A multistate empirical valence bond description of protonatable amino acids

Quantitative insights into the mechanism of proton conduction and selectivity for the human voltage-gated proton channel Hv1

Human voltage-gated proton (hHv1) channels are crucial for regulating essential biological processes such as immune cell respiratory burst, sperm capacitation, and cancer cell migration. Despite the significant concentration difference between protons and other ions in physiological conditions, hHv1 demonstrates remarkable proton selectivity. Our calculations of single-proton, cation, and anion permeation free energy profiles quantitatively demonstrate that the proton selectivity of the wild-type channel originates from its strong proton affinity via the titration of the key residues D112 and D174, although the channel imposes similar kinetic blocking effects for protons compared to other ions. A two-proton knock-on model is proposed to mathematically explain the electrophysiological measurements of the pH-dependent proton conductance in the conductive state. Moreover, it is shown that the anion selectivity of the D112N mutant channel is tied to impaired proton transport and substantial anion leakage.

Emerging Two-Dimensional Materials for Proton-Based Energy Storage

The rapid diffusion kinetics and smallest ion radius make protons the ideal cations toward the ultimate energy storage technology combining the ultrafast charging capabilities of supercapacitors and the high energy densities of batteries. Despite the concept existing for centuries, the lack of satisfactory electrode materials hinders its practical development. Recently, the rapid advancement of the emerging two-dimensional (2D) materials, characterized by their ultrathin morphology, interlayer van der Waals gaps, and distinctive electrochemical properties, injects promises into future proton-based energy storage systems. In this perspective, we comprehensively summarize the current advances in proton-based energy storage based on 2D materials. We begin by providing an overview of proton-based energy storage systems, including proton batteries, pseudocapacitors and electrical double layer capacitors. We then elucidate the fundamental knowledge about proton transport characteristics, including in electrolytes, at electrolyte/electrode interfaces, and within electrode materials, particularly in 2D material systems. We comprehensively summarize specific cases of 2D materials as proton electrodes, detailing their design concepts, proton transport mechanism and electrochemical performance. Finally, we provide insights into the prospects of proton-based energy storage systems, emphasizing the importance of rational design of 2D electrode materials and matching electrolyte systems.

Molecular Dynamics Simulation of Complex Reactivity with the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) Software Package

Simulating chemically reactive phenomena such as proton transport on nanosecond to microsecond and beyond time scales is a challenging task. Ab initio methods are unable to currently access these time scales routinely, and traditional molecular dynamics methods feature fixed bonding arrangements that cannot account for changes in the system's bonding topology. The Multiscale Reactive Molecular Dynamics (MS-RMD) method, as implemented in the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) software package for the LAMMPS molecular dynamics code, offers a method to routinely sample longer time scale reactive simulation data with statistical precision. RAPTOR may also be interfaced with enhanced sampling methods to drive simulations toward the analysis of reactive rare events, and a number of collective variables (CVs) have been developed to facilitate this. Key advances to this methodology, including GPU acceleration efforts and novel CVs to model water wire formation are reviewed, along with recent applications of the method which demonstrate its versatility and robustness.

Kinetic network modeling with molecular simulation inputs: A proton-coupled phosphate symporter

Phosphate, an essential metabolite involved in numerous cellular functions, is taken up by proton-coupled phosphate transporters of plants and fungi within the major facilitator family. Similar phosphate transporters have been identified across a diverse range of biological entities, including various protozoan parasites linked to human diseases, breast cancer cells with increased phosphate requirements, and osteoclast-like cells engaged in bone resorption. Prior studies have proposed an overview of the functional cycle of a proton-driven phosphate transporter (PiPT), yet a comprehensive understanding of the proposed reaction pathways necessitates a closer examination of each elementary reaction step within an overall kinetic framework. In this work, we leverage kinetic network modeling in conjunction with a "bottom-up" molecular dynamics approach to show how such an approach can characterize the proton-phosphate co-transport behavior of PiPT under different pH and phosphate concentration conditions. In turn, this allows us to reveal the prevailing reaction pathway within a high-affinity phosphate transporter under different experimental conditions and to uncover the molecular origin of the optimal pH condition of this transporter.

Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

Accurate pKa Calculations in Proteins with Reactive Molecular Dynamics Provide Physical Insight Into the Electrostatic Origins of Their Values

Classical molecular dynamics simulations are a versatile tool in the study of biomolecular systems, but they usually rely on a fixed bonding topology, precluding the explicit simulation of chemical reactivity. Certain modifications can permit the modeling of reactions. One such method, multiscale reactive molecular dynamics, makes use of a linear combination approach to describe condensed-phase free energy surfaces of reactive processes of biological interest. Before these simulations can be performed, models of the reactive moieties must first be parametrized using electronic structure data. A recent study demonstrated that gas-phase electronic structure data can be used to derive parameters for glutamate and lysine which reproduce experimental pKa values in both bulk water and the staphylococcal nuclease protein with remarkable accuracy and transferability between the water and protein environments. In this work, we first present a new model for aspartate derived in similar fashion and demonstrate that it too produces accurate pKa values in both bulk and protein contexts. We also describe a modification to the prior methodology, involving refitting some of the classical force field parameters to density functional theory calculations, which improves the transferability of the existing glutamate model. Finally and most importantly, this reactive molecular dynamics approach, based on rigorous statistical mechanics, allows one to specifically analyze the fundamental physical causes for the marked pKa shift of both aspartate and glutamate between bulk water and protein and also to demonstrate that local steric and electrostatic effects largely explain the observed differences.

Accurate and Transferable Reactive Molecular Dynamics Models from Constrained Density Functional Theory

Chemical reactions constitute the central feature of many liquid, material, and biomolecular processes. Conventional molecular dynamics (MD) is inadequate for simulating chemical reactions given the fixed bonding topology of most force fields, while modeling chemical reactions using ab initio molecular dynamics is limited to shorter time and length scales given its high computational cost. As such, the multiscale reactive molecular dynamics method provides one promising alternative for simulating complex chemical systems at atomistic detail on a reactive potential energy surface. However, the parametrization of such models is a key barrier to their applicability and success. In this work, we present reactive MD models derived from constrained density functional theory that are both accurate and transferable. We illustrate the features of these models for proton dissociation reactions of amino acids in both aqueous and protein environments. Specifically, we present models for ionizable glutamate and lysine that predict accurate absolute pK_a values in water as well as their significantly shifted pK_a in staphylococcal nuclease (SNase) without any modification of the models. As one outcome of the new methodology, the simulations show that the deprotonation of ionizable residues in SNase can be closely coupled with side chain rotations, which is a concept likely generalizable to many other proteins. Furthermore, the present approach is not limited to only pK_a prediction but can enable the fully atomistic simulation of many other reactive systems along with a determination of the key aspects of the reaction mechanisms.

Physics-based, neural network force fields for reactive molecular dynamics: Investigation of carbene formation from [EMIM+][OAc-]

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol^-1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization.

Multiscale Simulation Reveals Passive Proton Transport Through SERCA on the Microsecond Timescale

The sarcoplasmic reticulum Ca²⁺-ATPase (SERCA) transports two Ca²⁺ ions from the cytoplasm to the reticulum lumen at the expense of ATP hydrolysis. In addition to transporting Ca²⁺, SERCA facilitates bidirectional proton transport across the sarcoplasmic reticulum to maintain the charge balance of the transport sites and to balance the charge deficit generated by the exchange of Ca²⁺. Previous studies have shown the existence of a transient water-filled pore in SERCA that connects the Ca²⁺ binding sites with the lumen, but the capacity of this pathway to sustain passive proton transport has remained unknown. In this study, we used the multiscale reactive molecular dynamics method and free energy sampling to quantify the free energy profile and timescale of the proton transport across this pathway while also explicitly accounting for the dynamically coupled hydration changes of the pore. We find that proton transport from the central binding site to the lumen has a microsecond timescale, revealing a novel passive cytoplasm-to-lumen proton flow beside the well-known inverse proton countertransport occurring in active Ca²⁺ transport. We propose that this proton transport mechanism is operational and serves as a functional conduit for passive proton transport across the sarcoplasmic reticulum.

Understanding and Tracking the Excess Proton in Ab Initio Simulations; Insights from IR Spectra

Proton transport in aqueous media is ubiquitously important in chemical and biological processes. Although ab initio molecular dynamics (AIMD) simulations have made great progress in characterizing proton transport, there has been a long-standing challenge in defining and tracking the excess proton, or more properly, the center of excess charge (CEC) created when a hydrogen nucleus distorts the electron distributions of water molecules in a delocalized and highly dynamic nature. Yet, defining (and biasing) such a CEC is essential when combining AIMD with enhanced sampling methods to calculate the relevant macroscopic properties via free-energy landscapes, which is the standard practice for most processes of interest. Several CEC formulas have been proposed and used, but none have yet been systematically tested or rigorously derived. In this paper, we show that the CEC can be used as a computational tool to disentangle IR features of the solvated excess proton from its surrounding solvent, and in turn, how correlating the features in the excess charge spectrum with the behavior of CEC in simulations enables a systematic evaluation of various CEC definitions. We present a new definition of CEC and show how it overcomes the limitations of those currently available both from a spectroscopic point of view and from a practical perspective of performance in enhanced sampling simulations.

Infrared Spectra of Deprotonated Dicarboxylic Acids: IRMPD Spectroscopy and Empirical Valence‐Bond Modeling

Experimental infrared multiple-photon dissociation (IRMPD) spectra recorded for a series of deprotonated dicarboxylic acids, HO₂ (CH₂ )_n CO 2 - (n=2-4), are interpreted using a variety of computational methods. The broad bands centered near 1600 cm^-1 can be reproduced neither by static vibrational calculations based on quantum chemistry nor by a dynamical description of individual structures using the many-body polarizable AMOEBA force field, strongly suggesting that these molecules experience dynamical proton sharing between the two carboxylic ends. To confirm this assumption, AMOEBA was combined with a two-state empirical valence-bond (EVB) model to allow for proton transfer in classical molecular dynamics simulations. Upon suitable parametrization based on ab initio reference data, the EVB-AMOEBA model satisfactorily reproduces the experimental infrared spectra, and the finite temperature dynamics reveals a significant amount of proton sharing in such systems.

Classical Molecular Dynamics with Mobile Protons

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

Coupling Protein Dynamics with Proton Transport in Human Carbonic Anhydrase II

The role of protein dynamics in enzyme catalysis is one of the most highly debated topics in enzymology. The main controversy centers around what may be defined as functionally significant conformational fluctuations and how, if at all, these fluctuations couple to enzyme catalyzed events. To shed light on this debate, the conformational dynamics along the transition path surmounting the highest free energy barrier have been herein investigated for the rate limiting proton transport event in human carbonic anhydrase (HCA) II. Special attention has been placed on whether the motion of an excess proton is correlated with fluctuations in the surrounding protein and solvent matrix, which may be rare on the picosecond and subpicosecond time scales of molecular motions. It is found that several active site residues, which do not directly participate in the proton transport event, have a significant impact on the dynamics of the excess proton. These secondary participants are shown to strongly influence the active site environment, resulting in the creation of water clusters that are conducive to fast, moderately slow, or slow proton transport events. The identification and characterization of these secondary participants illuminates the role of protein dynamics in the catalytic efficiency of HCA II.

Computationally Efficient Multiscale Reactive Molecular Dynamics to Describe Amino Acid Deprotonation in Proteins

An important challenge in the simulation of biomolecular systems is a quantitative description of the protonation and deprotonation process of amino acid residues. Despite the seeming simplicity of adding or removing a positively charged hydrogen nucleus, simulating the actual protonation/deprotonation process is inherently difficult. It requires both the explicit treatment of the excess proton, including its charge defect delocalization and Grotthuss shuttling through inhomogeneous moieties (water and amino residues), and extensive sampling of coupled condensed phase motions. In a recent paper (J. Chem. Theory Comput. 2014, 10, 2729-2737), a multiscale approach was developed to map high-level quantum mechanics/molecular mechanics (QM/MM) data into a multiscale reactive molecular dynamics (MS-RMD) model in order to describe amino acid deprotonation in bulk water. In this article, we extend the fitting approach (called FitRMD) to create MS-RMD models for ionizable amino acids within proteins. The resulting models are shown to faithfully reproduce the free energy profiles of the reference QM/MM Hamiltonian for PT inside an example protein, the ClC-ec1 H(+)/Cl(-) antiporter. Moreover, we show that the resulting MS-RMD models are computationally efficient enough to then characterize more complex 2-dimensional free energy surfaces due to slow degrees of freedom such as water hydration of internal protein cavities that can be inherently coupled to the excess proton charge translocation. The FitRMD method is thus shown to be an effective way to map ab initio level accuracy into a much more computationally efficient reactive MD method in order to explicitly simulate and quantitatively describe amino acid protonation/deprotonation in proteins.

The Role of Electrostatic Interactions in Folding of β-Proteins

Atomic-level molecular dynamic simulations are capable of fully folding structurally diverse proteins; however, they are limited in their ability to accurately represent electrostatic interactions. Here we have experimentally tested the role of charged residues on stability and folding kinetics of one of the most widely simulated β-proteins, the WW domain. The folding of wild type Pin1 WW domain, which has two positively charged residues in the first turn, was compared to the fast folding mutant FiP35 Pin1, which introduces a negative charge into the first turn. A combination of FTIR spectroscopy and laser-induced temperature-jump coupled with infrared spectroscopy was used to probe changes in the amide I region. The relaxation dynamics of the peptide backbone, β-sheets and β-turns, and negatively charged aspartic acid side chain of FiP35 were measured independently by probing the corresponding bands assigned in the amide I region. Folding is initiated in the turns and the β-sheets form last. While the global folding mechanism is in good agreement with simulation predictions, we observe changes in the protonation state of aspartic acid during folding that have not been captured by simulation methods. The protonation state of aspartic acid is coupled to protein folding; the apparent pKa of aspartic acid in the folded protein is 6.4. The dynamics of the aspartic acid follow the dynamics of the intermediate phase, supporting assignment of this phase to formation of the first hairpin. These results demonstrate the importance of electrostatic interactions in turn stability and formation of extended β-sheet structures.

Multiscale simulation reveals a multifaceted mechanism of proton permeation through the influenza A M2 proton channel

The influenza A virus M2 channel (AM2) is crucial in the viral life cycle. Despite many previous experimental and computational studies, the mechanism of the activating process in which proton permeation acidifies the virion to release the viral RNA and core proteins is not well understood. Herein the AM2 proton permeation process has been systematically characterized using multiscale computer simulations, including quantum, classical, and reactive molecular dynamics methods. We report, to our knowledge, the first complete free-energy profiles for proton transport through the entire AM2 transmembrane domain at various pH values, including explicit treatment of excess proton charge delocalization and shuttling through the His37 tetrad. The free-energy profiles reveal that the excess proton must overcome a large free-energy barrier to diffuse to the His37 tetrad, where it is stabilized in a deep minimum reflecting the delocalization of the excess charge among the histidines and the cost of shuttling the proton past them. At lower pH values the His37 tetrad has a larger total charge that increases the channel width, hydration, and solvent dynamics, in agreement with recent 2D-IR spectroscopic studies. The proton transport barrier becomes smaller, despite the increased charge repulsion, due to backbone expansion and the more dynamic pore water molecules. The calculated conductances are in quantitative agreement with recent experimental measurements. In addition, the free-energy profiles and conductances for proton transport in several mutants provide insights for explaining our findings and those of previous experimental mutagenesis studies.

Multiscale Reactive Molecular Dynamics for Absolute pKa Predictions and Amino Acid Deprotonation

Accurately calculating a weak acid's pK_a from simulations remains a challenging task. We report a multiscale theoretical approach to calculate the free energy profile for acid ionization, resulting in accurate absolute pK_a values in addition to insights into the underlying mechanism. Importantly, our approach minimizes empiricism by mapping electronic structure data (QM/MM forces) into a reactive molecular dynamics model capable of extensive sampling. Consequently, the bulk property of interest (the absolute pK_a) is the natural consequence of the model, not a parameter used to fit it. This approach is applied to create reactive models of aspartic and glutamic acids. We show that these models predict the correct pK_a values and provide ample statistics to probe the molecular mechanism of dissociation. This analysis shows changes in the solvation structure and Zundel-dominated transitions between the protonated acid, contact ion pair, and bulk solvated excess proton.

The open gate of the K(V)1.2 channel: quantum calculations show the key role of hydration

The open gate of the Kv1.2 voltage-gated potassium channel can just hold a hydrated K(+) ion. Quantum calculations starting from the x-ray coordinates of the channel confirm this, showing little change from the x-ray coordinates for the protein. Water molecules not in the x-ray coordinates, and the ion itself, are placed by the calculation. The water molecules, including their orientation and hydrogen bonding, with and without an ion, are critical for the path of the ion, from the solution to the gate. A sequence of steps is postulated in which the potential experienced by the ion in the pore is influenced by the position of the ion. The gate structure, with and without the ion, has been optimized. The charges on the atoms and bond lengths have been calculated using natural bond orbital calculations, giving K(+) ~0.77 charges, rather than 1.0. The PVPV hinge sequence has been mutated in silico to PVVV (P407V in the 2A79 numbering). The water structure around the ion becomes discontinuous, separated into two sections, above and below the ion. PVPV conservation closely relates to maintaining the water structure. Finally, these results have implications concerning gating.

Computationally Efficient Multiconfigurational Reactive Molecular Dynamics

It is a computationally demanding task to explicitly simulate the electronic degrees of freedom in a system to observe the chemical transformations of interest, while at the same time sampling the time and length scales required to converge statistical properties and thus reduce artifacts due to initial conditions, finite-size effects, and limited sampling. One solution that significantly reduces the computational expense consists of molecular models in which effective interactions between particles govern the dynamics of the system. If the interaction potentials in these models are developed to reproduce calculated properties from electronic structure calculations and/or ab initio molecular dynamics simulations, then one can calculate accurate properties at a fraction of the computational cost. Multiconfigurational algorithms model the system as a linear combination of several chemical bonding topologies to simulate chemical reactions, also sometimes referred to as "multistate". These algorithms typically utilize energy and force calculations already found in popular molecular dynamics software packages, thus facilitating their implementation without significant changes to the structure of the code. However, the evaluation of energies and forces for several bonding topologies per simulation step can lead to poor computational efficiency if redundancy is not efficiently removed, particularly with respect to the calculation of long-ranged Coulombic interactions. This paper presents accurate approximations (effective long-range interaction and resulting hybrid methods) and multiple-program parallelization strategies for the efficient calculation of electrostatic interactions in reactive molecular simulations.

Expanding the view of proton pumping in cytochrome c oxidase through computer simulation

In cytochrome c oxidase (CcO), a redox-driven proton pump, protons are transported by the Grotthuss shuttling via hydrogen-bonded water molecules and protonatable residues. Proton transport through the D-pathway is a complicated process that is highly sensitive to alterations in the amino acids or the solvation structure in the channel, both of which can inhibit proton pumping and enzymatic activity. Simulations of proton transport in the hydrophobic cavity showed a clear redox state dependence. To study the mechanism of proton pumping in CcO, multi-state empirical valence bond (MS-EVB) simulations have been conducted, focusing on the proton transport through the D-pathway and the hydrophobic cavity next to the binuclear center. The hydration structures, transport pathways, effects of residues, and free energy surfaces of proton transport were revealed in these MS-EVB simulations. The mechanistic insight gained from them is herein reviewed and placed in context for future studies.

The curious case of the hydrated proton

Understanding the hydrated proton is a critically important problem that continues to engage the research efforts of chemists, physicists, and biologists because of its involvement in a wide array of phenomena. Only recently have several unique properties of the hydrated proton been unraveled through computer simulations. One such process is the detailed molecular mechanism by which protons hop between neighboring water molecules, thus giving rise to the anomalously high diffusion of protons relative to other simple cations. Termed Grotthuss shuttling, this process occurs over multiple time and length scales, presenting unique challenges for computer modeling and simulation. Because the hydrated proton is in reality a dynamical electronic charge defect that spans multiple water molecules, the simulation methodology must be able to dynamically readjust the chemical bonding topology. This reactive nature of the chemical process is automatically captured with ab initio molecular dynamics (AIMD) simulation methods, where the electronic degrees of freedom are treated explicitly. Unfortunately, these calculations can be prohibitively expensive for more complex proton solvation and transport phenomena in the condensed phase. These AIMD simulations remain extremely valuable, however, in validating empirical models, verifying results, and providing insight into molecular mechanisms. In this Account, we discuss recent progress in understanding the solvation and transport properties of the hydrated excess proton. The advances are based on results obtained from reactive molecular dynamics simulations using the multistate empirical valence bond (MS-EVB) methodology. This approach relies on a dynamic linear combination of chemical bond topologies to model charge delocalization and dynamic bonding environments. When parametrized via a variational force-matching algorithm from AIMD trajectories, the MS-EVB method can be viewed as a multiscale bridging of ab initio simulation results to a simpler and more efficient representation. The process allows sampling of longer time and length scales, which would normally be too computationally expensive with AIMD alone. With the MS-EVB methodology, the statistically important components of the excess proton solvation and hopping mechanisms in liquid water have been identified. The most likely solvation structure for the hydrated proton is a distorted Eigen-type complex (H(9)O(4)(+)). In this state, the excess proton charge defect rapidly resonates between three possible distorted Eigen-type structures until a successful proton hop occurs. This process, termed the "special-pair dance", serves as a kind of preparatory phase for the proton hopping while the neighboring water hydrogen-bonding network fluctuates and ultimately rearranges to facilitate a proton hop. The modifications of the solvation structure and transport properties of the excess proton in concentrated acid solutions were further investigated. The Eigen-type solvation structure also possesses both "hydrophilic" and "hydrophobic" sides, which accounts for the affinity of the hydrated proton for the air-water interface. This unusual "amphiphilic" character of the hydrated proton further leads to the metastable formation of contact ion pairs between two hydrated protons. It also engenders a surprisingly constant degree of solubility of hydrophobic species as a function of acid concentration, which contrasts with a markedly variable solubility as a function of salt (such as NaCl or KCl) concentration.

Constant pH Molecular Dynamics in Explicit Solvent with λ-Dynamics

pH is an important parameter in condensed-phase systems, because it determines the protonation state of titratable groups and thus influences the structure, dynamics, and function of molecules in solution. In most force field simulation protocols, however, the protonation state of a system (rather than its pH) is kept fixed and cannot adapt to changes of the local environment. Here, we present a method, implemented within the MD package GROMACS, for constant pH molecular dynamics simulations in explicit solvent that is based on the λ-dynamics approach. In the latter, the dynamics of the titration coordinate λ, which interpolates between the protonated and deprotonated states, is driven by generalized forces between the protonated and deprotonated states. The hydration free energy, as a function of pH, is included to facilitate constant pH simulations. The protonation states of titratable groups are allowed to change dynamically during a simulation, thus reproducing average protonation probabilities at a certain pH. The accuracy of the method is tested against titration curves of single amino acids and a dipeptide in explicit solvent.

Chemical rescue of enzymes: proton transfer in mutants of human carbonic anhydrase II

In human carbonic anhydrase II (HCA II), the mutation of position 64 from histidine to alanine (H64A) disrupts the rate limiting proton transfer (PT) event, resulting in a reduction of the catalytic activity of the enzyme as compared to the wild-type. Potential of mean force (PMF) calculations utilizing the multistate empirical valence bond (MS-EVB) methodology for H64A HCA II yields a PT free energy barrier significantly higher than that found in the wild-type enzyme. This high barrier, determined in the absence of exogenous buffer and assuming no additional ionizable residues in the PT pathway, indicates the likelihood of alternate enzyme pathways that utilize either ionizable enzyme residues (self-rescue) and/or exogenous buffers (chemical rescue). It has been shown experimentally that the catalytic activity of H64A HCA II can be chemically rescued to near wild-type levels by the addition of the exogenous buffer 4-methylimidazole (4MI). Crystallographic studies have identified two 4MI binding sites, yet site-specific mutations intended to disrupt 4MI binding have demonstrated these sites to be nonproductive. In the present work, MS-EVB simulations show that binding of 4MI near Thr199 in the H64A HCA II mutant, a binding site determined by NMR spectroscopy, results in a viable chemical rescue pathway. Additional viable rescue pathways are also identified where 4MI acts as a proton transport intermediary from the active site to ionizable residues on the rim of the active site, revealing a probable mode of action for the chemical rescue pathway.

Intricate role of water in proton transport through cytochrome c oxidase

Cytochrome c oxidase (CytcO), the final electron acceptor in the respiratory chain, catalyzes the reduction of O(2) to H(2)O while simultaneously pumping protons across the inner mitochondrial or bacterial membrane to maintain a transmembrane electrochemical gradient that drives, for example, ATP synthesis. In this work mutations that were predicted to alter proton translocation and enzyme activity in preliminary computational studies are characterized with extensive experimental and computational analysis. The mutations were introduced in the D pathway, one of two proton-uptake pathways, in CytcO from Rhodobacter sphaeroides . Serine residues 200 and 201, which are hydrogen-bonded to crystallographically resolved water molecules halfway up the D pathway, were replaced by more bulky hydrophobic residues (Ser200Ile, Ser200Val/Ser201Val, and Ser200Val/Ser201Tyr) to query the effects of changing the local structure on enzyme activity as well as proton uptake, release, and intermediate transitions. In addition, the effects of these mutations on internal proton transfer were investigated by blocking proton uptake at the pathway entrance (Asp132Asn replacement in addition to the above-mentioned mutations). Even though the overall activities of all mutant CytcO's were lowered, both the Ser200Ile and Ser200Val/Ser201Val variants maintained the ability to pump protons. The lowered activities were shown to be due to slowed oxidation kinetics during the P(R) → F and F → O transitions (P(R) is the "peroxy" intermediate formed at the catalytic site upon reaction of the four-electron-reduced CytcO with O(2), F is the oxoferryl intermediate, and O is the fully oxidized CytcO). Furthermore, the P(R) → F transition is shown to be essentially pH independent up to pH 12 (i.e., the apparent pK(a) of Glu286 is increased from 9.4 by at least 3 pK(a) units) in the Ser200Val/Ser201Val mutant. Explicit simulations of proton transport in the mutated enzymes revealed that the solvation dynamics can cause intriguing energetic consequences and hence provide mechanistic insights that would never be detected in static structures or simulations of the system with fixed protonation states (i.e., lacking explicit proton transport). The results are discussed in terms of the proton-pumping mechanism of CytcO.

A Non-Orthogonal Block-Localized Effective Hamiltonian Approach for Chemical and Enzymatic Reactions

The effective Hamiltonian-molecular orbital and valence bond (EH-MOVB) method based on non-orthogonal block-localized fragment orbitals has been implemented into the program CHARMM for molecular dynamics simulations of chemical and enzymatic reactions, making use of semiempirical quantum mechanical models. Building upon ab initio MOVB theory, we make use of two parameters in the EH-MOVB method to fit the barrier height and the relative energy between the reactant and product state for a given chemical reaction to be in agreement with experiment or high-level ab initio or density functional results. Consequently, the EH-MOVB method provides a highly accurate and computationally efficient QM/MM model for dynamics simulation of chemical reactions in solution. The EH-MOVB method is illustrated by examination of the potential energy surface of the hydride transfer reaction from trimethylamine to a flavin cofactor model in the gas phase. In the present study, we employed the semiempirical AM1 model, which yields a reaction barrier that is more than 5 kcal/mol too high. We use a parameter calibration procedure for the EH-MOVB method similar to that employed to adjust the results of semiempirical and empirical models. Thus, the relative energy of these two diabatic states can be shifted to reproduce the experimental energy of reaction, and the barrier height is optimized to reproduce the desired (accurate) value by adding a constant to the off-diagonal matrix element. The present EH-MOVB method offers a viable approach to characterizing solvent and protein-reorganization effects in the realm of combined QM/MM simulations.

Properties of hydrated excess protons near phospholipid bilayers

The behavior of the hydrated excess proton near different lipid membranes is studied with the third generation of the multistate empirical valence bond (MS-EVB3) model [Wu, Y. J.; Chen, H. N.; Wang, F.; Paesani, F.; Voth, G. A. J. Phys. Chem. B 2008, 112, 467]. Dioleoylphosphatidylcholine (DOPC), dioleoylphosphatidylethanolamine (DOPE), and dioleoylphosphatidylglycerol (DOPG) are selected as example lipids. In spite of the differences of the head groups, the molecular dynamics simulations show that all the lipid membranes have a proton-collecting antenna effect with no free energy barrier between the bulk water and interface regions. By comparison with classical hydronium model simulations, it is found that an appropriate description of proton Grotthuss shuttling and associated charge defect delocalization are necessary to obtain the correct free energy profile for the hydrated excess proton. In addition, nanosecond time scale sampling is essential to evaluate the free energy profiles, because certain slow motions are needed to stabilize the excess proton in the deep membrane interface region. It is also found that the lateral diffusion coefficients are 1 order of magnitude smaller in the interface region than in bulk water for all the lipids. These coefficients are almost the same as those of the lipid head groups. Finally, since the lipid phosphates may possibly be protonated due to the proton antenna effect of the membrane, phosphate group protonation is investigated and discussed within the MS-EVB framework.

Block-Localized Density Functional Theory (BLDFT), Diabatic Coupling, and Their Use in Valence Bond Theory for Representing Reactive Potential Energy Surfaces

A multistate density functional theory in the framework of the valence bond model is described. The method is based on a block-localized density functional theory (BLDFT) for the construction of valence-bond-like diabatic electronic states and is suitable for the study of electron transfer reactions and for the representation of reactive potential energy surfaces. The method is equivalent to a valence bond theory with the treatment of the localized configurations by using density functional theory (VBDFT). In VBDFT, the electron densities and energies of the valence bond states are determined by BLDFT. A functional estimate of the off-diagonal matrix elements of the VB Hamiltonian is proposed, making use of the overlap integral between Kohn-Sham determinants and the exchange-correlation functional for the ground state substituted with the transition (exchange) density. In addition, we describe an approximate approach, in which the off-diagonal matrix element is computed by wave function theory using block-localized Kohn-Sham orbitals. The key feature is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy; the energy is determined by diagonalization of the multistate valence bond Hamiltonian. This represents a departure from the standard single-determinant Kohn-Sham density functional theory. The multistate VBDFT method is illustrated by the bond dissociation of H2+ and a set of three nucleophilic substitution reactions in the DBH24 database. In the dissociation of H2+, the VBDFT method yields the correct asymptotic behavior as the two protons stretch to infinity, whereas approximate functionals fail badly. For the S(N)2 nucleophilic substitution reactions, the hybrid functional B3LYP severely underestimates the barrier heights, while the approximate two-state VBDFT method overcomes the self-interaction error, and overestimates the barrier heights. Inclusion of the ionic state in a three-state model, VBDFT(3), significantly improves the computed barrier heights, which are found to be in accord with accurate results. The BLDFT method is a versatile theory that can be used to analyze conventional DFT results to gain insight into chemical bonding properties, and it is illustrated by examining the intricate energy contributions to the ion-dipole complex stabilization.

Proton transport in carbonic anhydrase: Insights from molecular simulation

This article reviews the insights gained from molecular simulations of human carbonic anhydrase II (HCA II) utilizing non-reactive and reactive force fields. The simulations with a reactive force field explore protein transfer and transport via Grotthuss shuttling, while the non-reactive simulations probe the larger conformational dynamics that underpin the various contributions to the rate-limiting proton transfer event. Specific attention is given to the orientational stability of the His64 group and the characteristics of the active site water cluster, in an effort to determine both of their impact on the maximal catalytic rate. The explicit proton transfer and transport events are described by the multistate empirical valence bond (MS-EVB) method, as are alternative pathways for the excess proton charge defect to enter/leave the active site. The simulation results are interpreted in light of experimental results on the wild-type enzyme and various site-specific mutations of HCA II in order to better elucidate the key factors that contribute to its exceptional efficiency.

Elucidation of the proton transport mechanism in human carbonic anhydrase II

Human carbonic anhydrase II (HCA II) is one of the fastest known enzymes, which utilizes a rate-limiting proton transport (PT) step in its enzymatic reaction. To evaluate the PT event at an atomistic level, the multistate empirical valence bond (MS-EVB) method has been utilized in this work. It is observed that the PT event in HCA II exploits a transient active site water cluster to transport the excess proton between the catalytic zinc-bound water/hydroxide and the proton shuttling residue, His64. This PT event is found to be dependent on the enzyme's ability to form and stabilize the active site water cluster in addition to its ability to orient His64 in a favorable conformation. Evaluation of the PT free energy barrier for different orientations of His64 reveals this residue's vital role as a proton transporter and elucidates its direct effect on the barrier to PT through the active site water. It is suggested that the rate-limiting step oscillates between the active site water PT event to His64 and the de/protonation of His64 depending on the exogenous buffer concentration and the orientation of His64. In the absence of a PT acceptor/donor at position 64, it is found that the excess proton will utilize one of three distinct paths to enter/leave the active site. This latter result not only allows for an increased understanding of how enzymes capitalize on the protein/solvent interface to guide excess protons to/from areas of interest, it also provides valuable insight into the chemical rescue experiments on HCA II mutants.

An Effective Hamiltonian Molecular Orbital-Valence Bond (MOVB) Approach for Chemical Reactions Applied to the Nucleophilic Substitution Reaction of Hydrosulfide Ion and Chloromethane

An effective Hamiltonian mixed molecular orbital and valence bond (EH-MOVB) method is described to obtain an accurate potential energy surface for chemical reactions. Building upon previous results on the construction of diabatic and adiabatic potential surfaces using ab initio MOVB theory, we introduce a diabatic-coupling scaling factor to uniformly scale the ab initio off-diagonal matrix element H(12) such that the computed energy of reaction from the EH-MOVB method is in agreement with the target value. The scaling factor is very close to unity, resulting in minimal alteration of the potential energy surface of the original MOVB model. Furthermore, the relative energy between the reactant and product diabatic states in the EH-MOVB method can be improved to match the experimental energy of reaction. A key ingredient in the EH-MOVB theory is that the off-diagonal matrix elements are functions of all degrees of freedom of the system and the overlap matrix is explicitly evaluated. The EH-MOVB method has been applied to the nucleophilic substitution reaction between hydrosulfide and chloromethane to illustrate the methodology and the results were matched to reproduce the results from ab initio valence bond self-consistent valence bond (VBSCF) calculations. The diabatic coupling (the off-diagonal matrix element in the generalized secular equation) has small variations along the minimum energy reaction path in the EH-MOVB model, whereas it shows a maximum value at the transition state and has nearly zero values in the regions of the ion-dipole complexes from VBSCF calculations. The difference in the diabatic coupling stabilization is attributed to the large overlap integral in the computationally efficient MOVB method.

Reactive force fields for proton transfer dynamics

A force field-inspired method based on fitted, high-quality multidimensional potential energy surfaces to follow proton transfer (PT) reactions in molecular dynamics simulations is presented. In molecular mechanics with proton transfer (MMPT) a system is partitioned into a region where proton transfer takes place and the remaining degrees of freedom which are treated with a conventional force field. The implementation of the method and applications to specific chemically and biologically relevant scenarios are presented. MMPT is developed in view of two primary areas in mind: to follow the molecular dynamics of proton transfer in the condensed phase on realistic time scales and to adapt the shape (morphing) of the potential energy surface for specific applications. MMPT is applied to PT in protonated ammonia dimer, double proton transfer in 2-pyridone-2-hydroxypyridine, and the first step of PT from a protein side-chain towards a buried [3Fe4S] cluster in ferredoxin I. Specific findings of the work include the fundamental role of the N-N vibration as the gating mode for PT in NH4+...NH3 and the qualitative understanding of PT from the protein to a metastable active-site water molecule in Ferredoxin I.

Two-state model based on the block-localized wave function method

The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV).

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.