A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations

Comparison of Methods To Reweight from Classical Molecular Simulations to QM/MM Potentials

We examine methods to reweight classical molecular mechanics solvation calculations to more expensive QM/MM energy functions. We first consider the solvation free energy difference between ethane and methanol in a QM/MM Hamiltonian from configurations generated in a cheaper MM potential. The solute molecules in the QM/MM Hamiltonian are treated with B3LYP/6-31G*, and the solvent water molecules are treated classically. The free energy difference in the QM/MM Hamiltonian is estimated using Boltzmann reweighting with both the non-Boltzmann Bennett method (NBB) and the multistate Bennett acceptance ratio (MBAR), and the variance of each method is directly compared for an identical data set. For this system, MBAR-derived methods are found to produce smaller overall uncertainties than NBB-based methods. Additionally, we show that to reduce the variance in the overall free energy difference estimate in this system for a fixed amount of QM/MM calculations, the energy re-evaluations in the Boltzmann reweighting step should be concentrated on the physical MM states with the highest overlap to the QM/MM states, rather than allocated equally over all sampled MM states. We also show that reallocating the QM/MM re-evaluations can be used to diagnose poor overlap between the sampled and target state. The solvation free energies for molecules in the SAMPL4 solvation data set are also calculated in the QM/MM Hamiltonian with NBB and MBAR, and the variances are marginally smaller for MBAR. Overall, NBB and MBAR produce similar variances for systems with poor sampling efficiency, and MBAR provides smaller variances than NBB in systems with high sampling efficiency. Both NBB and MBAR converge to identical solvation free energy estimates in the QM/MM Hamiltonian, and the RMSD to experimental values for molecules in the SAMPL4 solvation data set decreases by approximately 28% when switching from the MM Hamiltonian to the QM/MM Hamiltonian.

Adaptive switching of interaction potentials in the time domain: an extended Lagrangian approach tailored to transmute force field to QM/MM simulations and back

An extended Lagrangian formalism that allows for a smooth transition between two different descriptions of interactions during a molecular dynamics simulation is presented. This time-adaptive method is particularly useful in the context of multiscale simulation as it provides a sound recipe to switch on demand between different hierarchical levels of theory, for instance between ab initio ("QM") and force field ("MM") descriptions of a given (sub)system in the course of a molecular dynamics simulation. The equations of motion can be integrated straightforwardly using the usual propagators, such as the Verlet algorithm. First test cases include a bath of harmonic oscillators, of which a subset is switched to a different force constant and/or equilibrium position, as well as an all-MM to QM/MM transition in a hydrogen-bonded water dimer. The method is then applied to a smectic 8AB8 liquid crystal and is shown to be able to switch dynamically a preselected 8AB8 molecule from an all-MM to a QM/MM description which involves partition boundaries through covalent bonds. These examples show that the extended Lagrangian approach is not only easy to implement into existing code but that it is also efficient and robust. The technique moreover provides easy access to a conserved energy quantity, also in cases when Nosé-Hoover chain thermostatting is used throughout dynamical switching. A simple quadratic driving potential proves to be sufficient to guarantee a smooth transition whose time scale can be easily tuned by varying the fictitious mass parameter associated with the auxiliary variable used to extend the Lagrangian. The method is general and can be applied to time-adaptive switching on demand between two different levels of theory within the framework of hybrid scale-bridging simulations.

An Efficient Linear-Scaling Ewald Method for Long-Range Electrostatic Interactions in Combined QM/MM Calculations

A method is presented for the efficient evaluation of long-range electrostatic forces in combined quantum mechanical and molecular mechanical (QM/MM) calculations of periodic systems. The QM/MM-Ewald method is a linear-scaling electrostatic method that utilizes the particle mesh Ewald algorithm for calculation of point charge interactions of molecular mechanical atoms and a real-space multipolar expansion for the quantum mechanical electrostatic terms plus a pairwise periodic correction factor for the QM and QM/MM interactions that does not need to be re-evaluated during the self-consistent field procedure. The method is tested in a series of molecular dynamics simulations of the ion-ion association of ammonium chloride and ammonium metaphosphate and the dissociative phosphoryl transfer of methyl phosphate and acetyl phosphate. Results from periodic boundary molecular dynamics (PBMD) simulations employing the QM/MM-Ewald method are compared with corresponding PBMD simulations using electrostatic cutoffs and with results from nonperiodic stochastic boundary molecular dynamics (SBMD) simulations, with cutoffs and with full electrostatics (no cutoff). The present method allows extension of linear-scaling Ewald methods to molecular simulations of enzyme and ribozyme reactions that use combined QM/MM potentials.

Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems

Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.

Practically Efficient QM/MM Alchemical Free Energy Simulations: The Orthogonal Space Random Walk Strategy

The difference between free energy changes occurring at two chemical states can be rigorously estimated via alchemical free energy (AFE) simulations. Traditionally, most AFE simulations are carried out under the classical energy potential treatment; then, accuracy and applicability of AFE simulations are limited. In the present work, we integrate a recent second-order generalized ensemble strategy, the orthogonal space random walk (OSRW) method, into the combined quantum mechanical/molecular mechanical (QM/MM) potential based AFE simulation scheme. Thereby, within a commonly affordable simulation length, accurate QM/MM alchemical free energy simulations can be achieved. As revealed by the model study on the equilibrium of a tautomerization process of hydrated 3-hydroxypyrazole and by the model calculations of the redox potentials of two flavin derivatives, lumichrome (LC) and riboflavin (RF) in aqueous solution, the present OSRW-based scheme could be a viable path toward the realization of practically efficient QM/MM AFE simulations.

A Multiscale Treatment of Angeli's Salt Decomposition

Sodium trioxodinitrate's (Na2N2O3, Angeli's salt) unique cardiovascular effects have been associated with its ability to yield HNO upon dissociation under physiological conditions. Due to its potential applications in new therapies for heart failure, the dissociation of Angeli's salt has recently received increased attention. The decomposition mechanism has been previously studied by quantum mechanical methods using a continuum approximation (PCM) for the solvent effects. In this work we use our recently developed interface of the Amber and Gaussian packages via the PUPIL package to study Angeli's salt dissociation in a hybrid QM/MM scheme where the water solvent molecules are treated explicitly with classical mechanics while the solute is treated with full quantum mechanics (UB3LYP/6-31+G(d) and UMP2/6-31+G(d)) level. Multiple steered molecular dynamics was used with the Jarzynski relationship to extract the free energy profile for the process. We obtain 4.8 kcal mol(-1) and 6.4 kcal mol(-1) free energy barriers for the N-N bond breaking for UB3LYP and UMP2, respectively. The geometries and Mulliken charges for reactant, transition state, and products have been characterized through a number of hybrid QM/MM molecular dynamics runs with the N-N distance restrained to representative values of each species. The results highlight the role of individual solvent molecules for the reaction energetics and provide a comparison point against implicit solvation methods.

Generalized X-Pol Theory and Charge Delocalization States

The mixed molecular orbital and valence bond (MOVB) method has been used to generalize the explicit polarization (X-Pol) potential to incorporate charge delocalization resonance effects in the framework of valence bond theory. In the original X-Pol method, a macromolecular system is partitioned into individual fragments or blocks, and the molecular orbitals of the system are strictly localized within each block. Consequently, these block-localized molecular orbitals (BLMOs) are nonorthogonal across different blocks. In the generalized X-Pol (GX-Pol) theory, we construct charge delocalization VB states by expanding the localization space from monomer blocks into pairwise delocalized blocks. Thus, the expansion of the basis space leads to charge delocalization between monomer pairs, and a series of pairwise delocalization states can be constructed. In general, L-body delocalized states can be analogously defined by grouping L monomer blocks into one. The Hartree product wave function for each state can be fully antisymmetrized, which introduces explicitly exchange repulsion among all blocks. The GX-Pol wave function is a linear combination of all L-body charge transfer (valence bond) states, which incorporates charge delocalization and their resonance as well as static correlation effects. The GX-Pol method provides a general and rigorous theory to incorporate charge delocalization explicitly into these fragment-based electronic structural methods for macromolecular systems.

Characterizing the protonation states of the catalytic residues in apo and substrate-bound human T-cell leukemia virus type 1 protease

Human T-cell leukemia virus type 1 (HTLV-1) protease is an attractive target when developing inhibitors to treat HTLV-1 associated diseases. To study the catalytic mechanism and design novel HTLV-1 protease inhibitors, the protonation states of the two catalytic aspartic acid residues must be determined. Free energy simulations have been conducted to study the proton transfer reaction between the catalytic residues of HTLV-1 protease using a combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulation. The free energy profiles for the reaction in the apo-enzyme and in an enzyme - substrate complex have been obtained. In the apo-enzyme, the two catalytic residues are chemically equivalent and are expected to be both unprotonated. Upon substrate binding, the catalytic residues of HTLV-1 protease evolve to a singly protonated state, in which the OD1 of Asp32 is protonated and forms a hydrogen bond with the OD1 of Asp32', which is unprotonated. The HTLV-1 protease-substrate complex structure obtained from this simulation can serve as the Michaelis complex structure for further mechanistic studies of HTLV-1 protease while providing a receptor structure with the correct protonation states for the active site residues toward the design of novel HTLV-1 protease inhibitors through virtual screening.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

Projected hybrid orbitals: a general QM/MM method

A projected hybrid orbital (PHO) method was described to model the covalent boundary in a hybrid quantum mechanical and molecular mechanical (QM/MM) system. The PHO approach can be used in ab initio wave function theory and in density functional theory with any basis set without introducing system-dependent parameters. In this method, a secondary basis set on the boundary atom is introduced to formulate a set of hybrid atomic orbtials. The primary basis set on the boundary atom used for the QM subsystem is projected onto the secondary basis to yield a representation that provides a good approximation to the electron-withdrawing power of the primary basis set to balance electronic interactions between QM and MM subsystems. The PHO method has been tested on a range of molecules and properties. Comparison with results obtained from QM calculations on the entire system shows that the present PHO method is a robust and balanced QM/MM scheme that preserves the structural and electronic properties of the QM region.

Density functional theory study on the activation of molecular oxygen on a stepped gold surface in an aqueous environment: a new approach for simulating reactions in solution

The activation of oxygen molecules is an important issue in the gold-catalyzed partial oxidation of alcohols in aqueous solution. The complexity of the solution arising from a large number of solvent molecules makes it difficult to study the reaction in the system. In this work, O2 activation on an Au catalyst is investigated using an effective approach to estimate the reaction barriers in the presence of solvent. Our calculations show that O2 can be activated, undergoing OOH* in the presence of water molecules. The OOH* can readily be formed on Au(211) via four possible pathways with almost equivalent free energy barriers at the aqueous-solid interface: the direct or indirect activation of O2 by surface hydrogen or the hydrolysis of O2 following a Langmuir-Hinshelwood mechanism or an Eley-Rideal mechanism. Among them, the Eley-Rideal mechanism may be slightly more favorable due to the restriction of the low coverage of surface H on Au(211) in the other mechanisms. The results shed light on the importance of water molecules on the activation of oxygen in gold-catalyzed systems. Solvent is found to facilitate the oxygen activation process mainly by offering extra electrons and stabilizing the transition states. A correlation between the energy barrier and the negative charge of the reaction center is found. The activation barrier is substantially reduced by the aqueous environment, in which the first solvation shell plays the most important role in the barrier reduction. Our approach may be useful for estimating the reaction barriers in aqueous systems.

Challenges in computational studies of enzyme structure, function and dynamics

In this review we give an overview of the field of Computational enzymology. We start by describing the birth of the field, with emphasis on the work of the 2013 chemistry Nobel Laureates. We then present key features of the state-of-the-art in the field, showing what theory, accompanied by experiments, has taught us so far about enzymes. We also briefly describe computational methods, such as quantum mechanics-molecular mechanics approaches, reaction coordinate treatment, and free energy simulation approaches. We finalize by discussing open questions and challenges.

Efficiently computing pathway free energies: New approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes

BACKGROUND

Accurately modeling condensed phase processes is one of computation's most difficult challenges. Include the possibility that conformational dynamics may be coupled to chemical reactions, where multiscale (i.e., QM/MM) methods are needed, and this task becomes even more daunting.

METHODS

Free energy simulations (i.e., molecular dynamics), multiscale modeling, and reweighting schemes.

RESULTS

Herein, we present two new approaches for mitigating the aforementioned challenges. The first is a new chain-of-replica method (off-path simulations, OPS) for computing potentials of mean force (PMFs) along an easily defined reaction coordinate. This development is coupled with a new distributed, highly-parallel replica framework (REPDstr) within the CHARMM package. Validation of these new schemes is carried out on two processes that undergo conformational changes. First is the simple torsional rotation of butane, while a much more challenging glycosidic rotation (in vacuo and solvated) is the second. Additionally, a new approach that greatly improves (i.e., possibly an order of magnitude) the efficiency of computing QM/MM PMFs is introduced and compared to standard schemes. Our efforts are grounded in the recently developed method for efficiently computing QM-based free energies (i.e., QM-Non-Boltzmann Bennett, QM-NBB). Again, we validate this new technique by computing the QM/MM PMF of butane's torsional rotation.

CONCLUSIONS

The OPS-REPDstr method is a promising new approach that overcomes many limitations of standard pathway simulations in CHARMM. The combination of QM-NBB with pathway techniques is very promising as it offers significant advantages over current procedures.

GENERAL SIGNIFICANCE

Efficiently computing potentials of mean force is a major, unresolved, area of interest. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Some practical approaches to treating electrostatic polarization of proteins

Conspectus Electrostatic interaction plays a significant role in determining many properties of biomolecules, which exist and function in aqueous solution, a highly polar environment. For example, proteins are composed of amino acids with charged, polar, and nonpolar side chains and their specific electrostatic properties are fundamental to the structure and function of proteins. An important issue that arises in computational study of biomolecular interaction and dynamics based on classical force field is lack of polarization. Polarization is a phenomenon in which the charge distribution of an isolated molecule will be distorted when interacting with another molecule or presented in an external electric field. The distortion of charge distribution is intended to lower the overall energy of the molecular system, which is counter balanced by the increased internal energy of individual molecules due to the distorted charge distributions. The amount of the charge redistribution, which characterizes the polarizability of a molecule, is determined by the level of the charge distortion. Polarization is inherently quantum mechanical, and therefore classical force fields with fixed atomic charges are incapable of capturing this important effect. As a result, simulation studies based on popular force fields, AMBER, CHARMM, etc., lack the polarization effect, which is a widely known deficiency in most computational studies of biomolecules today. Many efforts have been devoted to remedy this deficiency, such as adding additional movable charge on the atom, allowing atomic charges to fluctuate, or including induced multipoles. Although various successes have been achieved and progress at various levels has been reported over the past decades, the issue of lacking polarization in force field based simulations is far from over. For example, some of these methods do not always give converged results, and other methods require huge computational cost. This Account reviews recent work on developing polarized and polarizable force fields based on fragment quantum mechanical calculations for proteins. The methods described here are based on quantum mechanical calculations of proteins in solution, but with a different level of rigor and different computational efficiency for the molecular dynamics applications. In the general approach, a fragment quantum mechanical calculation for protein with implicit solvation is carried out to derive a polarized protein-specific charge (PPC) for any given protein structure. The PPC correctly reflects the polarization state of the protein in a given conformation, and it can also be dynamically changed as the protein changes conformation in dynamics simulations. Another approach that is computationally more efficient is the effective polarizable bond method in which only polar bonds or groups can be polarized and their polarizabilities are predetermined from quantum mechanical calculations of these groups in external electric fields. Both methods can be employed for applications in various situations by taking advantage of their unique features.

QM/MM through the 1990s: The First Twenty Years of Method Development and Applications

The 2013 Nobel Prize in Chemistry was awarded to the authors of the first two publications utilizing the concept of combined quantum mechanical and molecular mechanical (QM/MM) methods. In celebrating this great event in computational chemistry, we review the early development of combined QM/MM techniques and the associated events that took place through the mid-1990s. We also offer some prospects for the future development of quantum mechanical techniques for macromolecular systems.

Reaction Path Force Matching: A New Strategy of Fitting Specific Reaction Parameters for Semiempirical Methods in Combined QM/MM Simulations

We present a general strategy of reparametrizing semiempirical (SE) methods against ab initio (AI) methods for combined quantum mechanical and molecular mechanical (QM/MM) simulations of specific chemical reactions in condensed phases. The resulting approach, designated Reaction Path Force Matching (RP-FM), features cycles of sampling configurations along a reaction path on an efficient SE/MM potential energy surface (PES) and adjusting specific reaction parameters (SRPs) in the SE method such that the atomic forces computed at the target AI/MM level are reproduced. Iterative applications of the RP-FM cycle make possible achieving the accuracy of AI/MM simulations without explicitly sampling the computationally expensive AI/MM PES. The bypassed sampling, nevertheless, is implicitly accomplished through the aid of the efficient SE-SRP/MM PES, on which the target-level reaction path is expected to be obtained upon convergence. We demonstrate the effectiveness of the RP-FM procedure for a symmetric proton transfer reaction in the gas phase and in solution. The remarkable agreements between the RP-FM optimized SE-SRP methods and the target AI method on various properties, including energy profiles, potential of mean force free energy profiles, atomic forces, charge populations, and solvation effects, suggest that RP-FM can be used as an efficient and reliable strategy for simulating condensed-phase chemical reactions.

All-atom empirical potential for molecular modeling and dynamics studies of proteins

New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent-solvent, solvent-solute, and solute-solute interactions. Optimization of the internal parameters used experimental gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the atomic charges, were determined by fitting ab initio interaction energies and geometries of complexes between water and model compounds that represented the backbone and the various side chains. In addition, dipole moments, experimental heats and free energies of vaporization, solvation and sublimation, molecular volumes, and crystal pressures and structures were used in the optimization. The resulting protein parameters were tested by applying them to noncyclic tripeptide crystals, cyclic peptide crystals, and the proteins crambin, bovine pancreatic trypsin inhibitor, and carbonmonoxy myoglobin in vacuo and in crystals. A detailed analysis of the relationship between the alanine dipeptide potential energy surface and calculated protein φ, χ angles was made and used in optimizing the peptide group torsional parameters. The results demonstrate that use of ab initio structural and energetic data by themselves are not sufficient to obtain an adequate backbone representation for peptides and proteins in solution and in crystals. Extensive comparisons between molecular dynamics simulations and experimental data for polypeptides and proteins were performed for both structural and dynamic properties. Energy minimization and dynamics simulations for crystals demonstrate that the latter are needed to obtain meaningful comparisons with experimental crystal structures. The presented parameters, in combination with the previously published CHARMM all-atom parameters for nucleic acids and lipids, provide a consistent set for condensed-phase simulations of a wide variety of molecules of biological interest.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes

The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.

Isotropic magnetic shielding constants of retinal derivatives in aprotic and protic solvents

We investigate the nuclear isotropic shielding constants σ((13)C) and σ((17)O) of isomers of retinoic acid and retinal in gas-phase and in chloroform, acetonitrile, methanol, and water solutions via Monte Carlo simulation and quantum mechanics calculations using the GIAO-B3LYP∕6-311++G(2d,2p) approach. Electronic solute polarization effects due to protic and aprotic solvents are included iteratively and play an important role in the quantitative determination of oxygen shielding constants. Our MP2∕6-31G+(d) results show substantial increases of the dipole moment of both retinal derivatives in solution as compared with the gas-phase results (between 22% and 26% in chloroform and between 55% and 99% in water). For the oxygen atoms the influence of the solute polarization is mild for σ((17)O) of hydroxyl group, even in protic solvents, but it is particularly important for σ((17)O) of carbonyl group. For the latter, there is a sizable increase in the magnitude with increasing solvent polarity. For the carbon atoms, the solvent effects on the σ((13)C) values are in general small, being more appreciable in carbon atoms of the polyene chain than in the carbon atoms of the β-ionone ring and methyl groups. The results also show that isomeric changes on the backbones of the polyene chains have marked influence on the (13)C chemical shifts of carbon atoms near to the structural distortions, in good agreement with the experimental results measured in solution.

Quantum mechanical force field for water with explicit electronic polarization

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes.

Concerted hydrogen atom and electron transfer mechanism for catalysis by lysine-specific demethylase

We calculate the free energy profile for the postulated hydride transfer reaction mechanism for the catalysis of lysine demethylation by lysine-specific demethylase LSD1. The potential energy surface is obtained by using combined electrostatically embedded multiconfiguration molecular mechanics (EE-MCMM) and single-configuration molecular mechanics (MM). We employ a constant valence bond coupling term to obtain analytical energies and gradients of the EE-MCMM subsystem, which contains 45 quantum mechanics (QM) atoms and which is parametrized with density functional calculations employing specific reaction parameters obtained by matching high-level wave function calculations. In the MM region, we employ the Amber ff03 and TIP3P force fields. The free energy of activation at 300 K is calculated by molecular dynamics (MD) umbrella sampling on a system with 102,090 atoms as the maximum of the free energy profile along the reaction coordinate as obtained by the weighted histogram analysis method with 17 umbrella sampling windows. This yields a free energy of activation of only 10 kcal/mol, showing that the previously postulated direct hydride transfer reaction mechanism is plausible, although we find that it is better interpreted as a concerted transfer of a hydrogen atom and an electron.

A dynamic structural model of expanded RNA CAG repeats: a refined X-ray structure and computational investigations using molecular dynamics and umbrella sampling simulations

One class of functionally important RNA is repeating transcripts that cause disease through various mechanisms. For example, expanded CAG repeats can cause Huntington's and other disease through translation of toxic proteins. Herein, a crystal structure of r[5'UUGGGC(CAG)3GUCC]2, a model of CAG expanded transcripts, refined to 1.65 Å resolution is disclosed that shows both anti-anti and syn-anti orientations for 1 × 1 nucleotide AA internal loops. Molecular dynamics (MD) simulations using AMBER force field in explicit solvent were run for over 500 ns on the model systems r(5'GCGCAGCGC)2 (MS1) and r(5'CCGCAGCGG)2 (MS2). In these MD simulations, both anti-anti and syn-anti AA base pairs appear to be stable. While anti-anti AA base pairs were dynamic and sampled multiple anti-anti conformations, no syn-anti ↔ anti-anti transformations were observed. Umbrella sampling simulations were run on MS2, and a 2D free energy surface was created to extract transformation pathways. In addition, an explicit solvent MD simulation over 800 ns was run on r[5'GGGC(CAG)3GUCC]2, which closely represents the refined crystal structure. One of the terminal AA base pairs (syn-anti conformation), transformed to anti-anti conformation. The pathway followed in this transformation was the one predicted by umbrella sampling simulations. Further analysis showed a binding pocket near AA base pairs in syn-anti conformations. Computational results combined with the refined crystal structure show that global minimum conformation of 1 × 1 nucleotide AA internal loops in r(CAG) repeats is anti-anti but can adopt syn-anti depending on the environment. These results are important to understand RNA dynamic-function relationships and to develop small molecules that target RNA dynamic ensembles.

QM and QM/MM simulations of proteins

Molecular dynamics simulations of biomolecules have matured into powerful tools of structural biology. In addition to the commonly used empirical force field potentials, quantum mechanical descriptions are gaining popularity for structure optimization and dynamic simulations of peptides and proteins. In this chapter, we introduce methodological developments such as the QM/MM framework and linear-scaling QM that make efficient calculations on large biomolecules possible. We identify the most common scenarios in which quantum descriptions of peptides and proteins are employed, such as structural refinement, force field development, treatment of unusual residues, and predicting spectroscopic and exited state properties. The benefits and shortcomings of QM potentials, in comparison to classical force fields, are discussed, with special emphasis on the sampling problems of protein conformational space. Finally, recent examples of QM/MM calculations in light-sensitive membrane proteins illustrate typical applications of the reviewed methods.

Connecting protein conformational dynamics with catalytic function as illustrated in dihydrofolate reductase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations reveal that the M20 loop conformational dynamics of dihydrofolate reductase (DHFR) is severely restricted at the transition state of the hydride transfer as a result of the M42W/G121V double mutation. Consequently, the double-mutant enzyme has a reduced entropy of activation, i.e., increased entropic barrier, and altered temperature dependence of kinetic isotope effects in comparison with those of wild-type DHFR. Interestingly, in both wild-type DHFR and the double mutant, the average donor-acceptor distances are essentially the same in the Michaelis complex state (~3.5 Å) and the transition state (2.7 Å). It was found that an additional hydrogen bond is formed to stabilize the M20 loop in the closed conformation in the M42W/G121V double mutant. The computational results reflect a similar aim designed to knock out precisely the dynamic flexibility of the M20 loop in a different double mutant, N23PP/S148A.

Communication: variational many-body expansion: accounting for exchange repulsion, charge delocalization, and dispersion in the fragment-based explicit polarization method

A fragment-based variational many-body (VMB) expansion method is described to directly account for exchange repulsion, charge delocalization (charge transfer) and dispersion interactions in the explicit polarization (X-Pol) method. The present VMB/X-Pol approach differs from other fragment molecular orbital (FMO) techniques in two major aspects. First, the wave function for the monomeric system is variationally optimized using standard X-Pol method, as opposed to the iterative update procedure adopted in FMO. Second, the mutual polarizations in the dimeric terms are also variationally determined, whereas single-point energy calculations of the individual dimers embedded in a static monomer field are used in FMO. The second-order (two-body) VMB (VMB2) expansion method is illustrated on a series of water hexamer complexes and one decamer cluster, making use of Hartree-Fock theory, MP2, and the PBE1 and M06 density functionals to represent the monomer and dimer fragments. The computed binding energies are within 2 kcal/mol of the corresponding results from fully delocalized calculations. Energy decomposition analyses reveal specific dimeric contributions to exchange repulsion, charge delocalization, and dispersion. Since the wave functions for one-body and all two-body terms are variationally optimized in VMB2 and X-Pol, it is straightforward to obtain analytic gradient without the additional coupled-perturbed Hartree-Fock step. Thus, the method can be useful for molecular dynamics simulations.

Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions

We describe an Ewald-summation method to incorporate long-range electrostatic interactions into fragment-based electronic structure methods for periodic systems. The present method is an extension of the particle-mesh Ewald technique for combined quantum mechanical and molecular mechanical (QM/MM) calculations, and it has been implemented into the explicit polarization (X-Pol) potential to illustrate the computational details. As in the QM/MM-Ewald method, the X-Pol-Ewald approach is a linear-scaling electrostatic method, in which the short-range electrostatic interactions are determined explicitly in real space and the long-range Ewald pair potential is incorporated into the Fock matrix as a correction. To avoid the time-consuming Fock matrix update during the self-consistent field procedure, a mean image charge (MIC) approximation is introduced, in which the running average with a user-chosen correlation time is used to represent the long-range electrostatic correction as an average effect. Test simulations on liquid water show that the present X-Pol-Ewald method takes about 25% more CPU time than the usual X-Pol method using spherical cutoff, whereas the use of the MIC approximation reduces the extra costs for long-range electrostatic interactions by 15%. The present X-Pol-Ewald method provides a general procedure for incorporating long-range electrostatic effects into fragment-based electronic structure methods for treating biomolecular and condensed-phase systems under periodic boundary conditions.

Communication: Quantum polarized fluctuating charge model: a practical method to include ligand polarizability in biomolecular simulations

We present a simple and practical method to include ligand electronic polarization in molecular dynamics (MD) simulation of biomolecular systems. The method involves periodically spawning quantum mechanical (QM) electrostatic potential (ESP) calculations on an extra set of computer processors using molecular coordinate snapshots from a running parallel MD simulation. The QM ESPs are evaluated for the small-molecule ligand in the presence of the electric field induced by the protein, solvent, and ion charges within the MD snapshot. Partial charges on ligand atom centers are fit through the multi-conformer restrained electrostatic potential (RESP) fit method on several successive ESPs. The RESP method was selected since it produces charges consistent with the AMBER/GAFF force-field used in the simulations. The updated charges are introduced back into the running simulation when the next snapshot is saved. The result is a simulation whose ligand partial charges continuously respond in real-time to the short-term mean electrostatic field of the evolving environment without incurring additional wall-clock time. We show that (1) by incorporating the cost of polarization back into the potential energy of the MD simulation, the algorithm conserves energy when run in the microcanonical ensemble and (2) the mean solvation free energies for 15 neutral amino acid side chains calculated with the quantum polarized fluctuating charge method and thermodynamic integration agree better with experiment relative to the Amber fixed charge force-field.