lay out the rationale for designing CompEL as a method that models the driving force for ion permeation through channels the way it is established in cells, i.e., by electrochemical ion gradients across the membrane. This is followed by an outline of its implementation and a description of key settings and parameters helpful to users wishing to set up and conduct such simulations. In recent years, key mechanistic and biophysical insights have been obtained by employing the CompEL protocol to address a wide range of questions on ion channels and permeation. We summarize these recent findings on membrane proteins, which span a spectrum from highly ion-selective, narrow channels to wide diffusion pores. Finally we discuss the future potential of CompEL in light of its limitations and strengths. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Simulations of outer membrane channels and their permeability

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

LipidBuilder: A Framework To Build Realistic Models for Biological Membranes

The physical and chemical characterization of biological membranes is of fundamental importance for understanding the functional role of lipid bilayers in shaping cells and organelles, steering vesicle trafficking and promoting membrane-protein signaling. Molecular dynamics simulations stand as a powerful tool to probe the properties of membranes at atomistic level. However, the biological membrane is highly complex, and closely mimicking its physiological constitution in silico is not a straightforward task. Here, we present LipidBuilder, a framework for creating and storing models of biologically relevant phospholipid species with acyl tails of heterogeneous composition. LipidBuilder also enables the assembly of these database-stored lipids into realistic bilayers featuring asymmetric distribution on layer leaflets and concentration of given membrane constituents as defined, for example, by lipidomics experiments. The ability of LipidBuilder to assemble robust membrane models was validated by simulating membranes of homogeneous lipid composition for which experimental data are available. Furthermore, taking advantage of the extensive lipid headgroup repertoire, we assembled models of membranes of heterogeneous nature as naturally found in viral (phage PRD1), bacterial (Salmonella enterica, Laurinavicius , S. ; Kakela , R. ; Somerharju , P. ; Bamford , D. H. ; Virology 2004 , 322 , 328 - 336 ) and plant (Chlorella kessleri, Rezanka , T. ; Podojil , M. ; J. Chromatogr. 1989 , 463 , 397 - 408 ) organisms. These realistic membrane models were built using a near-exact lipid composition revealed from analytical chemistry experiments. We suggest LipidBuilder as a useful tool to model biological membranes of near-biological complexity, and as a robust complement to the current efforts to characterize the biophysical properties of biological membrane using molecular simulation.

Interfacial water screens the protein-induced transmembrane voltage

Transmembrane proteins are crucial in cellular traffic, signal transduction, and energy storage in a form of transmembrane voltage. These proteins are stabilized by hydrophobic and hydrophilic interactions, in which cytoplasmic and exoplasmic water plays a special role. Water structural ordering generates the dipole potential that typically overcompensates for an intrinsic membrane-protein potential gradient, and thus it modifies and sustains an overall cellular electrostatics. Although the transmembrane voltage has been extensively studied, the dipole potential has attracted very little attention. Here, by using molecular dynamics, we examined water electrostatic response to the transmembrane charge, field, and potential asymmetry introduced by the presence of four integral membrane proteins: typical of inner (α-helix) and outer membrane (β-barrel). In all cases, the protein presence introduces electrostatic directionality in the transmembrane dipole field and voltage. In particular, water generates a deep potential sink if strongly polar residues are densely packed on one side of bilayer, as frequently occurs in a selectivity filter of the K(+) channel. We also found that protein secondary structure is less important than the polar residue distribution along the protein channel. Our findings are relevant for understanding the driving force behind biomembrane conductivity: the ability of biological water to electrostatically screen the transmembrane voltage.

Computational modeling of membrane proteins

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

A structural study of ion permeation in OmpF porin from anomalous X-ray diffraction and molecular dynamics simulations

OmpF, a multiionic porin from Escherichia coli, is a useful protypical model system for addressing general questions about electrostatic interactions in the confinement of an aqueous molecular pore. Here, favorable anion locations in the OmpF pore were mapped by anomalous X-ray scattering of Br(–) ions from four different crystal structures and compared with Mg(2+) sites and Rb(+) sites from a previous anomalous diffraction study to provide a complete picture of cation and anion transfer paths along the OmpF channel. By comparing structures with various crystallization conditions, we find that anions bind in discrete clusters along the entire length of the OmpF pore, whereas cations find conserved binding sites with the extracellular, surface-exposed loops. Results from molecular dynamics simulations are consistent with the experimental data and help highlight the critical residues that preferentially contact either cations or anions during permeation. Analysis of these results provides new insights into the molecular mechanisms that determine ion selectivity in OmpF porin.