Toward QM/MM Simulation of Enzymatic Reactions with the Drude Oscillator Polarizable Force Field

System-Specific Parameter Optimization for Nonpolarizable and Polarizable Force Fields

The accuracy of classical force fields (FFs) has been shown to be limited for the simulation of cation-protein systems despite their importance in understanding the processes of life. Improvements can result from optimizing the parameters of classical FFs or by extending the FF formulation by terms describing charge transfer (CT) and polarization (POL) effects. In this work, we introduce our implementation of the CTPOL model in OpenMM, which extends the classical additive FF formula by adding CT and POL. Furthermore, we present an open-source parametrization tool, called FFAFFURR, that enables the (system-specific) parametrization of OPLS-AA and CTPOL models. The performance of our workflow was evaluated by its ability to reproduce quantum chemistry energies and by molecular dynamics simulations of a zinc-finger protein.

Biomolecular dynamics in the 21st century

The relevance of motions in biological macromolecules has been clear since the early structural analyses of proteins by X-ray crystallography. Computer simulations have been applied to provide a deeper understanding of the dynamics of biological macromolecules since 1976, and are now a standard tool in many labs working on the structure and function of biomolecules. In this mini-review we highlight some areas of current interest and active development for simulations, in particular all-atom molecular dynamics simulations.

Structure and Dynamics of Confined Water Inside Diphenylalanine Peptide Nanotubes

Diphenylalanine (FF) peptides exhibit a unique ability to self-assemble into nanotubes with confined water molecules playing pivotal roles in their structure and function. This study investigates the structure and dynamics of diphenylalanine peptide nanotubes (FFPNTs) using all-atom molecular dynamics (MD) and grand canonical Monte Carlo combined with MD (GCMC/MD) simulations with both the CHARMM additive and Drude polarizable force fields. The occupancy and dynamics of confined water molecules were also examined. It was found that less than 2 confined water molecules per FF help stabilize the FFPNTs on the x-y plane. Analyses of the kinetics of confined water molecules revealed distinctive transport behaviors for bound and free water, and their respective diffusion coefficients were compared. Our results validate the importance of polarizable force field models in studying peptide nanotubes and provide insights into our understanding of nanoconfined water.

Assessing the quality of QM/MM approaches to describe vacuo-to-water solvatochromic shifts

The performance of different quantum mechanics/molecular mechanics embedding models to compute vacuo-to-water solvatochromic shifts is investigated. In particular, both nonpolarizable and polarizable approaches are analyzed and computed results are compared to reference experimental data. We show that none of the approaches outperform the others and that errors strongly depend on the nature of the molecular transition to be described. Thus, we prove that the best choice of embedding model highly depends on the molecular system and that the use of a specific approach as a black box can lead to significant errors and, sometimes, totally wrong predictions.

The atomistic modeling of light-harvesting complexes from the physical models to the computational protocol

The function of light-harvesting complexes is determined by a complex network of dynamic interactions among all the different components: the aggregate of pigments, the protein, and the surrounding environment. Complete and reliable predictions on these types of composite systems can be only achieved with an atomistic description. In the last few decades, there have been important advances in the atomistic modeling of light-harvesting complexes. These advances have involved both the completeness of the physical models and the accuracy and effectiveness of the computational protocols. In this Perspective, we present an overview of the main theoretical and computational breakthroughs attained so far in the field, with particular focus on the important role played by the protein and its dynamics. We then discuss the open problems in their accurate modeling that still need to be addressed. To illustrate an effective computational workflow for the modeling of light harvesting complexes, we take as an example the plant antenna complex CP29 and its H111N mutant.

Quantum Mechanics/Fluctuating Charge Protocol to Compute Solvatochromic Shifts

Despite the potentialities of the quantum mechanics (QM)/fluctuating charge (FQ) approach to model the spectral properties of solvated systems, its extensive use has been hampered by the lack of reliable parametrizations of solvents other than water. In this paper, we substantially extend the applicability of QM/FQ to solvating environments of different polarities and hydrogen-bonding capabilities. The reliability and robustness of the approach are demonstrated by challenging the model to simulate solvatochromic shifts of four organic chromophores, which display large shifts when dissolved in apolar, aprotic or polar, protic solvents.

Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

Energy-Based Molecular Orbital Localization in a Specific Spatial Region

We present a novel energy-based localization procedure able to localize molecular orbitals into predefined spatial regions. The method is defined in a multiscale framework based on the multilevel Hartree-Fock approach. In particular, the system is partitioned into active and inactive fragments. The localized molecular orbitals are obtained maximizing the repulsion between the two fragments. The method is applied to several cases including both conjugated and non-conjugated systems. Our multiscale approach is compared with reference values for both ground-state properties, such as dipole moments, and local excitation energies. The proposed approach is useful to extend the application range of high-level electron correlation methods. In fact, the reduced number of molecular orbitals can lead to a large reduction in the computational cost of correlated calculations.

The influence of base pair tautomerism on single point mutations in aqueous DNA

The relationship between base pair hydrogen bond proton transfer and the rate of spontaneous single point mutations at ambient temperatures and pressures in aqueous DNA is investigated. By using an ensemble-based multiscale computational modelling method, statistically robust rates of proton transfer for the A:T and G:C base pairs within a solvated DNA dodecamer are calculated. Several different proton transfer pathways are observed within the same base pair. It is shown that, in G:C, the double proton transfer tautomer is preferred, while the single proton transfer process is favoured in A:T. The reported range of rate coefficients for double proton transfer is consistent with recent experimental data. Notwithstanding the approximately 1000 times more common presence of single proton transfer products from A:T, observationally there is bias towards G:C to A:T mutations in a wide range of living organisms. We infer that the double proton transfer reactions between G:C base pairs have a negligible contribution towards this bias for the following reasons: (i) the maximum half-life of the G*:C* tautomer is in the range of picoseconds, which is significantly smaller than the milliseconds it takes for DNA to unwind during replication, (ii) statistically, the majority of G*:C* tautomers revert back to their canonical forms through a barrierless process, and (iii) the thermodynamic instability of the tautomers with respect to the canonical base pairs. Through similar reasoning, we also deduce that proton transfer in the A:T base pair does not contribute to single point mutations in DNA.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Avoiding Electron Spill-Out in QM/MM Calculations on Excited States with Simple Pseudopotentials

QM/MM calculations of electronic excitations with diffuse basis sets often have large errors due to spill-out of electrons from the quantum subsystem. The Pauli repulsion of the electrons by the environment has to be included to avoid this. We propose transferable atomic all-electron pseudopotentials that can readily be combined with most MM force fields to avoid electron spill-out. QM/MM excitation energies computed with time-dependent Hartree-Fock and the algebraic diagrammatic construction through second-order are benchmarked against supermolecular calculations to validate these new pseudopotentials. The QM/MM calculations with pseudopotentials give accurate results that are stable with augmentation of the basis set with diffuse functions. We show that the largest contribution to residual deviations from full QM calculations is caused by the missing London dispersion interaction.

Polarisable force fields: what do they add in biomolecular simulations?

The quality of biomolecular simulations critically depends on the accuracy of the force field used to calculate the potential energy of the molecular configurations. Currently, most simulations employ non-polarisable force fields, which describe electrostatic interactions as the sum of Coulombic interactions between fixed atomic charges. Polarisation of these charge distributions is incorporated only in a mean-field manner. In the past decade, extensive efforts have been devoted to developing simple, efficient, and yet generally applicable polarisable force fields for biomolecular simulations. In this review, we summarise the latest developments in accounting for key biomolecular interactions with polarisable force fields and applications to address challenging biological questions. In the end, we provide an outlook for future development in polarisable force fields.

Mutually polarizable QM/MM model with in situ optimized localized basis functions

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem - with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K⁺, and Cl^-. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface.

Enhanced QM/MM sampling for free energy calculation of chemical reactions: A case study of double proton transfer

Free energy calculations for chemical reactions with a steep energy barrier require well defined reaction coordinates (RCs). However, when multiple parallel channels exist along selected RC, the application of conventional enhanced samplings is difficult to generate correct sampling within limited simulation time and thus cannot give correct prediction about the favorable pathways, the relative stability of multiple products or intermediates. Here, we implement the selective integrated tempering sampling (SITS) method with quantum mechanical and molecular mechanical (QM/MM) potential to investigate the chemical reactions in solution. The combined SITS-QM/MM scheme is used to identify possible reaction paths, intermediate and product states, and the free energy profiles for the different reaction paths. Two double proton transfer reactions were studied to validate the implemented method and simulation protocol, from which the independent and correlated proton transfer processes are identified in two representative systems, respectively. This protocol can be generalized to various kinds of chemical reactions for both academic studies and industry applications, such as in exploration and optimization of potential reactions in DNA encoded compound library and halogen or deuterium substitution of the hit discovery and lead optimization stages of drug design via providing a better understanding of the reaction mechanism along the designed chemical reaction pathways.

Interfacing the Core-Shell or the Drude Polarizable Force Field With Car-Parrinello Molecular Dynamics for QM/MM Simulations

We report a quantum mechanics/polarizable–molecular mechanics (QM/p–MM) potential based molecular dynamics (MD) technique where the core–shell (or the Drude) type polarizable MM force field is interfaced with the plane-wave density functional theory based QM force field which allows Car–Parrinello MD for the QM subsystem. In the QM/p-MM Lagrangian proposed here, the shell (or the Drude) MM variables are treated as extended degrees of freedom along with the Kohn–Sham (KS) orbitals describing the QM wavefunction. The shell and the KS orbital degrees of freedom are then adiabatically decoupled from the nuclear degrees of freedom. In this respect, we also present here the Nosé–Hoover Chain thermostat implementation for the dynamical subsystems. Our approach is then used to investigate the effect of MM polarization on the QM/MM results. Especially, the consequence of MM polarization on reaction free energy barriers, defect formation energy, and structural and dynamical properties are investigated. A low point charge polarizable potential (p–MZHB) for pure siliceous systems is also reported here.

Mapping the Drude polarizable force field onto a multipole and induced dipole model

The induced dipole and the classical Drude oscillator represent two major approaches for the explicit inclusion of electronic polarizability into force field-based molecular modeling and simulations. In this work, we explore the equivalency of these two models by comparing condensed phase properties computed using the Drude force field and a multipole and induced dipole (MPID) model. Presented is an approach to map the electrostatic model optimized in the context of the Drude force field onto the MPID model. Condensed phase simulations on water and 15 small model compounds show that without any reparametrization, the MPID model yields properties similar to the Drude force field with both models yielding satisfactory reproduction of a range of experimental values and quantum mechanical data. Our results illustrate that the Drude oscillator model and the point induced dipole model are different representations of essentially the same physical model. However, results indicate the presence of small differences between the use of atomic multipoles and off-center charge sites. Additionally, results on the use of dispersion particle mesh Ewald further support its utility for treating long-range Lennard Jones dispersion contributions in the context of polarizable force fields. The main motivation in demonstrating the transferability of parameters between the Drude and MPID models is that the more than 15 years of development of the Drude polarizable force field can now be used with MPID formalism without the need for dual-thermostat integrators nor self-consistent iterations. This opens up a wide range of new methodological opportunities for polarizable models.

QM/MM methods for free energies and photochemistry

Hybrid computational methods describing a small region of a biomolecular system with quantum mechanics and the bulk with molecular mechanics, referred to as QM/MM methods, are now a central part of computational biochemistry. This review considers developments in the QM/MM approach that make it easier to calculate free energies using accurate QM-based potential energy expressions. We also describe techniques to treat electronic coupling between the core region and the MM environment. Polarizability of the protein matrix is important but so is electronic coupling. Applications of these new methods, especially to photochemistry, are discussed.

Optimization and benchmarking of a perturbative Metropolis Monte Carlo quantum mechanics/molecular mechanics program

In this work, we present an optimized perturbative quantum mechanics/molecular mechanics (QM/MM) method for use in Metropolis Monte Carlo simulations. The model adopted is particularly tailored for the simulation of molecular systems in solution but can be readily extended to other applications, such as catalysis in enzymatic environments. The electrostatic coupling between the QM and MM systems is simplified by applying perturbation theory to estimate the energy changes caused by a movement in the MM system. This approximation, together with the effective use of GPU acceleration, leads to a negligible added computational cost for the sampling of the environment. Benchmark calculations are carried out to evaluate the impact of the approximations applied and the overall computational performance.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH₃, NH₄⁺, CN^-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Applications of large-scale density functional theory in biology

Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.

A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase

Projector-based embedding has recently emerged as a robust multiscale method for the calculation of various electronic molecular properties. We present the coupling of projector embedding with quantum mechanics/molecular mechanics modeling and apply it for the first time to an enzyme-catalyzed reaction. Using projector-based embedding, we combine coupled-cluster theory, density-functional theory (DFT), and molecular mechanics to compute energies for the proton abstraction from acetyl-coenzyme A by citrate synthase. By embedding correlated ab initio methods in DFT we eliminate functional sensitivity and obtain high-accuracy profiles in a procedure that is straightforward to apply.

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields

We introduce an initial implementation of the LICHEM software package. LICHEM can interface with Gaussian, PSI4, NWChem, TINKER, and TINKER-HP to enable QM/MM calculations using multipolar/polarizable force fields. LICHEM extracts forces and energies from unmodified QM and MM software packages to perform geometry optimizations, single-point energy calculations, or Monte Carlo simulations. When the QM and MM regions are connected by covalent bonds, the pseudo-bond approach is employed to smoothly transition between the QM region and the polarizable force field. A series of water clusters and small peptides have been employed to test our initial implementation. The results obtained from these test systems show the capabilities of the new software and highlight the importance of including explicit polarization. © 2016 Wiley Periodicals, Inc.

Numerical study on the partitioning of the molecular polarizability into fluctuating charge and induced atomic dipole contributions

In order to carry out a detailed analysis of the molecular static polarizability, which is the response of the molecule to a uniform external electric field, the molecular polarizability was computed using the finite-difference method for 21 small molecules, using density functional theory. Within nine charge population schemes (Löwdin, Mulliken, Becke, Hirshfeld, CM5, Hirshfeld-I, NPA, CHELPG, MK-ESP) in common use, the charge fluctuation contribution is found to dominate the molecular polarizability, with its ratio ranging from 59.9% with the Hirshfeld or CM5 scheme to 96.2% with the Mulliken scheme. The Hirshfeld-I scheme is also used to compute the other contribution to the molecular polarizability coming from the induced atomic dipoles, and the atomic polarizabilities in eight small molecules and water pentamer are found to be highly anisotropic for most atoms. Overall, the results suggest that (a) more emphasis probably should be placed on the charge fluctuation terms in future polarizable force field development and (b) an anisotropic polarizability might be more suitable than an isotropic one in polarizable force fields based entirely or partially on the induced atomic dipoles.

The CHARMM-TURBOMOLE interface for efficient and accurate QM/MM molecular dynamics, free energies, and excited state properties

The quantum mechanical (QM)/molecular mechanical (MM) interface between Chemistry at HARvard Molecular Mechanics (CHARMM) and TURBOMOLE is described. CHARMM provides an extensive set of simulation algorithms, like molecular dynamics (MD) and free energy perturbation, and support for mature nonpolarizable and Drude polarizable force fields. TURBOMOLE provides fast QM calculations using density functional theory or wave function methods and excited state properties. CHARMM-TURBOMOLE is well-suited for extended QM/MM MD simulations using first principles methods with large (triple-ζ) basis sets. We demonstrate these capabilities with a QM/MM simulation of Mg(2+) (aq), where the MM outer sphere water molecules are represented using the SWM4-NDP Drude polarizable force field and the ion and inner coordination sphere are represented using QM PBE, PBE0, and MP2 methods. The relative solvation free energies of Mg(2+) and Zn(2+) were calculated using thermodynamic integration. We also demonstrate the features for excited state properties. We calculate the time-averaged solution absorption spectrum of indole, the emission spectrum of the indole 1La excited state, and the electronic circular dichroism spectrum of an oxacepham.

QM/MM studies of contemporary and novel membrane raft fluorescent probes

We have studied a number of contemporary and novel membrane probes, selected for their structural similarity to membrane raft components, in order to properly anchor themselves within a sphingolipid/cholesterol rich region. A QM/MM approach was adopted in order to understand the structural and electrostatic influences of fluorescence emission shifts of the probes in different lipid and solvation environments. The proposed modifications to the membrane probes have shown encouraging data relating not only to emission shifts within the membrane, but also their ability to anchor within a membrane raft domain and the stability to internalization within a membrane system.