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

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.

Understanding the Multifaceted Mechanism of Compound I Formation in Unspecific Peroxygenases through Multiscale Simulations

Unspecific peroxygenases (UPOs) can selectively oxyfunctionalize unactivated hydrocarbons by using peroxides under mild conditions. They circumvent the oxygen dilemma faced by cytochrome P450s and exhibit greater stability than the latter. As such, they hold great potential for industrial applications. A thorough understanding of their catalysis is needed to improve their catalytic performance. However, it remains elusive how UPOs effectively convert peroxide to Compound I (CpdI), the principal oxidizing intermediate in the catalytic cycle. Previous computational studies of this process primarily focused on heme peroxidases and P450s, which have significant differences in the active site from UPOs. Additionally, the roles of peroxide unbinding in the kinetics of CpdI formation, which is essential for interpreting existing experiments, have been understudied. Moreover, there has been a lack of free energy characterizations with explicit sampling of protein and hydration dynamics, which is critical for understanding the thermodynamics of the proton transport (PT) events involved in CpdI formation. To bridge these gaps, we employed multiscale simulations to comprehensively characterize the CpdI formation in wild-type UPO from Agrocybe aegerita (AaeUPO). Extensive free energy and potential energy calculations were performed in a quantum mechanics/molecular mechanics setting. Our results indicate that substrate-binding dehydrates the active site, impeding the PT from H2O2 to a nearby catalytic base (Glu196). Furthermore, the PT is coupled with considerable hydrogen bond network rearrangements near the active site, facilitating subsequent O-O bond cleavage. Finally, large unbinding free energy barriers kinetically stabilize H2O2 at the active site. These findings reveal a delicate balance among PT, hydration dynamics, hydrogen bond rearrangement, and cosubstrate unbinding, which collectively enable efficient CpdI formation. Our simulation results are consistent with kinetic measurements and offer new insights into the CpdI formation mechanism at atomic-level details, which can potentially aid the design of next-generation biocatalysts for sustainable chemical transformations of feedstocks.

Transient water wires mediate selective proton transport in designed channel proteins

Selective proton transport through proteins is essential for forming and using proton gradients in cells. Protons are conducted along hydrogen-bonded 'wires' of water molecules and polar side chains, which, somewhat surprisingly, are often interrupted by dry apolar stretches in the conduction pathways, inferred from static protein structures. Here we hypothesize that protons are conducted through such dry spots by forming transient water wires, often highly correlated with the presence of the excess protons in the water wire. To test this hypothesis, we performed molecular dynamics simulations to design transmembrane channels with stable water pockets interspersed by apolar segments capable of forming flickering water wires. The minimalist designed channels conduct protons at rates similar to viral proton channels, and they are at least 106-fold more selective for H+ over Na+. These studies inform the mechanisms of biological proton conduction and the principles for engineering proton-conductive materials.

Modeling the Solvation and Acidity of Carboxylic Acids Using an Ab Initio Deep Neural Network Potential

Formic and acetic acid constitute the simplest of carboxylic acids, yet they exhibit fascinating chemistry in the condensed phase such as proton transfer and dimerization. The go-to method of choice for modeling these rare events have been accurate but expensive ab initio molecular dynamics simulations. In this study, we present a deep neural network potential trained using accurate ab initio data that can be used in tandem with enhanced-sampling methods to perform an efficient exploration of the free-energy surface of aqueous solutions of weak carboxylic acids. In particular, we show that our model captures proton dissociation and provides a good estimate of the pK_a, as well as the dimerization of formic and acetic acid. This provides a suitable starting point for applications in different research areas where computational efficiency coupled with the accuracy of ab initio methods is required.

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.

Advanced Theory and Simulation to Guide the Development of CO2 Capture Solvents

Increasing atmospheric concentrations of greenhouse gases due to industrial activity have led to concerning levels of global warming. Reducing carbon dioxide (CO₂) emissions, one of the main contributors to the greenhouse effect, is key to mitigating further warming and its negative effects on the planet. CO₂ capture solvent systems are currently the only available technology deployable at scales commensurate with industrial processes. Nonetheless, designing these solvents for a given application is a daunting task requiring the optimization of both thermodynamic and transport properties. Here, we discuss the use of atomic scale modeling for computing reaction energetics and transport properties of these chemically complex solvents. Theoretical studies have shown that in many cases, one is dealing with a rich ensemble of chemical species in a coupled equilibrium that is often difficult to characterize and quantify by experiment alone. As a result, solvent design is a balancing act between multiple parameters which have optimal zones of effectiveness depending on the operating conditions of the application. Simulation of reaction mechanisms has shown that CO₂ binding and proton transfer reactions create chemical equilibrium between multiple species and that the agglomeration of resulting ions and zwitterions can have profound effects on bulk solvent properties such as viscosity. This is balanced against the solvent systems needing to perform different functions (e.g., CO₂ uptake and release) depending on the thermodynamic conditions (e.g., temperature and pressure swings). The latter constraint imposes a "Goldilocks" range of effective parameters, such as binding enthalpy and pK _a, which need to be tuned at the molecular level. The resulting picture is that solvent development requires an integrated approach where theory and simulation can provide the necessary ingredients to balance competing factors.

Multiscale Simulation of an Influenza A M2 Channel Mutant Reveals Key Features of Its Markedly Different Proton Transport Behavior

The influenza A M2 channel, a prototype for viroporins, is an acid-activated viroporin that conducts protons across the viral membrane, a critical step in the viral life cycle. Four central His37 residues control channel activation by binding subsequent protons from the viral exterior, which opens the Trp41 gate and allows proton flux to the interior. Asp44 is essential for maintaining the Trp41 gate in a closed state at high pH, resulting in asymmetric conduction. The prevalent D44N mutant disrupts this gate and opens the C-terminal end of the channel, resulting in increased conduction and a loss of this asymmetric conduction. Here, we use extensive Multiscale Reactive Molecular Dynamics (MS-RMD) and quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with an explicit, reactive excess proton to calculate the free energy of proton transport in this M2 mutant and to study the dynamic molecular-level behavior of D44N M2. We find that this mutation significantly lowers the barrier of His37 deprotonation in the activated state and shifts the barrier for entry to the Val27 tetrad. These free energy changes are reflected in structural shifts. Additionally, we show that the increased hydration around the His37 tetrad diminishes the effect of the His37 charge on the channel's water structure, facilitating proton transport and enabling activation from the viral interior. Altogether, this work provides key insight into the fundamental characteristics of PT in WT M2 and how the D44N mutation alters this PT mechanism, and it expands understanding of the role of emergent mutations in viroporins.

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.

Using Constrained Density Functional Theory to Track Proton Transfers and to Sample Their Associated Free Energy Surface

Ab initio molecular dynamics (AIMD) and quantum mechanics/molecular mechanics (QM/MM) methods are powerful tools for studying proton solvation, transfer, and transport processes in various environments. However, due to the high computational cost of such methods, achieving sufficient sampling of rare events involving excess proton motion-especially when Grotthuss proton shuttling is involved-usually requires enhanced free energy sampling methods to obtain informative results. Moreover, an appropriate collective variable (CV) that describes the effective position of the net positive charge defect associated with an excess proton is essential both for tracking the trajectory of the defect and for the free energy sampling of the processes associated with the resulting proton transfer and transport. In this work, such a CV is derived from first principles using constrained density functional theory (CDFT). This CV is applicable to a broad array of proton transport and transfer processes as studied via AIMD and QM/MM simulations.

Influenza A M2 Inhibitor Binding Understood through Mechanisms of Excess Proton Stabilization and Channel Dynamics

Prevalent resistance to inhibitors that target the influenza A M2 proton channel has necessitated a continued drug design effort, supported by a sustained study of the mechanism of channel function and inhibition. Recent high-resolution X-ray crystal structures present the first opportunity to see how the adamantyl amine class of inhibitors bind to M2 and disrupt and interact with the channel’s water network, providing insight into the critical properties that enable their effective inhibition in wild-type M2. In this work, we examine the hypothesis that these drugs act primarily as mechanism-based inhibitors by comparing hydrated excess proton stabilization during proton transport in M2 with the interactions revealed in the crystal structures, using the Multiscale Reactive Molecular Dynamics (MS-RMD) methodology. MS-RMD, unlike classical molecular dynamics, models the hydrated proton (hydronium-like cation) as a dynamic excess charge defect and allows bonds to break and form, capturing the intricate interactions between the hydrated excess proton, protein atoms, and water. Through this, we show that the ammonium group of the inhibitors is effectively positioned to take advantage of the channel’s natural ability to stabilize an excess protonic charge and act as a hydronium mimic. Additionally, we show that the channel is especially stable in the drug binding region, highlighting the importance of this property for binding the adamantane group. Finally, we characterize an additional hinge point near Val27, which dynamically responds to charge and inhibitor binding. Altogether, this work further illuminates a dynamic understanding of the mechanism of drug inhibition in M2, grounded in the fundamental properties that enable the channel to transport and stabilize excess protons, with critical implications for future drug design efforts.

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.

First-Principles Calculation of Water pKa Using the Newly Developed SCAN Functional

Acid/base chemistry is an intriguing topic that still constitutes a challenge for computational chemistry. While estimating the acid dissociation constant (or pK_a) could shed light on many chemistry processes, especially in the fields of biochemistry and geochemistry, evaluating the relative stability between protonated and nonprotonated species is often very difficult. Indeed, a prerequisite for calculating the pK_a of any molecule is an accurate description of the energetics of water dissociation. Here, we applied constrained molecular dynamics simulations, a noncanonical sampling technique, to investigate the water deprotonation process by selecting the OH distance as the reaction coordinate. The calculation is based on density functional theory and the newly developed SCAN functional, which has shown excellent performance in describing water structure. This first benchmark of SCAN on a chemical reaction shows that this functional accurately models the energetics of proton transfer reactions in an aqueous environment. After taking Coulomb long-range corrections and nuclear quantum effects into account, the estimated water pK_a is only 1.0 pK_a unit different from the target experimental value. Our results show that the combination of SCAN and constrained MD successfully reproduces the chemistry of water and constitutes a good framework for calculating the free energy of chemical reactions of interest.

Dynamic Protonation Dramatically Affects the Membrane Permeability of Drug-like Molecules

Permeability (P_m) across biological membranes is of fundamental importance and a key factor in drug absorption, distribution, and development. Although the majority of drugs will be charged at some point during oral delivery, our understanding of membrane permeation by charged species is limited. The canonical model assumes that only neutral molecules partition into and passively permeate across membranes, but there is mounting evidence that these processes are also facile for certain charged species. However, it is unknown whether such ionizable permeants dynamically neutralize at the membrane surface or permeate in their charged form. To probe protonation-coupled permeation in atomic detail, we herein apply continuous constant-pH molecular dynamics along with free energy sampling to study the permeation of a weak base propranolol (PPL), and evaluate the impact of including dynamic protonation on P_m. The simulations reveal that PPL dynamically neutralizes at the lipid-tail interface, which dramatically influences the permeation free energy landscape and explains why the conventional model overestimates the assigned intrinsic permeability. We demonstrate how fixed-charge-state simulations can account for this effect, and propose a revised model that better describes pH-coupled partitioning and permeation. Our results demonstrate how dynamic changes in protonation state may play a critical role in the permeation of ionizable molecules, including pharmaceuticals and drug-like molecules, thus requiring a revision of the standard picture.

Proton-Induced Conformational and Hydration Dynamics in the Influenza A M2 Channel

The influenza A M2 protein is an acid-activated proton channel responsible for acidification of the inside of the virus, a critical step in the viral life cycle. This channel has four central histidine residues that form an acid-activated gate, binding protons from the outside until an activated state allows proton transport to the inside. While previous work has focused on proton transport through the channel, the structural and dynamic changes that accompany proton flux and enable activation have yet to be resolved. In this study, extensive Multiscale Reactive Molecular Dynamics simulations with explicit Grotthuss-shuttling hydrated excess protons are used to explore detailed molecular-level interactions that accompany proton transport in the +0, + 1, and +2 histidine charge states. The results demonstrate how the hydrated excess proton strongly influences both the protein and water hydrogen-bonding network throughout the channel, providing further insight into the channel's acid-activation mechanism and rectification behavior. We find that the excess proton dynamically, as a function of location, shifts the protein structure away from its equilibrium distributions uniquely for different pH conditions consistent with acid-activation. The proton distribution in the xy-plane is also shown to be asymmetric about the channel's main axis, which has potentially important implications for the mechanism of proton conduction and future drug design efforts.

Modulating the Chemical Transport Properties of a Transmembrane Antiporter via Alternative Anion Flux

ClC-ec1 is a prototype of the ClC antiporters, proteins that stoichiometrically exchange Cl^– and H⁺ ions in opposite directions across a membrane. It has been shown that other polyatomic anions, such as NO₃^– and SCN^–, can also be transported by ClC-ec1, but with partially or completely uncoupled proton flux. Herein, with the help of multiscale computer simulations in which the Grotthuss mechanism of proton transport (PT) is treated explicitly, we demonstrate how the chemical nature of these anions alters the coupling mechanism and qualitatively explain the shifts in the ion stoichiometry. Multidimensional free energy profiles for PT and the coupled changes in hydration are presented for NO₃^– and SCN^–. The calculated proton conductances agree with experiment, showing reduced or abolished proton flux. Surprisingly, the proton affinity of the anion is less influential on the PT, while its size and interactions with the protein significantly alter hydration and shift its influence on PT from facilitating to inhibiting. We find that the hydration of the cavity below the anion is relatively fast, but connecting the water network past the steric hindrance of these polyatomic anions is quite slow. Hence, the most relevant coordinate to the PT free energy barrier is the water connectivity along the PT pathway, but importantly only in the presence of the excess proton, and this coordinate is significantly affected by the nature of the bound anion. This work again demonstrates how PT is intrinsically coupled with protein cavity hydration changes as well as influenced by the protein environment. It additionally suggests ways in which ion exchange can be modulated and exchange stoichiometries altered.

Does Proton Conduction in the Voltage-Gated H+ Channel hHv1 Involve Grotthuss-Like Hopping via Acidic Residues?

Hv1s are ubiquitous highly selective voltage-gated proton channels involved in male fertility, immunology, and the invasiveness of certain forms of breast cancer. The mechanism of proton extrusion in Hv1 is not yet understood, while it constitutes the first step toward the design of high-affinity drugs aimed at this important pharmacological target. In this contribution, we explore the details of the mechanism via an integrative approach, using classical and QM/MM molecular dynamics simulations of a monomeric hHv1 model. We propose that protons localize in three binding sites along the channel lumen, formed by three pairs of conserved negatively charged residues lining the pore: D174/E153, D112/D185, and E119/D123. Local rearrangements, involving notably a dihedral transition of F150, a conserved phenylalanine lining the permeation pathway, appear to allow protons to hop from one acidic residue to the next through a bridging water molecule. These results constitute a first attempt at rationalizing hHv1 selectivity for H+ and the role played by D112 in this process. They pave the way for further quantitative characterization of H+ transport in hHv1.

Simulating Protein Mediated Hydrolysis of ATP and Other Nucleoside Triphosphates by Combining QM/MM Molecular Dynamics with Advances in Metadynamics

The protein mediated hydrolysis of nucleoside triphosphates such as ATP or GTP is one of the most important and challenging biochemical reactions in nature. The chemical environment (water structure, catalytic metal, and amino acid residues) adjacent to the hydrolysis site contains hundreds of atoms, usually greatly limiting the amount of the free energy sampling that one can achieve from computationally demanding electronic structure calculations such as QM/MM simulations. Therefore, the combination of QM/MM molecular dynamics with the recently developed transition-tempered metadynamics (TTMetaD), an enhanced sampling method that can provide a high-quality free energy estimate at an early stage in a simulation, is an ideal approach to address the biomolecular nucleoside triphosphate hydrolysis problem. In this work the ATP hydrolysis process in monomeric and filamentous actin is studied as an example application of the combined methodology. The performance of TTMetaD in these demanding QM/MM simulations is compared with that of the more conventional well-tempered metadynamics (WTMetaD). Our results show that TTMetaD exhibits much better exploration of the hydrolysis reaction free energy surface in two key collective variables (CVs) during the early stages of the QM/MM simulation than does WTMetaD. The TTMetaD simulations also reveal that a key third degree of freedom, the O-H bond-breaking and proton transfer from the lytic water, must be biased for TTMetaD to converge fully. To perturb the NTP hydrolysis dynamics to the least extent and to properly focus the MetaD free energy sampling, we also adopt here the recently developed metabasin metadynamics (MBMetaD) to construct a self-limiting bias potential that only applies to the lytic water after its nucleophilic attack of the phosphate of ATP. With these new, state-of-the-art enhanced sampling metadynamics techniques, we present an effective and accurate computational strategy for combining QM/MM molecular dynamics simulation with free energy sampling methodology, including a means to analyze the convergence of the calculations through robust numerical criteria.

Multiscale Simulations Reveal Key Aspects of the Proton Transport Mechanism in the ClC-ec1 Antiporter

Multiscale reactive molecular dynamics simulations are used to study proton transport through the central region of ClC-ec1, a widely studied ClC transporter that enables the stoichiometric exchange of 2 Cl(-) ions for 1 proton (H(+)). It has long been known that both Cl(-) and proton transport occur through partially congruent pathways, and that their exchange is strictly coupled. However, the nature of this coupling and the mechanism of antiporting remain topics of debate. Here multiscale simulations have been used to characterize proton transport between E203 (Glu(in)) and E148 (Glu(ex)), the internal and external intermediate proton binding sites, respectively. Free energy profiles are presented, explicitly accounting for the binding of Cl(-) along the central pathway, the dynamically coupled hydration changes of the central region, and conformational changes of Glu(in) and Glu(ex). We find that proton transport between Glu(in) and Glu(ex) is possible in both the presence and absence of Cl(-) in the central binding site, although it is facilitated by the anion presence. These results support the notion that the requisite coupling between Cl(-) and proton transport occurs elsewhere (e.g., during proton uptake or release). In addition, proton transport is explored in the E203K mutant, which maintains proton permeation despite the substitution of a basic residue for Glu(in). This collection of calculations provides for the first time, to our knowledge, a detailed picture of the proton transport mechanism in the central region of ClC-ec1 at a molecular level.

Acid activation mechanism of the influenza A M2 proton channel

The homotetrameric influenza A M2 channel (AM2) is an acid-activated proton channel responsible for the acidification of the influenza virus interior, an important step in the viral lifecycle. Four histidine residues (His37) in the center of the channel act as a pH sensor and proton selectivity filter. Despite intense study, the pH-dependent activation mechanism of the AM2 channel has to date not been completely understood at a molecular level. Herein we have used multiscale computer simulations to characterize (with explicit proton transport free energy profiles and their associated calculated conductances) the activation mechanism of AM2. All proton transfer steps involved in proton diffusion through the channel, including the protonation/deprotonation of His37, are explicitly considered using classical, quantum, and reactive molecular dynamics methods. The asymmetry of the proton transport free energy profile under high-pH conditions qualitatively explains the rectification behavior of AM2 (i.e., why the inward proton flux is allowed when the pH is low in viral exterior and high in viral interior, but outward proton flux is prohibited when the pH gradient is reversed). Also, in agreement with electrophysiological results, our simulations indicate that the C-terminal amphipathic helix does not significantly change the proton conduction mechanism in the AM2 transmembrane domain; the four transmembrane helices flanking the channel lumen alone seem to determine the proton conduction mechanism.

The Origin of Coupled Chloride and Proton Transport in a Cl-/H+ Antiporter

The ClC family of transmembrane proteins functions throughout nature to control the transport of Cl^– ions across biological membranes. ClC-ec1 from Escherichia coli is an antiporter, coupling the transport of Cl^– and H⁺ ions in opposite directions and driven by the concentration gradients of the ions. Despite keen interest in this protein, the molecular mechanism of the Cl^–/H⁺ coupling has not been fully elucidated. Here, we have used multiscale simulation to help identify the essential mechanism of the Cl^–/H⁺ coupling. We find that the highest barrier for proton transport (PT) from the intra- to extracellular solution is attributable to a chemical reaction, the deprotonation of glutamic acid 148 (E148). This barrier is significantly reduced by the binding of Cl^– in the “central” site (Cl^–_cen), which displaces E148 and thereby facilitates its deprotonation. Conversely, in the absence of Cl^–_cen E148 favors the “down” conformation, which results in a much higher cumulative rotation and deprotonation barrier that effectively blocks PT to the extracellular solution. Thus, the rotation of E148 plays a critical role in defining the Cl^–/H⁺ coupling. As a control, we have also simulated PT in the ClC-ec1 E148A mutant to further understand the role of this residue. Replacement with a non-protonatable residue greatly increases the free energy barrier for PT from E203 to the extracellular solution, explaining the experimental result that PT in E148A is blocked whether or not Cl^–_cen is present. The results presented here suggest both how a chemical reaction can control the rate of PT and also how it can provide a mechanism for a coupling of the two ion transport processes.

Linear Response Function of Bond-Order

We present the linear response function of bond-orders (LRF-BO) based on a real space integration scheme for molecular systems. As in the case of the LRF of density, the LRF-BO is defined as the response of the bond order of the molecule for the virtual perturbation. Our calculations show that the LRF-BO enables us not only to detect inductive and resonating effects of conjugating systems, but also to predict pK_a values on substitution groups via linear relationships between the Hammett constants and the LRF-BO values for meta- and para-substituted benzoic acids. More importantly, the LRF-BO values for the O-H bonds strongly depend on the sites to which the virtual perturbation is applied, implying that the LRF-BO values include essential information about reaction mechanism of the acid-dissociation of substituted benzoic acids.

Multiscale simulations reveal key features of the proton-pumping mechanism in cytochrome c oxidase

Cytochrome c oxidase (CcO) reduces oxygen to water and uses the released free energy to pump protons across the membrane. We have used multiscale reactive molecular dynamics simulations to explicitly characterize (with free-energy profiles and calculated rates) the internal proton transport events that enable proton pumping during first steps of oxidation of the fully reduced enzyme. Our results show that proton transport from amino acid residue E286 to both the pump loading site (PLS) and to the binuclear center (BNC) are thermodynamically driven by electron transfer from heme a to the BNC, but that the former (i.e., pumping) is kinetically favored whereas the latter (i.e., transfer of the chemical proton) is rate-limiting. The calculated rates agree with experimental measurements. The backflow of the pumped proton from the PLS to E286 and from E286 to the inside of the membrane is prevented by large free-energy barriers for the backflow reactions. Proton transport from E286 to the PLS through the hydrophobic cavity and from D132 to E286 through the D-channel are found to be strongly coupled to dynamical hydration changes in the corresponding pathways and, importantly, vice versa.

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.

Ab Initio Molecular Dynamics Simulations of Amino Acids in Aqueous Solutions: Estimating pKa Values from Metadynamics Sampling

Changes in the protonation and deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. Here, we report calculations of the free-energy profile for the protonation-deprotonation reaction of the 20 canonical α amino acids in aqueous solutions using ab initio Car-Parrinello molecular dynamics simulations coupled with metadynamics sampling. We show here that the calculated change in free energy of the dissociation reaction provides estimates of the multiple pKa values of the amino acids that are in good agreement with experiment. We use the bond-length-dependent number of the protons coordinated to the hydroxyl oxygen of the carboxylic and the amine groups as the collective variables to explore the free-energy profiles of the Bronsted acid-base chemistry of amino acids in aqueous solutions. We ensure that the amino acid undergoing dissociation is solvated by at least three hydrations shells with all water molecules included in the simulations. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pKa values with a mean relative error, with respect to experimental results, of 0.2 pKa units.

Estimating successive pKa values of polyprotic acids from ab initio molecular dynamics using metadynamics: the dissociation of phthalic acid and its isomers

pKa values of polyprotic acids estimated from ab initio molecular dynamics computation of the change in free energy upon dissociation.

Unraveling the intramolecular cyclization mechanism of oxidized tryptophan in aqueous solution as a function of pH

pH tunes the mechanism of the intramolecular cyclization of 3a-substituted tryptophan derivatives.