Ab initio molecular dynamics study of proton transfer in a polyglycine analog of the ion channel gramicidin A

Dynamics and Surface Propensity of H+ and OH- within Rigid Interfacial Water: Implications for Electrocatalysis

Facile solvent reorganization promoting ion transfer across the solid-liquid interface is considered a prerequisite for efficient electrocatalysis. We provide first-principles insight into this notion by examining water self-ion dynamics at a highly rigid NaCl(100)-water interface. Through extensive density functional theory molecular dynamics simulations, we demonstrate for both acidic and alkaline solutions that Grotthuss dynamics is not impeded by a rigid water structure. Conversely, decreased proton transfer barriers and a striking propensity of H₃O⁺ and OH^- for stationary interfacial water are found. Differences in the ideal hydration structure of the ions, however, distinguish their behavior at the water contact layer. While hydronium can maintain its optimal solvation, the preferentially hypercoordinated hydroxide is repelled from the immediate vicinity of the surface due to interfacial coordination reduction. This has implications for alkaline hydrogen electrosorption in which the formation of undercoordinated OH^- at the surface is proposed to contribute to the observed sluggish kinetics.

Quantum-Classical Path Integral Simulation of Excess Proton Dynamics in a Water Dimer Embedded in the Gramicidin Channel

We use the quantum-classical path integral (QCPI) methodology to investigate the relaxation dynamics of an excess proton that has been inserted in a water dimer embedded in the gramicidin A channel at room temperature. We obtain one-dimensional potential slices for the quantum degree of freedom through a proper transformation to internal coordinates. Our results indicate that the proton transfer is driven by the oscillation of the oxygen pair, and that the transfer occurs primarily at single-well or nearby low-barrier configurations. Yet, we find that tunneling and zero-point energy lead to a significant acceleration of the proton transfer dynamics.

Quantifying the Stability of the Hydronium Ion in Organic Solvents With Molecular Dynamics Simulations

The solution-phase stability of the hydronium ion catalyst significantly affects the rates of acid-catalyzed reactions, which are ubiquitously utilized to convert biomass to valuable chemicals. In this work, classical molecular dynamics simulations were performed to quantify the stability of hydronium and chloride ions by measuring their solvation free energies in water, 1,4-dioxane (DIOX), tetrahydrofuran (THF), γ-valerolactone (GVL), N-methyl-2-pyrrolidone (NMP), acetone (ACE), and dimethyl sulfoxide (DMSO). By measuring the free energy for transferring a hydronium ion from pure water to pure organic solvent, we found that the hydronium ion is destabilized in DIOX, THF, and GVL and stabilized in NMP, ACE, and DMSO relative to water. The distinction between these organic solvents can be used to predict the preference of the hydronium ion for specific regions in aqueous mixtures of organic solvents. We then incorporated the stability of the hydronium ion into a correlative model for the acid-catalyzed conversion of 1,2-propanediol to propanal. The revised model is able to predict experimental reaction rates across solvent systems with different organic solvents. These results demonstrate the ability of classical molecular dynamics simulations to screen solvent systems for improved acid-catalyzed reaction performance.

Permeability across lipid membranes

Molecular permeation through lipid membranes is a fundamental biological process that is important for small neutral molecules and drug molecules. Precise characterization of free energy surface and diffusion coefficients along the permeation pathway is required in order to predict molecular permeability and elucidate the molecular mechanisms of permeation. Several recent technical developments, including improved molecular models and efficient sampling schemes, are illustrated in this review. For larger penetrants, explicit consideration of multiple collective variables, including orientational, conformational degrees of freedom, are required to be considered in addition to the distance from the membrane center along the membrane normal. Although computationally demanding, this method can provide significant insights into the molecular mechanisms of permeation for molecules of medical and pharmaceutical importance. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Multisurface Adiabatic Reactive Molecular Dynamics

Adiabatic reactive molecular dynamics (ARMD) simulation method is a surface-crossing algorithm for modeling chemical reactions in classical molecular dynamics simulations using empirical force fields. As the ARMD Hamiltonian is time dependent during crossing, it allows only approximate energy conservation. In the current work, the range of applicability of conventional ARMD is explored, and a new multisurface ARMD (MS-ARMD) method is presented, implemented in CHARMM and applied to the vibrationally induced photodissociation of sulfuric acid (H2SO4) in the gas phase. For this, an accurate global potential energy surface (PES) involving 12 H2SO4 and 4 H2O + SO3 force fields fitted to MP2/6-311G++(2d,2p) reference energies is employed. The MS-ARMD simulations conserve total energy and feature both intramolecular H-transfer reactions and water elimination. An analytical treatment of the dynamics in the crossing region finds that conventional ARMD can approximately conserve total energy for limiting cases. In one of them, the reduced mass of the system is large, which often occurs for simulations of solvated biomolecular systems. On the other hand, MS-ARMD is a general approach for modeling chemical reactions including gas-phase, homogeneous, heterogeneous, and enzymatic catalytic reactions while conserving total energy in atomistic simulations.

Density-functional theory study of gramicidin A ion channel geometry and electronic properties

Understanding the mechanisms underlying ion channel function from the atomic-scale requires accurate ab initio modelling as well as careful experiments. Here, we present a density functional theory (DFT) study of the ion channel gramicidin A (gA), whose inner pore conducts only monovalent cations and whose conductance has been shown to depend on the side chains of the amino acids in the channel. We investigate the ground state geometry and electronic properties of the channel in vacuum, focusing on their dependence on the side chains of the amino acids. We find that the side chains affect the ground state geometry, while the electrostatic potential of the pore is independent of the side chains. This study is also in preparation for a full, linear scaling DFT study of gA in a lipid bilayer with surrounding water. We demonstrate that linear scaling DFT methods can accurately model the system with reasonable computational cost. Linear scaling DFT allows ab initio calculations with 10,000-100,000 atoms and beyond, and will be an important new tool for biomolecular simulations.

Role of the Membrane Dipole Potential for Proton Transport in Gramicidin A Embedded in a DMPC Bilayer

The membrane potential at the water/phospholipid interfaces may play a key role for proton conduction of gramicidin A (gA). Here we address this issue by Density Functional Theory-based molecular dynamics and metadynamics simulations. The calculations, performed on gA embedded in a solvated 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) model membrane environment (about 2,000 atoms), indicate that (i) the membrane dipole potential rises at the channel mouth by ∼0.4 V. A similar value has been measured for gA embedded in a DMPC monolayer; (ii) the calculated free energy barrier is located at the channel entrance, consistent with experiments comparing gA proton conduction in different bilayers. The electronic structures of the proton ligands (water molecules and peptide units) are similar to those in the bulk solvent. Based on these results, we suggest an important role of the membrane dipole potential for the free energy barrier of proton permeation of gA. This may provide a rationale for the large increase in the rate of proton conduction under application of a transmembrane voltage, as observed experimentally. Our calculations might suggest also a role for proton desolvation for the permeation process. This role has already emerged from EVB calculations on gA embedded in a model membrane.

Ab initio molecular dynamics

In this chapter, an introduction to ab initio molecular dynamics (AIMD) has been given. Many of the basic concepts, like the Hellman-Feynman forces, the difference between the Car-Parrinello molecular dynamics and AIMD, have been explained. Also a very versatile AIMD code, the CP2K, has been introduced. On the application, the emphasis was on the aqueous systems and chemical reactions. The biochemical applications have not been discussed in depth.

Hydroxide ion can move faster than an excess proton through one-dimensional water chains in hydrophobic narrow pores

Carbon nanotubes (CNT) are known to provide a hydrophobic, confined environment for water where its structure and dynamics can be very different from those of bulk water. In particular, narrow CNTs of the type (6,6) allow only a single one-dimensional (1D) chain of water molecules inside them, thus providing an idealized scenario to study motion in 1D along water chains. In the present study, we have investigated structural and dynamic behavior of water and also of an excess proton and hydroxide ion in water-filled narrow CNTs by means of ab initio molecular dynamics and combined quantum-classical simulations. The main focus of the present work is on the molecular mechanism and kinetics of hydronium and hydroxide ion migration along 1D water chains of different lengths in confinement. It is found that the hydrogen-bonded structures of water and the excess proton and hydroxide ion in CNTs can be very different from those in bulk, and these altered solvation structures play critical roles in determining the proton-transfer (PT) rates along water chains. For the present 1D chain systems, the hydroxide ion is found to migrate at a slightly faster rate than the excess proton, unlike their relative mobilities in bulk water. This faster migration of the hydroxide ion is found not only in CNTs with periodicity along the tube axis but also in isolated CNTs where the excess proton and the hydroxide ion are allowed to move under the influence of an electric field of an oppositely charged ion. The roles of rotational jumps and hydrogen-bond fluctuations in the PT events are discussed. In addition, the significance of hydrogen-bonding defects on the dynamics of an excess proton and hydroxide ion is also discussed for varying chain lengths.

Lewis-inspired representation of dissociable water in clusters and Grotthuss chains

Proton transfer to and from water is critical to the function of water in many settings. However, it has been challenging to model. Here, we present proof-of-principle for an efficient yet robust model based on Lewis-inspired submolecular particles with interactions that deviate from Coulombic at short distances to take quantum effects into account. This "LEWIS" model provides excellent correspondence with experimental structures for water molecules and water clusters in their neutral, protonated and deprotonated forms; reasonable values for the proton affinities of water and hydroxide; a good value for the strength of the hydrogen bond in the water dimer; the correct order of magnitude for the stretch and bend force constants of water; and the expected time course for Grotthuss transport in water chains.

Ab initio molecular dynamics of proton networks in narrow polymer electrolyte pores

It is well established that proton conductivity in fuel cell membrane materials such as Nafion decreases strongly with decreasing water content. Proton transport in almost dry membranes is thought to proceed through narrow channels. In the present work we investigate proton structure and dynamics in two narrow cylindrical pores, which differ by their radius and the spacing of SO(3)H groups inside the channel. Pores are modelled through eight CF(3)CF(3) and four CF(3)SO(3)H entities in a helical arrangement. The water content λ (the ratio between the number of water molecules and the number of sulfonic acid groups) in the pores varies between 2.5 and 4.5. We observe a transition from the undissociated acid at very low λ through more or less localized H(3)O(+) entities to more delocalized H(5)O(2)(+) entities for the investigated range of λ. In the narrower pore, where S-S distances vary in a more favourable range (between 6 and 8.5 Å) than in the wider pore, we find that the molecular mobility is significantly higher, even at a rather high density of water molecules inside the pore.

Proton transport in biological systems can be probed by two-dimensional infrared spectroscopy

We propose a new method to determine the proton transfer (PT) rate in channel proteins by two-dimensional infrared (2DIR) spectroscopy. Proton transport processes in biological systems, such as proton channels, trigger numerous fundamental biochemical reactions. Due to the limitation in both spatial and time resolution of the traditional experimental approaches, describing the whole proton transport process and identifying the rate limiting steps at the molecular level is challenging. In the present paper, we focus on proton transport through the Gramicidin A channel. Using a kinetic PT model derived from all-atom molecular dynamics simulations, we model the amide I region of the 2DIR spectrum of the channel protein to examine its sensitivity to the proton transport process. We demonstrate that the 2DIR spectrum of the isotope-labeled channel contain information on the PT rate, which may be extracted by analyzing the antidiagonal linewidth of the spectral feature related to the labeled site. Such experiments in combination with detailed numerical simulations should allow the extraction of site dependent PT rates, providing a method for identifying possible rate limiting steps for proton channel transfer.

Simulating proton transport through a simplified model for trans-membrane proteins

Ab initio MD simulations on a polyglycine helix and water-wire expressed under periodic boundary conditions have created a channel that supports proton transfer up to distances of 10.5 A. The effect of varying the density of water molecules in the channel has been investigated. A range of cationic states are identified with widely varying lifetimes. The mechanism of proton transport in this model shares some features with the simulations reported for bulk water, with, e.g., the hydrogen bond distance shortening in the time period leading up to successful proton transfer. However, there are also some important differences such as the observation of a heightened number of proton rattling events. We also observe that the helix plays an important role in directing the behavior of the water wire: the most active proton transport regions of the water-wire are found in areas where the helix is most tightly coiled. Finally, we report on the effects of different DFT functionals to model a water-wire and on the importance of including dispersion corrections to stabilize the alpha-helical structure.

Quantum-chemical calculations of a long proton wire. Application of a harmonic model to analysis of the structure of an ionic defect in a water chain with an excess proton

Quantum-chemical calculations of molecular complexes (NH(3))(3)Zn(2+)...(H(2)O)(n)...NH(3) (C(n), n = 11, 16, 21, and 30) simulating a proton wire donor-water chain-acceptor were carried out. Earlier found periodicity in the length of the O-H bonds in water chain is explained within the framework of a one-component harmonic model. In complexes C(n), the geometry and electronic structure of ionic defect in water chain with an excess proton were studied. Calculations carried out at ab initio (B3LYP/6-31+G**) and semiempirical (PM3) levels of theory predict different patterns of distribution of the O-H bonds lengths and positive charge on the H-bond hydrogen atoms in the region of ionic defect. The obtained data show how a length of water chain and position of a protonated water link in the chain influence the ionic defect structure. To describe the observed structures of ionic defect, the harmonic model was used and the role of parameters of the H-bonded chain was investigated. The performed analysis explains different mechanisms (concerted and stepwise) of proton transfer along the H-bonded chain derived from ab initio and semiempirical calculation schemes.

Noncontact dipole effects on channel permeation. III. Anomalous proton conductance effects in gramicidin

Proton transport on water wires, of interest for many problems in membrane biology, is analyzed in side-chain analogs of gramicidin A channels. In symmetrical 0.1N HCl solutions, fluorination of channel Trp(11), Trp-(13), or Trp(15) side chains is found to inhibit proton transport, and replacement of one or more Trps with Phe enhances proton transport, the opposite of the effects on K(+) transport in lecithin bilayers. The current-voltage relations are superlinear, indicating that some membrane field-dependent process is rate limiting. The interfacial dipole effects are usually assumed to affect the rate of cation translocation across the channel. For proton conductance, however, water reorientation after proton translocation is anticipated to be rate limiting. We propose that the findings reported here are most readily interpreted as the result of dipole-dipole interactions between channel waters and polar side chains or lipid headgroups. In particular, if reorientation of the water column begins with the water nearest the channel exit, this hypothesis explains the negative impact of fluorination and the positive impact of headgroup dipole on proton conductance.

Proton transfer 200 years after von Grotthuss: insights from ab initio simulations

In the last decade, ab initio simulations and especially Car-Parrinello molecular dynamics have significantly contributed to the improvement of our understanding of both the physical and chemical properties of water, ice, and hydrogen-bonded systems in general. At the heart of this family of in silico techniques lies the crucial idea of computing the many-body interactions by solving the electronic structure problem "on the fly" as the simulation proceeds, which circumvents the need for pre-parameterized potential models. In particular, the field of proton transfer in hydrogen-bonded networks greatly benefits from these technical advances. Here, several systems of seemingly quite different nature and of increasing complexity, such as Grotthuss diffusion in water, excited-state proton-transfer in solution, phase transitions in ice, and protonated water networks in the membrane protein bacteriorhodopsin, are discussed in the realms of a unifying viewpoint.

Proton solvation and transport in aqueous and biomolecular systems: insights from computer simulations

The excess proton in aqueous media plays a pivotal role in many fundamental chemical (e.g., acid-base chemistry) and biological (e.g., bioenergetics and enzyme catalysis) processes. Understanding the hydrated proton is, therefore, crucial for chemistry, biology, and materials sciences. Although well studied for over 200 years, excess proton solvation and transport remains to this day mysterious, surprising, and perhaps even misunderstood. In this feature article, various efforts to address this problem through computer modeling and simulation will be described. Applications of computer simulations to a number of important and interesting systems will be presented, highlighting the roles of charge delocalization and Grotthuss shuttling, a phenomenon unique in many ways to the excess proton in water.

Exploration on Regulating Factors for Proton Transfer along Hydrogen-Bonded Water Chains

Proton transfer along a single-file hydrogen-bonded water chain is elucidated with a special emphasis on the investigation of chain length, side water, and solvent effects, as well as the temperature and pressure dependences. The number of water molecules in the chain varies from one to nine. The proton can be transported to the acceptor fragment through the single-file hydrogen-bonded water wire which contains at most five water molecules. If the number of water molecule is more than five, the proton is trapped by the chain in the hydroxyl-centered H(7)O(3) (+) state. The farthest water molecule involved in the formation of H(7)O(3) (+) is the fifth one away from the donor fragment. These phenomena reappear in the molecular dynamics simulations. The energy of the system is reduced along with the proton conduction. The proton transfer mechanism can be altered by excess proton. The augmentation of the solvent dielectric constant weakens the stability of the system, but favors the proton transfer. NMR spin-spin coupling constants can be used as a criterion in judging whether the proton is transferred or not. The enhancement of temperature increases the thermal motion of the molecule, augments the internal energy of the system, and favors the proton transfer. The lengthening of the water wire increases the entropy of the system, concomitantly, the temperature dependence of the Gibbs free energy increases. The most favorable condition for the proton transfer along the H-bonded water wire is the four-water contained chain with side water attached near to the acceptor fragment in polar solvent under higher temperature.

Ab initio molecular-dynamics simulation of aqueous proton solvation and transport revisited

The solvation and transport of the hydrated excess proton is studied using the Car-Parrinello molecular-dynamics (CPMD) simulation method. The simulations were performed using BLYP and HCTH gradient-corrected exchange-correlation energy functionals. The fictitious electronic mass was chosen to be small enough so that the underlying water structural and dynamical properties were converged with respect to this important CPMD simulation parameter. An unphysical overstructuring of liquid water in the CPMD simulations using the BLYP functional resulted in the formation of long-lived hydrogen-bonding structures involving the excess proton and a particular (special) water oxygen. The excess proton was observed to be attracted to the special oxygen through the entire length of the BLYP CPMD simulations. Consequently, the excess proton diffusion was limited by the mobility of the special oxygen in the slowly diffusing water network and, in turn, the excess proton self-diffusion coefficient was found to be significantly below the experimental value. On the other hand, the structural properties of liquid water in the HCTH CPMD simulation were seen to be in better agreement with experiment, although the water and excess proton diffusions were still well below the experimental value.

A polarizable multistate empirical valence bond model for proton transport in aqueous solution

A multistate empirical valence bond model for proton transport in water, which explicitly includes solvent polarization, is presented. Polarization is included for each valence-bond state via induced point dipoles, and the model is parametrized to be used with an effective path integral derived potential surface, so as to include quantum effects of the transferring proton. The new model is shown to reproduce ab initio geometries and energetics for small protonated clusters. It is also shown that the new model gives a diffusion constant for the excess proton in water, which is in good agreement with experiment, and that the qualitative features of ab initio path integral simulations [D. Marx, M. E. Tuckerman, J. Hutter, and M. Parrinello, Nature (London) 397, 601 (1999)] are well reproduced.

Water molecules and hydrogen-bonded networks in bacteriorhodopsin--molecular dynamics simulations of the ground state and the M-intermediate

Protein crystallography provides the structure of a protein, averaged over all elementary cells during data collection time. Thus, it has only a limited access to diffusive processes. This article demonstrates how molecular dynamics simulations can elucidate structure-function relationships in bacteriorhodopsin (bR) involving water molecules. The spatial distribution of water molecules and their corresponding hydrogen-bonded networks inside bR in its ground state (G) and late M intermediate conformations were investigated by molecular dynamics simulations. The simulations reveal a much higher average number of internal water molecules per monomer (28 in the G and 36 in the M) than observed in crystal structures (18 and 22, respectively). We found nine water molecules trapped and 19 diffusive inside the G-monomer, and 13 trapped and 23 diffusive inside the M-monomer. The exchange of a set of diffusive internal water molecules follows an exponential decay with a 1/e time in the order of 340 ps for the G state and 460 ps for the M state. The average residence time of a diffusive water molecule inside the protein is approximately 95 ps for the G state and 110 ps for the M state. We have used the Grotthuss model to describe the possible proton transport through the hydrogen-bonded networks inside the protein, which is built up in the picosecond-to-nanosecond time domains. Comparing the water distribution and hydrogen-bonded networks of the two different states, we suggest possible pathways for proton hopping and water movement inside bR.

Protons trap NR1/NR2B NMDA receptors in a nonconducting state

NMDA receptors are highly expressed in the CNS and are involved in excitatory synaptic transmission, as well as synaptic plasticity. Given that overstimulation of NMDA receptors can cause cell death, it is not surprising that these channels are under tight control by a series of inhibitory extracellular ions, including zinc, magnesium, and H+. We studied the inhibition by extracellular protons of recombinant NMDA receptor NR1/NR2B single-channel and macroscopic responses in transiently transfected human embryonic kidney HEK 293 cells using patch-clamp techniques. We report that proton inhibition proceeds identically in the absence or presence of agonist, which rules out the possibility that protonation inhibits receptors by altering coagonist binding. The response of macroscopic currents in excised patches to rapid jumps in pH was used to estimate the microscopic association and dissociation rates for protons, which were 1.4 x 10(9) m(-1) sec(-1) and 110-196 sec(-1), respectively (K(d) corresponds to pH 7.2). Protons reduce the open probability without altering the time course of desensitization or deactivation. Protons appear to slow at least one time constant describing the intra-activation shut-time histogram and modestly reduce channel open time, which we interpret to reflect a reduction in the overall channel activation rate and possible proton-induced termination of openings. This is consistent with a modest proton-dependent slowing of the macroscopic response rise time. From these data, we propose a physical model of proton inhibition that can describe macroscopic and single-channel properties of NMDA receptor function over a range of pH values.

Water alignment, dipolar interactions, and multiple proton occupancy during water-wire proton transport

A discrete multistate kinetic model for water-wire proton transport is constructed and analyzed using Monte Carlo simulations. In the model, each water molecule can be in one of three states: oxygen lone-pairs pointing leftward, pointing rightward, or protonated (H(3)O(+)). Specific rules for transitions among these states are defined as protons hop across successive water oxygens. Our model also includes water-channel interactions that preferentially align the water dipoles, nearest-neighbor dipolar coupling interactions, and Coulombic repulsion. Extensive Monte Carlo simulations were performed and the observed qualitative physical behaviors discussed. We find the parameters that allow the model to exhibit superlinear and sublinear current-voltage relationships, and show why alignment fields, whether generated by interactions with the pore interior or by membrane potentials, always decrease the proton current. The simulations also reveal a "lubrication" mechanism that suppresses water dipole interactions when the channel is multiply occupied by protons. This effect can account for an observed sublinear-to-superlinear transition in the current-voltage relationship.

Protonation state of the equatorial ligands and dynamics of the OH...O units in a cobaloxime biomimetic

The protonation state of the dimethylglyoxime ligands in the B(12) coenzyme biomimetic [Co(CCl=CHCl)(dmgH)(2)(py)].CHCl(3) was investigated by using first-principles molecular dynamics. Our simulations at 173 and 300 K reveal that one of the oxime protons remains bonded to a nitroxyl group, while the proton of the second NO...H-ON unit is essentially shared with similar probability between the two oxygen atoms. This reconciles the results of the experimental determination (Jones, P. G.; Yang, L.; Steinborn, D. Acta Cryst. 1996, C52, 2399), showing all N-O distances as equivalent, with the commonly accepted rule that the protonation state of the dimethylglyoxime ligands can be identified by the different N-O distances. Further aspects of the dynamics of the OH...O units, in relation to the occurrence of weak CH...O intermolecular interactions, are analyzed.

Molecular mechanism of H+ conduction in the single-file water chain of the gramicidin channel

The conduction of protons in the hydrogen-bonded chain of water molecules (or "proton wire") embedded in the lumen of gramicidin A is studied with molecular dynamics free energy simulations. The process may be described as a "hop-and-turn" or Grotthuss mechanism involving the chemical exchange (hop) of hydrogen nuclei between hydrogen-bonded water molecules arranged in single file in the lumen of the pore, and the subsequent reorganization (turn) of the hydrogen-bonded network. Accordingly, the conduction cycle is modeled by two complementary steps corresponding respectively to the translocation 1) of an ionic defect (H+) and 2) of a bonding defect along the hydrogen-bonded chain of water molecules in the pore interior. The molecular mechanism and the potential of mean force are analyzed for each of these two translocation steps. It is found that the mobility of protons in gramicidin A is essentially determined by the fine structure and the dynamic fluctuations of the hydrogen-bonded network. The translocation of H+ is mediated by spontaneous (thermal) fluctuations in the relative positions of oxygen atoms in the wire. In this diffusive mechanism, a shallow free-energy well slightly favors the presence of the excess proton near the middle of the channel. In the absence of H+, the water chain adopts either one of two polarized configurations, each of which corresponds to an oriented donor-acceptor hydrogen-bond pattern along the channel axis. Interconversion between these two conformations is an activated process that occurs through the sequential and directional reorientation of water molecules of the wire. The effect of hydrogen-bonding interactions between channel and water on proton translocation is analyzed from a comparison to the results obtained previously in a study of model nonpolar channels, in which such interactions were missing. Hydrogen-bond donation from water to the backbone carbonyl oxygen atoms lining the pore interior has a dual effect: it provides a coordination of water molecules well suited both to proton hydration and to high proton mobility, and it facilitates the slower reorientation or turn step of the Grotthuss mechanism by stabilizing intermediate configurations of the hydrogen-bonded network in which water molecules are in the process of flipping between their two preferred, polarized states. This mechanism offers a detailed molecular model for the rapid transport of protons in channels, in energy-transducing membrane proteins, and in enzymes.

Theoretical and computational models of ion channels

Computational studies can make meaningful contributions to our understanding of biological ion channels. A wide variety of methods, at different levels of approximation, can be used. Over the past few years, progress in the experimental determination of three-dimensional structures has given a fresh impetus to the theorists. Noteworthy progress has been made in carefully constructing realistic models of a number of complex biological channels to address important questions about their function.