Molecular dynamics and brownian dynamics investigation of ion permeation and anesthetic halothane effects on a proton-gated ion channel

Effect of Terahertz Electromagnetic Field on the Permeability of Potassium Channel Kv1.2

In this paper, the influence of external terahertz electromagnetic fields with different frequencies of 4 THz, 10 THz, 15 THz, and 20 THz on the permeability of the Kv1.2 voltage-gated potassium ion channel on the nerve cell membrane was studied using the combined model of the "Constant Electric Field-Ion Imbalance" method by molecular dynamics. We found that although the applied terahertz electric field does not produce strong resonance with the -C=O groups of the conservative sequence T-V-G-Y-G amino acid residue of the selective filter (SF) of the channel, it would affect the stability of the electrostatic bond between potassium ions and the carbonyl group of T-V-G-Y-G of SF, and it would affect the stability of the hydrogen bond between water molecules and oxygen atoms of the hydroxyl group of the 374THR side chain at the SF entrance, changing the potential and occupied states of ions in the SF and the occurrence probability of the permeation mode of ions and resulting in the change in the permeability of the channel. Compared with no external electric field, when the external electric field with 15 THz frequency is applied, the lifetime of the hydrogen bond is reduced by 29%, the probability of the "soft knock on" mode is decreased by 46.9%, and the ion flux of the channel is activated by 67.7%. Our research results support the view that compared to "direct knock-on", "soft knock-on" is a slower permeation mode.

Regulation of Ion Permeation of the KcsA Channel by Applied Midinfrared Field

Ion transport molecules are involved in many physiological and pathological processes and are considered potential targets for cancer treatment. In the large family of ion transport molecules, potassium (K) ion channels, as surface-expressed proteins, show the highest variability and most frequent expression changes in many tumor types. The key to exploring the permeation of K⁺ through potassium channels lies in the conserved sequence TVGYG, which is common in the selectivity filter (SF) region of all potassium channels. We found that the K⁺ flux significantly increased with the help of a specific frequency terahertz electromagnetic wave (51.87 THz) in the KcsA channel using a molecular dynamics combined model through the combined simulation of the constant electric field method and ion imbalance method. This frequency has the strongest absorption peak in the infrared spectrum of -C=O groups in the SF region. With the applied electric field of 51.87 THz, the Y78 residue at the S₁ site of the SF has a smaller vibration amplitude and a more stable structure, which enables the K⁺ to bind closely with the carbonyl oxygen atoms in the SF and realize ion conduction in a more efficient direct Coulomb knock-on.

Markov state models of proton- and pore-dependent activation in a pentameric ligand-gated ion channel

Ligand-gated ion channels conduct currents in response to chemical stimuli, mediating electrochemical signaling in neurons and other excitable cells. For many channels, the details of gating remain unclear, partly due to limited structural data and simulation timescales. Here, we used enhanced sampling to simulate the pH-gated channel GLIC, and construct Markov state models (MSMs) of gating. Consistent with new functional recordings, we report in oocytes, our analysis revealed differential effects of protonation and mutation on free-energy wells. Clustering of closed- versus open-like states enabled estimation of open probabilities and transition rates, while higher-order clustering affirmed conformational trends in gating. Furthermore, our models uncovered state- and protonation-dependent symmetrization. This demonstrates the applicability of MSMs to map energetic and conformational transitions between ion-channel functional states, and how they reproduce shifts upon activation or mutation, with implications for modeling neuronal function and developing state-selective drugs.

Mutational analysis to explore long-range allosteric couplings involved in a pentameric channel receptor pre-activation and activation

Pentameric ligand-gated ion channels (pLGICs) mediate chemical signaling through a succession of allosteric transitions that are yet not completely understood as intermediate states remain poorly characterized by structural approaches. In a previous study on the prototypic bacterial proton-gated channel GLIC, we generated several fluorescent sensors of the protein conformation that report a fast transition to a pre-active state, which precedes the slower process of activation with pore opening. Here, we explored the phenotype of a series of allosteric mutations, using simultaneous steady-state fluorescence and electrophysiological measurements over a broad pH range. Our data, fitted to a three-state Monod-Wyman-Changeux model, show that mutations at the subunit interface in the extracellular domain (ECD) principally alter pre-activation, while mutations in the lower ECD and in the transmembrane domain principally alter activation. We also show that propofol alters both transitions. Data are discussed in the framework of transition pathways generated by normal mode analysis (iModFit). It further supports that pre-activation involves major quaternary compaction of the ECD, and suggests that activation involves principally a reorganization of a ‘central gating region’ involving a contraction of the ECD β-sandwich and the tilt of the channel lining M2 helix.

Elephants in the Dark: Insights and Incongruities in Pentameric Ligand-gated Ion Channel Models

The superfamily of pentameric ligand-gated ion channels (pLGICs) comprises key players in electrochemical signal transduction across evolution, including historic model systems for receptor allostery and targets for drug development. Accordingly, structural studies of these channels have steadily increased, and now approach 250 depositions in the protein data bank. This review contextualizes currently available structures in the pLGIC family, focusing on morphology, ligand binding, and gating in three model subfamilies: the prokaryotic channel GLIC, the cation-selective nicotinic acetylcholine receptor, and the anion-selective glycine receptor. Common themes include the challenging process of capturing and annotating channels in distinct functional states; partially conserved gating mechanisms, including remodeling at the extracellular/transmembrane-domain interface; and diversity beyond the protein level, arising from posttranslational modifications, ligands, lipids, and signaling partners. Interpreting pLGIC structures can be compared to describing an elephant in the dark, relying on touch alone to comprehend the many parts of a monumental beast: each structure represents a snapshot in time under specific experimental conditions, which must be integrated with further structure, function, and simulations data to build a comprehensive model, and understand how one channel may fundamentally differ from another.

Field-Dependent Dehydration and Optimal Ionic Escape Paths for C2N Membranes

Most analytic theories describing electrostatically driven ion transport through water-filled nanopores assume that the corresponding permeation barriers are bias-independent. While this assumption may hold for sufficiently wide pores under infinitely small bias, transport through subnanometer pores under finite bias is difficult to interpret analytically. Given recent advances in subnanometer pore fabrication and the rapid progress in detailed computer simulations, it is important to identify and understand the specific field-induced phenomena arising during ion transport. Here we consider an atomistic model of electrostatically driven ion permeation through subnanoporous C2N membranes. We analyze probability distributions of ionic escape trajectories and show that the optimal escape path switches between two different configurations depending on the bias magnitude. We identify two distinct mechanisms contributing to field-induced changes in transport-opposing barriers: a weak one arising from field-induced ion dehydration and a strong one due to the field-induced asymmetry of the hydration shells. The simulated current-voltage characteristics are compared with the solution of the 1D Nernst-Planck model. Finally, we show that the deviation of simulated currents from analytic estimates for large fields is consistent with the field-induced barriers and the observed changes in the optimal ion escape path.

Terahertz Wave Enhances Permeability of the Voltage-Gated Calcium Channel

A deficiency of Ca²⁺ fluxes arising from dysfunctional voltage-gated calcium channels has been associated with a list of calcium channelopathies such as epilepsy, hypokalemic periodic paralysis, episodic ataxia, etc. Apart from analyzing the pathogenic channel mutations, understanding how the channel regulates the ion conduction would be instructive to the treatment as well. In the present work, in relating the free energetics of Ca²⁺ transport to the calcium channel, we demonstrate the importance of bridging Ca²⁺ hydration waters, which form hydrogen bonds with channel -COO^- and -C═O groups and enable a long-distance effect on the Ca²⁺ permeation. By firing a terahertz wave which resonates with the stretching mode of either the -COO^- or the -C═O group, we obtain significantly enhanced selectivity and conductance of Ca²⁺. The Ca²⁺ free energy negatively grows nearly 5-fold. The direct evidence is the reinforced hydrogen bonds. In addition, thanks to forced vibrations, -COO^- contributes to raised permeation as well even under a field in resonance with -C═O, and vice versa. Since the resonant terahertz field could manipulate the conduction of calcium channels, it has potential applications in therapeutic intervention such as rectifying a Ca²⁺ deficiency in degraded calcium channels, inducing apoptosis of tumor cells with overloaded calcium etc.

Thermodynamics and Kinetics of Ion Permeation in Wild-Type and Mutated Open Active Conformation of the Human α7 Nicotinic Receptor

Molecular studies of human pentameric ligand-gated ion channels (LGICs) expressed in neurons and at neuromuscular junctions are of utmost importance in the development of therapeutic strategies for neurological disorders. We focus here on the nicotinic acetylcholine receptor nAChR-α7, a homopentameric channel widely expressed in the human brain, with a proven role in a wide spectrum of disorders including schizophrenia and Alzheimer’s disease. By exploiting an all-atom structural model of the full (transmembrane and extracellular) protein in the open, agonist-bound conformation we recently developed, we evaluate the free energy and the mean first passage time of single-ion permeation using molecular dynamics simulations and the milestoning method with Voronoi tessellation. The results for the wild-type channel provide the first available mapping of the potential of mean force in the full-length α7 nAChR, reveal its expected cationic nature, and are in good agreement with simulation data for other channels of the LGIC family and with experimental data on nAChRs. We then investigate the role of a specific mutation directly related to ion selectivity in LGICs, the E-1′ → A-1′ substitution at the cytoplasmatic selectivity filter. We find that the mutation strongly affects sodium and chloride permeation in opposite directions, leading to a complete inversion of selectivity, at variance with the limited experimental results available that classify this mutant as cationic. We thus provide structural determinants for the observed cationic-to-anionic inversion, revealing a key role of the protonation state of residue rings far from the mutation, in the proximity of the hydrophobic channel gate.

Modulation of the Gloeobacter violaceus Ion Channel by Fentanyl: A Molecular Dynamics Study

Fentanyl is an opioid analgesic, which is routinely used in general surgery to suppress the sensation of pain and as the analgesic component in the induction and maintenance of anesthesia. Fentanyl is also used as the main component to induce anesthesia and as a potentiator to the general anesthetic propofol. The mechanism by which fentanyl induces its anesthetic action is still unclear, and we have therefore employed fully atomistic molecular dynamics simulations to probe this process by simulating the interactions of fentanyl with the Gloeobacter violaceus ligand-gated ion channel (GLIC). In this paper, we identify multiple extracellular fentanyl binding sites, which are different from the transmembrane general anesthetic binding sites observed for propofol and other general anesthetics. Our simulations identify a novel fentanyl binding site within the GLIC that results in conformational changes that inhibit conduction through the channel.

Chasing the open-state structure of pentameric ligand-gated ion channels

Members of the pentameric ligand-gated ion channel family have been crystallized in different conformations, including one in which the transmembrane pore is surprisingly wide. Gonzalez-Gutierrez et al. show that the open-channel conformation of animal members is more similar to the models with narrow pores.

Remarkable advances have been made toward the structural characterization of ion channels in the last two decades. However, the unambiguous assignment of well-defined functional states to the obtained structural models has proved challenging. In the case of the superfamily of nicotinic-receptor channels (also referred to as pentameric ligand-gated ion channels [pLGICs]), for example, two different types of model of the open-channel conformation have been proposed on the basis of structures solved to resolutions better than 4.0 Å. At the level of the transmembrane pore, the open-state models of the proton-gated pLGIC from Gloeobacter violaceus (GLIC) and the invertebrate glutamate-gated Cl^– channel (GluCl) are very similar to each other, but that of the glycine receptor (GlyR) is considerably wider. Indeed, the mean distances between the axis of ion permeation and the Cα atoms at the narrowest constriction of the pore (position −2′) differ by ∼2 Å in these two classes of model, a large difference when it comes to understanding the physicochemical bases of ion conduction and charge selectivity. Here, we take advantage of the extreme open-channel stabilizing effect of mutations at pore-facing position 9′. We find that the I9′A mutation slows down entry into desensitization of GLIC to the extent that macroscopic currents decay only slightly by the end of pH 4.5 solution applications to the extracellular side for several minutes. We crystallize (at pH 4.5) two variants of GLIC carrying this mutation and solve their structures to resolutions of 3.12 Å and 3.36 Å. Furthermore, we perform all-atom molecular dynamics simulations of ion permeation and picrotoxinin block, using the different open-channel structural models. On the basis of these results, we favor the notion that the open-channel structure of pLGICs from animals is much closer to that of the narrow models (of GLIC and GluCl) than it is to that of the GlyR.

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

Ketamine Inhibition of the Pentameric Ligand-Gated Ion Channel GLIC

Ketamine inhibits pentameric ligand-gated ion channels (pLGICs), including the bacterial pLGIC from Gloeobacter violaceus (GLIC). The crystal structure of GLIC shows R-ketamine bound to an extracellular intersubunit cavity. Here, we performed molecular dynamics simulations of GLIC in the absence and presence of R- or S-ketamine. No stable binding of S-ketamine in the original cavity was observed in the simulations, largely due to its unfavorable access to residue D154, which provides important electrostatic interactions to stabilize R-ketamine binding. Contrary to the symmetric binding shown in the crystal structure, R-ketamine moved away from some of the binding sites and was bound to GLIC asymmetrically at the end of simulations. The asymmetric binding is consistent with the experimentally measured negative cooperativity of ketamine binding to GLIC. In the presence of R-ketamine, all subunits showed changes in structure and dynamics, irrespective of binding stability; the extracellular intersubunit cavity expanded and intersubunit electrostatic interactions involved in channel activation were altered. R-ketamine binding promoted a conformational shift toward closed GLIC. Conformational changes near the ketamine-binding site were propagated to the interface between the extracellular and transmembrane domains, and further to the pore-lining TM2 through two pathways: pre-TM1 and the β1-β2 loop. Both signaling pathways have been predicted previously using the perturbation-based Markovian transmission model. The study provides a structural and dynamics basis for the inhibitory modulation of ketamine on pLGICs.

A membrane-embedded pathway delivers general anesthetics to two interacting binding sites in the Gloeobacter violaceus ion channel

General anesthetics exert their effects on the central nervous system by acting on ion channels, most notably pentameric ligand-gated ion channels. Although numerous studies have focused on pentameric ligand-gated ion channels, the details of anesthetic binding and channel modulation are still debated. A better understanding of the anesthetic mechanism of action is necessary for the development of safer and more efficacious drugs. Herein, we present a computational study identifying two anesthetic binding sites in the transmembrane domain of the Gloeobacter violaceus ligand-gated ion channel (GLIC) channel, characterize the putative binding pathway, and observe structural changes associated with channel function. Molecular simulations of desflurane reveal a binding pathway to GLIC via a membrane-embedded tunnel using an intrasubunit protein lumen as the conduit, an observation that explains the Meyer-Overton hypothesis, or why the lipophilicity of an anesthetic and its potency are generally proportional. Moreover, employing high concentrations of ligand led to the identification of a second transmembrane site (TM2) that inhibits dissociation of anesthetic from the TM1 site and is consistent with the high concentrations of anesthetics required to achieve clinical effects. Finally, asymmetric binding patterns of anesthetic to the channel were found to promote an iris-like conformational change that constricts and dehydrates the ion pore, creating a 13.5 kcal/mol barrier to ion translocation. Together with previous studies, the simulations presented herein demonstrate a novel anesthetic binding site in GLIC that is accessed through a membrane-embedded tunnel and interacts with a previously known site, resulting in conformational changes that produce a non-conductive state of the channel.

Pore dilatation increases the bicarbonate permeability of CFTR, ANO1 and glycine receptor anion channels

KEY POINTS

Cellular stimuli can modulate the ion selectivity of some anion channels, such as CFTR, ANO1 and the glycine receptor (GlyR), by changing pore size. Ion selectivity of CFTR, ANO1 and GlyR is critically affected by the electric permittivity and diameter of the channel pore. Pore size change affects the energy barriers of ion dehydration as well as that of size-exclusion of anion permeation. Pore dilatation increases the bicarbonate permeability (P HC O3/ Cl ) of CFTR, ANO1 and GlyR. Dynamic change in P HC O3/ Cl may mediate many physiological and pathological processes.

ABSTRACT

Chloride (Cl(-) ) and bicarbonate (HCO3 (-) ) are two major anions and their permeation through anion channels plays essential roles in our body. However, the mechanism of ion selection by the anion channels is largely unknown. Here, we provide evidence that pore dilatation increases the bicarbonate permeability (P HC O3/ Cl ) of anion channels by reducing energy barriers of size-exclusion and ion dehydration of HCO3 (-) permeation. Molecular, physiological and computational analyses of major anion channels, such as cystic fibrosis transmembrane conductance regulator (CFTR), anoctamin-1(ANO1/TMEM16A) and the glycine receptor (GlyR), revealed that the ion selectivity of anion channels is basically determined by the electric permittivity and diameter of the pore. Importantly, cellular stimuli dynamically modulate the anion selectivity of CFTR and ANO1 by changing the pore size. In addition, pore dilatation by a mutation in the pore-lining region alters the anion selectivity of GlyR. Changes in pore size affected not only the energy barriers of size exclusion but that of ion dehydration by altering the electric permittivity of water-filled cavity in the pore. The dynamic increase in P HC O3/ Cl by pore dilatation may have many physiological and pathophysiological implications ranging from epithelial HCO3 (-) secretion to neuronal excitation.

An electrostatic mechanism for Ca(2+)-mediated regulation of gap junction channels

Gap junction channels mediate intercellular signalling that is crucial in tissue development, homeostasis and pathologic states such as cardiac arrhythmias, cancer and trauma. To explore the mechanism by which Ca(2+) blocks intercellular communication during tissue injury, we determined the X-ray crystal structures of the human Cx26 gap junction channel with and without bound Ca(2+). The two structures were nearly identical, ruling out both a large-scale structural change and a local steric constriction of the pore. Ca(2+) coordination sites reside at the interfaces between adjacent subunits, near the entrance to the extracellular gap, where local, side chain conformational rearrangements enable Ca(2+)chelation. Computational analysis revealed that Ca(2+)-binding generates a positive electrostatic barrier that substantially inhibits permeation of cations such as K(+) into the pore. Our results provide structural evidence for a unique mechanism of channel regulation: ionic conduction block via an electrostatic barrier rather than steric occlusion of the channel pore.

Atomistic models of general anesthetics for use in in silico biological studies

While small molecules have been used to induce anesthesia in a clinical setting for well over a century, a detailed understanding of the molecular mechanism remains elusive. In this study, we utilize ab initio calculations to develop a novel set of CHARMM-compatible parameters for the ubiquitous modern anesthetics desflurane, isoflurane, sevoflurane, and propofol for use in molecular dynamics (MD) simulations. The parameters generated were rigorously tested against known experimental physicochemical properties including dipole moment, density, enthalpy of vaporization, and free energy of solvation. In all cases, the anesthetic parameters were able to reproduce experimental measurements, signifying the robustness and accuracy of the atomistic models developed. The models were then used to study the interaction of anesthetics with the membrane. Calculation of the potential of mean force for inserting the molecules into a POPC bilayer revealed a distinct energetic minimum of 4–5 kcal/mol relative to aqueous solution at the level of the glycerol backbone in the membrane. The location of this minimum within the membrane suggests that anesthetics partition to the membrane prior to binding their ion channel targets, giving context to the Meyer–Overton correlation. Moreover, MD simulations of these drugs in the membrane give rise to computed membrane structural parameters, including atomic distribution, deuterium order parameters, dipole potential, and lateral stress profile, that indicate partitioning of anesthetics into the membrane at the concentration range studied here, which does not appear to perturb the structural integrity of the lipid bilayer. These results signify that an indirect, membrane-mediated mechanism of channel modulation is unlikely.

Conductance simulation of the purinergic P2X2, P2X4, and P2X7 ionic channels using a combined Brownian dynamics and molecular dynamics approach

This paper investigates the application of an original combined approach of molecular and Brownian dynamic methods with quantum chemistry calculations for modeling the process of conductance of ion channels using purinergic P2X family receptors P2X2, P2X4, and P2X7 as a case study. A simplified model of the ionic channel in the lipid bilayer has been developed. A high level of conductance (30 pS) of P2X2 ionic channel together with the key role of Asp349 in forming the selectivity filter of P2X2 has been shown by using this approach. Calculated P2X2 permeability to monovalent cations Li(+), Na(+), and K(+) conforms to the free diffusion coefficient of these ions, which shows the low selectivity of P2X2 ionic channel.

P-loop conformation governed crizotinib resistance in G2032R-mutated ROS1 tyrosine kinase: clues from free energy landscape

Tyrosine kinases are regarded as excellent targets for chemical drug therapy of carcinomas. However, under strong purifying selection, drug resistance usually occurs in the cancer cells within a short term. Many cases of drug resistance have been found to be associated with secondary mutations in drug target, which lead to the attenuated drug-target interactions. For example, recently, an acquired secondary mutation, G2032R, has been detected in the drug target, ROS1 tyrosine kinase, from a crizotinib-resistant patient, who responded poorly to crizotinib within a very short therapeutic term. It was supposed that the mutation was located at the solvent front and might hinder the drug binding. However, a different fact could be uncovered by the simulations reported in this study. Here, free energy surfaces were characterized by the drug-target distance and the phosphate-binding loop (P-loop) conformational change of the crizotinib-ROS1 complex through advanced molecular dynamics techniques, and it was revealed that the more rigid P-loop region in the G2032R-mutated ROS1 was primarily responsible for the crizotinib resistance, which on one hand, impaired the binding of crizotinib directly, and on the other hand, shortened the residence time induced by the flattened free energy surface. Therefore, both of the binding affinity and the drug residence time should be emphasized in rational drug design to overcome the kinase resistance.

Cancers can eventually confer drug resistance to the continued medication. In most cases, mutations occurred in a drug target can attenuate the binding affinity of the drugs. Here, we studied the drug resistance mechanisms of the mutations G2032R in the ROS1 tyrosine kinase in fusion-type NSCLC. It is well known that the phosphate-binding loop (P-loop) plays a vital role in the binding of competitive inhibitors in tyrosine kinases, and numerous mutations have been found occurred around the P-loop, which may affect the binding/unbinding process of a drug. Free energy surfaces were constructed to characterize the impact of the mutation to the binding/unbinding process of a well-known NSCLC drug, crizotinib. Two advanced free energy calculation methods, namely funnel based well-tempered metadynamics and umbrella sampling based absolute binding free energy calculation achieved consistent results with the experimental data, suggesting that the rigid P-loop of the mutated target was mainly responsible for the crizotinib resistance to ROS1 tyrosine kinase.

Pentameric Ligand-gated Ion Channels : Insights from Computation

Pentameric ligand-gated ion channels (pLGICs) conduct upon the binding of an agonist and are fundamental to neurotransmission. New insights into the complex mechanisms underlying pLGIC gating, ion selectivity, and modulation have recently been gained via a series of crystal structures in prokaryotes and C .elegans, as well as computational studies relying on these structures. Here we review contributions from a variety of computational approaches, including normal mode analysis, automated docking, and fully atomistic molecular dynamics simulation. Examples from our own research, particularly concerning interactions with general anesthetics and lipids, are used to illustrate predictive results complementary to crystallographic studies.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Molecular dynamics investigation of Cl(-) transport through the closed and open states of the 2α12β2γ2 GABA(A) receptor

The α1β2γ2 gamma-aminobutyric type A receptor (GABA(A)R) is one of the most widely expressed GABA(A)R subtypes in the mammalian brain. GABA(A)Rsbelonging to the Cys-loop superfamily of ligand-gated ion channels have been identified as key targets for many clinical drugs, and the motions that govern the gating mechanism are still not well understood. In this study, an open-state GABA(A)R was constructed using the structure of the glutamate-gated chloride channel (GluCl), which has a high sequence identity to GABA(A)R. A closed-state model was constructed using the structure of the nicotinic acetylcholine receptor (nAChR). Molecular dynamics simulations of the open-state and closed-state GABA(A)R were performed. We calculated the electrostatic potential of the two conformations, the pore radius of the two ion channels and the root-mean-square fluctuation. We observed the presence of two positively charged girdles around the ion channel and found flexible regions in the GABA(A)R. Then, the free-energy of chloride ion permeations through the closed-state and open-state G GABA(A)R has been estimated using adaptive biasing force (ABF) simulation. For the closed-state G GABA(A)R, we observed two major energy barriers for chloride ion translocation in the transmembrane domain (TMD). For the open-state GABA(A)R, there was only one energy barrier formed by two Thr261 (α1), two Thr255 (β2) and one Thr271 (γ2). By using ABF simulation, the overall free-energy profile is obtained for Cl(-) transporting through GABA(A)R, which gives a complete map of the ion channel of Cl(-) permeation.

Structural basis for ion permeation mechanism in pentameric ligand-gated ion channels

To understand the molecular mechanism of ion permeation in pentameric ligand-gated ion channels (pLGIC), we solved the structure of an open form of GLIC, a prokaryotic pLGIC, at 2.4 Å. Anomalous diffraction data were used to place bound anions and cations. This reveals ordered water molecules at the level of two rings of hydroxylated residues (named Ser6' and Thr2') that contribute to the ion selectivity filter. Two water pentagons are observed, a self-stabilized ice-like water pentagon and a second wider water pentagon, with one sodium ion between them. Single-channel electrophysiology shows that the side-chain hydroxyl of Ser6' is crucial for ion translocation. Simulations and electrostatics calculations complemented the description of hydration in the pore and suggest that the water pentagons observed in the crystal are important for the ion to cross hydrophobic constriction barriers. Simulations that pull a cation through the pore reveal that residue Ser6' actively contributes to ion translocation by reorienting its side chain when the ion is going through the pore. Generalization of these findings to the pLGIC family is proposed.

Asymmetric ligand binding facilitates conformational transitions in pentameric ligand-gated ion channels

The anesthetic propofol inhibits the currents of the homopentameric ligand-gated ion channel GLIC, yet the crystal structure of GLIC with five propofol molecules bound symmetrically shows an open-channel conformation. To address this dilemma and determine if the symmetry of propofol binding sites affects the channel conformational transition, we performed a total of 1.5 μs of molecular dynamics simulations for different GLIC systems with propofol occupancies of 0, 1, 2, 3, and 5. GLIC without propofol binding or with five propofol molecules bound symmetrically, showed similar channel conformation and hydration status over multiple replicates of 100-ns simulations. In contrast, asymmetric binding to one, two or three equivalent sites in different subunits accelerated the channel dehydration, increased the conformational heterogeneity of the pore-lining TM2 helices, and shifted the lateral and radial tilting angles of TM2 toward a closed-channel conformation. The results differentiate two groups of systems based on the propofol binding symmetry. The difference between symmetric and asymmetric groups is correlated with the variance in the propofol-binding cavity adjacent to the hydrophobic gate and the force imposed by the bound propofol. Asymmetrically bound propofol produced greater variance in the cavity size that could further elevate the conformation heterogeneity. The force trajectory generated by propofol in each subunit over the course of a simulation exhibits an ellipsoidal shape, which has the larger component tangential to the pore. Asymmetric propofol binding creates an unbalanced force that expedites the channel conformation transitions. The findings from this study not only suggest that asymmetric binding underlies the propofol functional inhibition of GLIC, but also advocate for the role of symmetry breaking in facilitating channel conformational transitions.

Reversal of ion-charge selectivity renders the pentameric ligand-gated ion channel GLIC insensitive to anaesthetics

pLGICs (pentameric ligand-gated ion channels) are a family of structurally homologous cation and anion channels involved in neurotransmission. Cation-selective members of the pLGIC family are typically inhibited by general anaesthetics, whereas anion-selective members are potentiated. GLIC is a prokaryotic cation pLGIC and can be inhibited by clinical concentrations of general anaesthetics. The introduction of three mutations, Y221A (Y-3'A), E222P (E-2'P) and N224R (N0'R), at the selectivity filter and one, A237T (A13'T), at the hydrophobic gate, converted GLIC into an anion channel. The mutated GLIC (GLIC4) became insensitive to the anaesthetics propofol and etomidate, as well as the channel blocker picrotoxin. MD (molecular dynamics) simulations revealed changes in the structure and dynamics of GLIC4 in comparison with GLIC, particularly in the tilting angles of the pore-lining helix [TM2 (transmembrane helix 2)] that consequently resulted in different pore radius and hydration profiles. Propofol binding to an intra-subunit site of GLIC shifted the tilting angles of TM2 towards closure at the hydrophobic gate region, consistent with propofol inhibition of GLIC. In contrast, the pore of GLIC4 was much more resilient to perturbation from propofol binding. The present study underscores the importance of pore dynamics and conformation to anaesthetic effects on channel functions.

Energetics and ion permeation characteristics in a glutamate-gated chloride (GluCl) receptor channel

An invertebrate glutamate-gated chloride channel (GluCl) has recently been crystallized in an open-pore state. This channel is homologous to the human Cys-loop receptor family of pentameric ligand-gated ion channels, including anion-selective GlyR and GABAR and cation-selective nAChR and 5HT(3). We implemented molecular dynamics (MD) in conjunction with an elastic network model to perturb the X-ray structure of GluCl and investigated the open channel stability and its ion permeation characteristics. Our study suggests that TM2 helical tilting may close GluCl near the hydrophobic constriction L254 (L9'), similar to its cation-selective homologues. Ion permeation characteristics were determined by Brownian dynamics simulations using a hybrid MD/continuum electrostatics approach to evaluate the free energy profiles for ion transport. Near the selectivity filter region (P243 or P-2'), the free energy barrier for Na(+) transport is over 4 k(B)T higher than that for Cl(-), indicating anion selectivity of the channel. Furthermore, three layers of positivity charged rings in the extracellular domain also contribute to charge selectivity and facilitate Cl(-) permeability over Na(+). Collectively, the charge selectivity of GluCl may be determined by overall electrostatic and ion dehydration effects, perhaps not deriving from a single region of the channel (the selectivity filter region near the intracellular entrance).

Modeling complex biological systems: From solution chemistry to membranes and channels

Complex biological systems are intimately linked to their environment, a very crowded and equally complex solution compartmentalized by fluid membranes. Modeling such systems remains challenging and requires a suitable representation of these solutions and their interfaces. Here, we focus on particle-based modeling at an atomistic level using molecular dynamics (MD) simulations. As an example, we discuss important steps in modeling the solution chemistry of an ion channel of the ligand-gated ion channel receptor family, a major target of many drugs including anesthetics and addiction treatments. The bacterial pentameric ligand-gated ion channel (pLGIC) called GLIC provides clues about the functional importance of solvation, in particular for mechanisms such as permeation and gating. We present some current challenges along with promising novel modeling approaches.

Molecular mechanism for the dual alcohol modulation of Cys-loop receptors

Cys-loop receptors constitute a superfamily of pentameric ligand-gated ion channels (pLGICs), including receptors for acetylcholine, serotonin, glycine and γ-aminobutyric acid. Several bacterial homologues have been identified that are excellent models for understanding allosteric binding of alcohols and anesthetics in human Cys-loop receptors. Recently, we showed that a single point mutation on a prokaryotic homologue (GLIC) could transform it from a channel weakly potentiated by ethanol into a highly ethanol-sensitive channel. Here, we have employed molecular simulations to study ethanol binding to GLIC, and to elucidate the role of the ethanol-enhancing mutation in GLIC modulation. By performing 1-µs simulations with and without ethanol on wild-type and mutated GLIC, we observed spontaneous binding in both intra-subunit and inter-subunit transmembrane cavities. In contrast to the glycine receptor GlyR, in which we previously observed ethanol binding primarily in an inter-subunit cavity, ethanol primarily occupied an intra-subunit cavity in wild-type GLIC. However, the highly ethanol-sensitive GLIC mutation significantly enhanced ethanol binding in the inter-subunit cavity. These results demonstrate dramatic effects of the F(14′)A mutation on the distribution of ligands, and are consistent with a two-site model of pLGIC inhibition and potentiation.

Communication from one nerve cell to the next is an essential process for brain and muscle function. Nerve impulses result in release of transmitter molecules from one cell that bind to receptors on the next cell. Transmitter binding opens a pore in each receptor and ions flow across the membrane, leading to either enhancement or inhibition of new nerve impulses. These receptors are modulated by numerous drugs, including alcohols and anesthetics; identifying the precise location of modulator binding is critical for drug development. We have used computer simulation methods to model alcohol diffusion and binding to a receptor. By modifying a single residue in the receptor, we were able to move the location of the binding site and dramatically alter alcohol modulation, which supports a model with two separate binding sites for enhancement and inhibition in this family of receptors.

Drying transition in the hydrophobic gate of the GLIC channel blocks ion conduction

The theoretical prediction of water drying transitions near nonpolar surfaces has stimulated an intensive search for biological processes exploiting this extreme form of hydrophobicity. Here we quantitatively demonstrate that drying of a hydrophobic constriction is the major determinant of ion conductance in the GLIC pentameric ion channel. Molecular-dynamics simulations show that in the closed state, the channel conductance is ∼12 orders-of-magnitude lower than in the open state. This large drop in conductance is remarkable because even in the functionally closed conformation the pore constriction remains wide enough for the passage of sodium ions, aided by a continuous bridge of ∼12 water molecules. However, we find that the free energy cost of hydrating the hydrophobic gate is large, accounting almost entirely for the energetic barrier blocking ion passage. The free energies of transferring a sodium ion into a prehydrated gate in functionally closed and open states differ by only 1.2 kcal/mol, compared to an 11 kcal/mol difference in the costs of hydrating the hydrophobic gate. Conversely, ion desolvation effects play only minor roles in GLIC ion channel gating. Our simulations help rationalize experiments probing the gating kinetics of the nicotinic acetylcholine receptor in response to mutations of pore-lining residues. The molecular character and phase behavior of water should thus be included in quantitative descriptions of ion channel gating.

Theory and simulation of ion conduction in the pentameric GLIC channel

GLIC is a bacterial member of the large family of pentameric ligand-gated ion channels. To study ion conduction through GLIC and other membrane channels, we combine the one-dimensional potential of mean force for ion passage with a Smoluchowski diffusion model, making it possible to calculate single-channel conductance in the regime of low ion concentrations from all-atom molecular dynamics (MD) simulations. We then perform MD simulations to examine sodium ion conduction through the GLIC transmembrane pore in two systems with different bulk ion concentrations. The ion potentials of mean force, calculated from umbrella sampling simulations with Hamiltonian replica exchange, reveal a major barrier at the hydrophobic constriction of the pore. The relevance of this barrier for ion transport is confirmed by a committor function that rises sharply in the barrier region. From the free evolution of Na(+) ions starting at the barrier top, we estimate the effective diffusion coefficient in the barrier region, and subsequently calculate the conductance of the pore. The resulting diffusivity compares well with the position-dependent ion diffusion coefficient obtained from restrained simulations. The ion conductance obtained from the diffusion model agrees with the value determined via a reactive-flux rate calculation. Our results show that the conformation in the GLIC crystal structure, with an estimated conductance of ~1 picosiemens at 140 mM ion concentration, is consistent with a physiologically open state of the channel.

Variational multiscale models for charge transport

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field.

Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations

The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.

Second-order Poisson Nernst-Planck solver for ion channel transport

The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements.