Towards large scale hybrid QM/MM dynamics of complex systems with advanced point dipole polarizable embeddings

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

Deciphering Photoreceptors Through Atomistic Modeling from Light Absorption to Conformational Response

In this review, we discuss the successes and challenges of the atomistic modeling of photoreceptors. Throughout our presentation, we integrate explanations of the primary methodological approaches, ranging from quantum mechanical descriptions to classical enhanced sampling methods, all while providing illustrative examples of their practical application to specific systems. To enhance the effectiveness of our analysis, our primary focus has been directed towards the examination of applications across three distinct photoreceptors. These include an example of Blue Light-Using Flavin (BLUF) domains, a bacteriophytochrome, and the orange carotenoid protein (OCP) employed by cyanobacteria for photoprotection. Particular emphasis will be placed on the pivotal role played by the protein matrix in fine-tuning the initial photochemical event within the embedded chromophore. Furthermore, we will investigate how this localized perturbation initiates a cascade of events propagating from the binding pocket throughout the entire protein structure, thanks to the intricate network of interactions between the chromophore and the protein.

A Quasi Time-Reversible Scheme Based on Density Matrix Extrapolation on the Grassmann Manifold for Born-Oppenheimer Molecular Dynamics

This Letter introduces the so-called Quasi Time-Reversible scheme based on Grassmann extrapolation (QTR G-Ext) of density matrices for an accurate calculation of initial guesses in Born-Oppenheimer Molecular Dynamics (BOMD) simulations. The method shows excellent results on four large molecular systems that are representative of real-life production applications, ranging from 21 to 94 atoms simulated with Kohn-Sham (KS) density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations while at the same time achieving energy-conserving simulations, resulting in a considerable speed-up of BOMD simulations even when tight convergence of the KS equations is required.

Scalable hybrid deep neural networks/polarizable potentials biomolecular simulations including long-range effects

Deep-HP is a scalable extension of the Tinker-HP multi-GPU molecular dynamics (MD) package enabling the use of Pytorch/TensorFlow Deep Neural Network (DNN) models. Deep-HP increases DNNs' MD capabilities by orders of magnitude offering access to ns simulations for 100k-atom biosystems while offering the possibility of coupling DNNs to any classical (FFs) and many-body polarizable (PFFs) force fields. It allows therefore the introduction of the ANI-2X/AMOEBA hybrid polarizable potential designed for ligand binding studies where solvent-solvent and solvent-solute interactions are computed with the AMOEBA PFF while solute-solute ones are computed by the ANI-2X DNN. ANI-2X/AMOEBA explicitly includes AMOEBA's physical long-range interactions via an efficient Particle Mesh Ewald implementation while preserving ANI-2X's solute short-range quantum mechanical accuracy. The DNN/PFF partition can be user-defined allowing for hybrid simulations to include key ingredients of biosimulation such as polarizable solvents, polarizable counter ions, etc.… ANI-2X/AMOEBA is accelerated using a multiple-timestep strategy focusing on the model's contributions to low-frequency modes of nuclear forces. It primarily evaluates AMOEBA forces while including ANI-2X ones only via correction-steps resulting in an order of magnitude acceleration over standard Velocity Verlet integration. Simulating more than 10 μs, we compute charged/uncharged ligand solvation free energies in 4 solvents, and absolute binding free energies of host-guest complexes from SAMPL challenges. ANI-2X/AMOEBA average errors are discussed in terms of statistical uncertainty and appear in the range of chemical accuracy compared to experiment. The availability of the Deep-HP computational platform opens the path towards large-scale hybrid DNN simulations, at force-field cost, in biophysics and drug discovery.

Evaluating the Transition State Stabilization/Destabilization Effects of the Electric Fields from Scaffold Residues by a QM/MM Approach

The protein scaffolds of enzymes not only provide structural support for the catalytic center but also exert preorganized electric fields for electrostatic catalysis. In recent years, uniform oriented external electric fields (OEEFs) have been widely applied to enzymatic reactions to mimic the electrostatic effects of the environment. However, the electric fields exerted by individual residues in proteins may be quite heterogeneous across the active site, with varying directions and strengths at different positions of the active site. Here, we propose a QM/MM-based approach to evaluate the effects of the electric fields exerted by individual residues in the protein scaffold. In particular, the heterogeneity of the residue electric fields and the effect of the native protein environment can be properly accounted for by this QM/MM approach. A case study of the O-O heterolysis reaction in the catalytic cycle of TyrH shows that (1) for scaffold residues that are relatively far from the active site, the heterogeneity of the residue electric field in the active site is not very significant and the electrostatic stabilization/destabilization due to each residue can be well approximated with the interaction energy between a uniform electric field and the QM region dipole; (2) for scaffold residues near the active site, the residue electric fields can be highly heterogeneous along the breaking O-O bond. In such a case, approximating the residue electric fields as uniform fields may misrepresent the overall electrostatic effect of the residue. The present QM/MM approach can be applied to evaluate the residues' electrostatic impact on enzymatic reactions, which also can be useful in computational optimization of electric fields to boost the enzyme catalysis.

Fast Method for Excited-State Dynamics in Complex Systems and Its Application to the Photoactivation of a Blue Light Using Flavin Photoreceptor

The excited-state dynamics of molecules embedded in complex (bio)matrices is still a challenging goal for quantum chemical models. Hybrid QM/MM models have proven to be an effective strategy, but an optimal combination of accuracy and computational cost still has to be found. Here, we present a method which combines the accuracy of a polarizable embedding QM/MM approach with the computational efficiency of an excited-state self-consistent field method. The newly implemented method is applied to the photoactivation of the blue-light-using flavin (BLUF) domain of the AppA protein. We show that the proton-coupled electron transfer (PCET) process suggested for other BLUF proteins is still valid also for AppA.

State averaged CASSCF in AMOEBA polarizable water model for simulating nonadiabatic molecular dynamics with nonequilibrium solvation effects

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water.

Newton-X Platform: New Software Developments for Surface Hopping and Nuclear Ensembles

Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photophysical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.

Trajectory Surface Hopping for a Polarizable Embedding QM/MM Formulation

We present the implementation of trajectory surface-hopping nonadiabatic dynamics for a polarizable embedding QM/MM formulation. Time-dependent density functional theory was used at the quantum mechanical level of theory, whereas the molecular mechanics description involved the polarizable AMOEBA force field. This implementation has been obtained by integrating the surface-hopping program Newton-X NS with an interface between the Gaussian 16 and the Tinker suites of codes to calculate QM/AMOEBA energies and forces. The implementation has been tested on a photoinduced electron-driven proton-transfer reaction involving pyrimidine and a hydrogen-bonded water surrounded by a small cluster of water molecules and within a large water droplet.

Computer-aided drug design, quantum-mechanical methods for biological problems

Quantum chemistry enables to study systems with chemical accuracy (<1 kcal/mol from experiment) but is restricted to a handful of atoms due to its computational expense. This has led to ongoing interest to optimize and simplify these methods while retaining accuracy. Implementing quantum mechanical (QM) methods on modern hardware such as multiple-GPUs is one example of how the field is optimizing performance. Multiscale approaches like the so-called QM/molecular mechanical method are gaining popularity in drug discovery because they focus the application of QM methods on the region of choice (e.g., the binding site), while using efficient MM models to represent less relevant areas. The creation of simplified QM methods is another example, including the use of machine learning to create ultra-fast and accurate QM models. Herein, we summarize recent advancements in the development of optimized QM methods that enhance our ability to use these methods in computer aided drug discovery.

Recent Developments in Polarizable Molecular Dynamics Simulations of Electrolyte Solutions

Polarizable molecular dynamics simulations are a fast progressing field in the scientific research of ionic liquids. The fundamentals of polarizable simulations, as well as their application to ionic liquids, were summarized in a review [Bedrov, D.; Piquemal, J.-P.; Borodin, O.; MacKerell, Jr., A. D.; Roux, B.; Schröder, C. Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields. Chem. Rev. 2019, 119, 7940–7995] in 2019. Since then, new methods to treat intermolecular interaction of induced dipoles in these highly charged systems were developed. This concerns the damping of these interactions and additional charge transfer as well as the prediction of ionic materials with ultrahigh refractive indices. In addition to the progress of the polarizable force fields, also thermostats and barostats for polarizable simulations evolved recently.

Computationally driven discovery of SARS-CoV-2 Mpro inhibitors: from design to experimental validation

We report a fast-track computationally driven discovery of new SARS-CoV-2 main protease (Mpro) inhibitors whose potency ranges from mM for the initial non-covalent ligands to sub-μM for the final covalent compound (IC50 = 830 ± 50 nM). The project extensively relied on high-resolution all-atom molecular dynamics simulations and absolute binding free energy calculations performed using the polarizable AMOEBA force field. The study is complemented by extensive adaptive sampling simulations that are used to rationalize the different ligand binding poses through the explicit reconstruction of the ligand-protein conformation space. Machine learning predictions are also performed to predict selected compound properties. While simulations extensively use high performance computing to strongly reduce the time-to-solution, they were systematically coupled to nuclear magnetic resonance experiments to drive synthesis and for in vitro characterization of compounds. Such a study highlights the power of in silico strategies that rely on structure-based approaches for drug design and allows the protein conformational multiplicity problem to be addressed. The proposed fluorinated tetrahydroquinolines open routes for further optimization of Mpro inhibitors towards low nM affinities.

Factors That Determine the Variation of Equilibrium and Kinetic Properties of QM/MM Enzyme Simulations: QM Region, Conformation, and Boundary Condition

To analyze the impact of various technical details on the results of quantum mechanical (QM)/molecular mechanical (MM) enzyme simulations, including the QM region size, catechol-O-methyltransferase (COMT) is studied as a model system using an approximate QM/MM method (DFTB3/CHARMM). The results show that key equilibrium and kinetic properties for methyl transfer in COMT exhibit limited variations with respect to the size of the QM region, which ranges from ∼100 to ∼500 atoms in this study. With extensive sampling, local and global structural characteristics of the enzyme are largely conserved across the studied QM regions, while the nature of the transition state (e.g., secondary kinetic isotope effect) and reaction exergonicity are largely maintained. Deviations in the free energy profile with different QM region sizes are similar in magnitude to those observed with changes in other simulation protocols, such as different initial enzyme conformations and boundary conditions. Electronic structural properties, such as the covariance matrix of residual charge fluctuations, appear to exhibit rather long-range correlations, especially when the peptide backbone is included in the QM region; this observation holds when a range-separated DFT approach is used as the QM region, suggesting that delocalization error is unlikely the origin. Overall, the analyses suggest that multiple simulation details determine the results of QM/MM enzyme simulations with comparable contributions.

Grassmann Extrapolation of Density Matrices for Born-Oppenheimer Molecular Dynamics

Born-Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory BOMD calculation is the solution to the Kohn-Sham (KS) equations that requires an iterative procedure that starts from a guess for the density matrix. Converged densities from previous points in the trajectory can be used to extrapolate a new guess; however, the nonlinear constraint that an idempotent density needs to satisfy makes the direct use of standard linear extrapolation techniques not possible. In this contribution, we introduce a locally bijective map between the manifold where the density is defined and its tangent space so that linear extrapolation can be performed in a vector space while, at the same time, retaining the correct physical properties of the extrapolated density using molecular descriptors. We apply the method to real-life, multiscale, polarizable QM/MM BOMD simulations, showing that sizeable performance gains can be achieved, especially when a tighter convergence to the KS equations is required.

Molecular Dynamics Driven by the Many-Body Expansion (MBE-MD)

We present a protocol for classical and nuclear quantum dynamics, in which the energies and forces are generated by the many-body expansion (MBE), and apply it to water clusters using the TTM2.1-F and MB-Pol interaction potentials at various temperatures. We carry out MBE-molecular dynamics (MD) classical and nuclear quantum dynamical simulations, in which the energies and forces of the full system are approximated by the two-, three-, and four-body terms of the MBE, and compare the average potential and the vibrational density of states with the full simulation, i.e., the one for which no MBE is used. Our results indicate that the thermally averaged potential energy from the MBE up to the four-body term converges with near-identical behavior to the one from the full simulation. The three-body makes a substantial contribution (∼20%) to the energy, whereas the four-body is necessary for obtaining quantitatively accurate energetics and forces, albeit making a small contribution to each (∼2%). We further show that the harmonic frequencies are reproduced to within a few wavenumbers (cm^-1) at the four-body level and that the slowest modes to converge with the MBE rank are those involving the strongest hydrogen bonds. Anharmonicity exacerbates this effect, so that a four-body description of the energies and forces is needed to achieve accurate anharmonic vibrational frequencies in the hydrogen-bonded OH-stretching region. We also discuss the asymptotic scaling of the MBE-MD protocol with respect to the cost of the underlying potential energy evaluation, suggesting that electronic structure methods that scale at least as N⁴, N being the size of the system, are needed to result in savings over the traditional full MD simulation. We anticipate that the MBE-MD protocol can evolve into a powerful and practical method, which will allow for highly accurate ab initio MD simulations on a much broader range of molecular systems than can be currently handled.

Ultrafast Transient Infrared Spectroscopy of Photoreceptors with Polarizable QM/MM Dynamics

Ultrafast transient infrared (TRIR) spectroscopy is widely used to measure the excitation-induced structural changes of protein-bound chromophores. Here, we design a novel and general strategy to compute TRIR spectra of photoreceptors by combining μs-long MM molecular dynamics with ps-long QM/AMOEBA Born-Oppenheimer molecular dynamics (BOMD) trajectories for both ground and excited electronic states. As a proof of concept, the strategy is here applied to AppA, a blue-light-utilizing flavin (BLUF) protein, found in bacteria. We first analyzed the short-time evolution of the embedded flavin upon excitation revealing that its dynamic Stokes shift is ultrafast and mainly driven by the internal reorganization of the chromophore. A different normal-mode representation was needed to describe ground- and excited-state IR spectra. In this way, we could assign all of the bands observed in the measured transient spectrum. In particular, we could characterize the flavin isoalloxazine-ring region of the spectrum, for which a full and clear description was missing.

Combining Evolutionary Conservation and Quantum Topological Analyses To Determine Quantum Mechanics Subsystems for Biomolecular Quantum Mechanics/Molecular Mechanics Simulations

Selection of residues and other molecular fragments for inclusion in the quantum mechanics (QM) region for QM/molecular mechanics (MM) simulations is an important step for these calculations. Here, we present an approach that combines protein sequence/structure evolution and electron localization function (ELF) analyses. The combination of these two analyses allows the determination of whether a residue needs to be included in the QM subsystem or can be represented by the MM environment. We have applied this approach on two systems previously investigated by QM/MM simulations, 4-oxalocrotonate tautomerase (4OT) and ten-eleven translocation-2 (TET2), that provide examples where fragments may or may not need to be included in the QM subsystem. Subsequently, we present the use of this approach to determine the appropriate QM subsystem to calculate the minimum energy path (MEP) for the reaction catalyzed by human DNA polymerase λ (Polλ) with a third cation in the active site. Our results suggest that the combination of protein evolutionary and ELF analyses provides insights into residue/molecular fragment selection for QM/MM simulations.

Atomistic Polarizable Embeddings: Energy, Dynamics, Spectroscopy, and Reactivity

The computational modeling of realistic extended systems, relevant in, e.g., Chemistry and Biophysics, is a fundamental problem of paramount importance in contemporary research. Enzymatic catalysis and photoinduced processes in pigment-protein complexes are typical problems targeted by computer-aided approaches, to complement experiments as interpretative tools at a molecular scale. The daunting complexity of this task lies in between the opposite stringent requirements of results' reliability for structural/dynamical properties and related intermolecular interactions, and a mandatory principle of realism in the modeling strategy. Therefore, in practice, a truly realistic computational model of a biologically relevant system can easily fail to meet the accuracy requirement, in order to balance the excessive computational cost necessary to reach the desired precision.To address such an "accuracy vs reality" dualistic requirement, mixed quantum mechanics/classical mechanics approaches within Atomistic (i.e., preserving the discrete particle configuration) Polarizable Embeddings (QM/APEs) methods have been proposed over the years. In this Account, we review recent developments in the design and application of general QM/APE methods, targeting situations where a local intrinsically quantum behavior is coupled to a large molecular system (i.e., an environment), often involving processes with different dynamical time scales, in order to avoid brute-force, unpractical quantum chemistry calculations on the complete system.In the first place, our interest is devoted to the available APEs models presently implemented in computational software, highlighting the quantum chemistry methods that can be used to treat the QM subsystem. We review the coupling strategy between the QM subsystem and the APE, which requires to examine the way the QM/MM mutual interactions are accounted for and how the polarization of the classical environment is considered with respect to (wrt) the quantum variables. Because of the need of reliable molecular and macromolecular structures, a pivotal aspect to address here is the handling of the system dynamics (i.e., gradients wrt nuclear positions are required), especially for large molecular assemblies composed by an overwhelming number of atoms, exploring many conformations on a complex energy landscape.Alongside, we highlight our views on the necessary steps to take toward more accurate general-purposes and transferable explicit embeddings. The main objective to achieve here is to design a more physically grounded multiscale approach. To do so, one should apply advanced new generation classical models to account for refined induction effects that are able to (i) improve the quality of QM/MM interaction energies; (ii) enhance transferability by avoiding the compulsory partial (or total) reparameterization of the classical model. Moreover, the extension of recent developments originating from the field of advanced classical molecular dynamics (MD) to the realm of QM/APE methods is a key direction to improve both speed and efficiency for the phase space exploration of systems of growing size and complexity.Lastly, we point out specific research topics where an advanced QM/APE dynamics can certainly shed some light. For example, we discuss chemical reactions in "harsh" environments and the case of spectroscopic theoretical modeling where the inclusion of refined environment effects is often mandatory.

Development and application of quantum mechanics/molecular mechanics methods with advanced polarizable potentials

Quantum mechanics/molecular mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and biological systems. The combination of QM and MM methods to represent a system gives rise to several challenges that need to be addressed. The increase in computational speed has allowed the expanded use of more complicated and accurate methods for both QM and MM simulations. Here, we review some approaches that address several common challenges encountered in QM/MM simulations with advanced polarizable potentials, from methods to account for boundary across covalent bonds and long-range effects, to polarization and advanced embedding potentials.

An enhanced sampling QM/AMOEBA approach: The case of the excited state intramolecular proton transfer in solvated 3-hydroxyflavone

We present an extension of the polarizable quantum mechanical (QM)/AMOEBA approach to enhanced sampling techniques. This is achieved by connecting the enhanced sampling PLUMED library to the machinery based on the interface of Gaussian and Tinker to perform QM/AMOEBA molecular dynamics. As an application, we study the excited state intramolecular proton transfer of 3-hydroxyflavone in two solvents: methanol and methylcyclohexane. By using a combination of molecular dynamics and umbrella sampling, we find an ultrafast component of the transfer, which is common to the two solvents, and a much slower component, which is active in the protic solvent only. The mechanisms of the two components are explained in terms of intramolecular vibrational redistribution and intermolecular hydrogen-bonding, respectively. Ground and excited state free energies along an effective reaction coordinate are finally obtained allowing for a detailed analysis of the solvent mediated mechanism.

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.

Multiscale Models for Light-Driven Processes

Multiscale models combining quantum mechanical and classical descriptions are a very popular strategy to simulate properties and processes of complex systems. Many alternative formulations have been developed, and they are now available in all of the most widely used quantum chemistry packages. Their application to the study of light-driven processes, however, is more recent, and some methodological and numerical problems have yet to be solved. This is especially the case for the polarizable formulation of these models, the recent advances in which we review here. Specifically, we identify and describe the most important specificities that the polarizable formulation introduces into both the simulation of excited-state dynamics and the modeling of excitation energy and electron transfer processes.

High-resolution mining of the SARS-CoV-2 main protease conformational space: supercomputer-driven unsupervised adaptive sampling

We provide an unsupervised adaptive sampling strategy capable of producing μs-timescale molecular dynamics (MD) simulations of large biosystems using many-body polarizable force fields (PFFs). The global exploration problem is decomposed into a set of separate MD trajectories that can be restarted within a selective process to achieve sufficient phase-space sampling. Accurate statistical properties can be obtained through reweighting. Within this highly parallel setup, the Tinker-HP package can be powered by an arbitrary large number of GPUs on supercomputers, reducing exploration time from years to days. This approach is used to tackle the urgent modeling problem of the SARS-CoV-2 Main Protease (Mpro) producing more than 38 μs of all-atom simulations of its apo (ligand-free) dimer using the high-resolution AMOEBA PFF. The first 15.14 μs simulation (physiological pH) is compared to available non-PFF long-timescale simulation data. A detailed clustering analysis exhibits striking differences between FFs, with AMOEBA showing a richer conformational space. Focusing on key structural markers related to the oxyanion hole stability, we observe an asymmetry between protomers. One of them appears less structured resembling the experimentally inactive monomer for which a 6 μs simulation was performed as a basis for comparison. Results highlight the plasticity of the Mpro active site. The C-terminal end of its less structured protomer is shown to oscillate between several states, being able to interact with the other protomer, potentially modulating its activity. Active and distal site volumes are found to be larger in the most active protomer within our AMOEBA simulations compared to non-PFFs as additional cryptic pockets are uncovered. A second 17 μs AMOEBA simulation is performed with protonated His172 residues mimicking lower pH. Data show the protonation impact on the destructuring of the oxyanion loop. We finally analyze the solvation patterns around key histidine residues. The confined AMOEBA polarizable water molecules are able to explore a wide range of dipole moments, going beyond bulk values, leading to a water molecule count consistent with experimental data. Results suggest that the use of PFFs could be critical in drug discovery to accurately model the complexity of the molecular interactions structuring Mpro.

Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?

QM/MM simulations have become an indispensable tool in many chemical and biochemical investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chemistry, are there still "burning challenges" in QM/MM methods, especially for biomolecular systems? In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quantitative applicability of QM/MM simulations to many, if not all, biomolecules. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate additional developments that help push the field forward in meaningful directions.

A simplified charge projection scheme for long-range electrostatics in ab initio QM/MM calculations

In a previous work [Pan et al., Molecules 23, 2500 (2018)], a charge projection scheme was reported, where outer molecular mechanical (MM) charges [>10 Å from the quantum mechanical (QM) region] were projected onto the electrostatic potential (ESP) grid of the QM region to accurately and efficiently capture long-range electrostatics in ab initio QM/MM calculations. Here, a further simplification to the model is proposed, where the outer MM charges are projected onto inner MM atom positions (instead of ESP grid positions). This enables a representation of the long-range MM electrostatic potential via augmentary charges (AC) on inner MM atoms. Combined with the long-range electrostatic correction function from Cisneros et al. [J. Chem. Phys. 143, 044103 (2015)] to smoothly switch between inner and outer MM regions, this new QM/MM-AC electrostatic model yields accurate and continuous ab initio QM/MM electrostatic energies with a 10 Å cutoff between inner and outer MM regions. This model enables efficient QM/MM cluster calculations with a large number of MM atoms as well as QM/MM calculations with periodic boundary conditions.

A Many-Body, Fully Polarizable Approach to QM/MM Simulations

We present a new development in quantum mechanics/molecular mechanics (QM/MM) methods by replacing conventional MM models with data-driven many-body (MB) representations rigorously derived from high-level QM calculations. The new QM/MM approach builds on top of mutually polarizable QM/MM schemes developed for polarizable force fields with inducible dipoles and uses permutationally invariant polynomials to effectively account for quantum-mechanical contributions (e.g., exchange-repulsion and charge transfer and penetration) that are difficult to describe by classical expressions adopted by conventional MM models. Using the many-body MB-pol and MB-DFT potential energy functions for water, which include explicit two-body and three-body terms fitted to reproduce the corresponding CCSD(T) and PBE0 two-body and three-body energies for water, we demonstrate a smooth energetic transition as molecules are transferred between QM and MM regions, without the need of a transition layer. By effectively elevating the accuracy of both the MM region and the QM/MM interface to that of the QM region, the new QM/MB-MM approach achieves an accuracy comparable to that obtained with a fully QM treatment of the entire system.

Excited state Born-Oppenheimer molecular dynamics through coupling between time dependent DFT and AMOEBA

We present the implementation of excited state Born-Oppenheimer molecular dynamics (BOMD) using a polarizable QM/MM approach based on a time-dependent density functional theory (TDDFT) formulation and the AMOEBA force field. The implementation relies on an interface between Tinker and Gaussian software and it uses an algorithm for the calculation of QM/MM energy and forces which scales linearly with the number of MM atoms. The resulting code can perform TDDFT/AMOEBA BOMD simulations on real-life systems with standard computational resources. As a test case, the method is applied to the study of the mechanism of locally-excited to charge-transfer conversion in dimethylaminobenzonitrile in a polar solvent. Our simulations confirm that such a conversion is governed by the twisting of the dimethylamino group which is accompanied by an important reorientation of solvent molecules.

Solvation effects drive the selectivity in Diels-Alder reaction under hyperbaric conditions

High pressure effects on the Diels-Alder reaction in condensed phase are investigated by means of theoretical methods, employing advanced multiscale modeling approaches based on physically grounded models. The simulations reveal how the increase of pressure from 1 to 10 000 atm (10 katm) does not affect the stability of the reaction products, modifying the kinetics of the process by lowering considerably the transition state energy. The reaction profile at high pressure remarkably differs from that at 1 atm, showing a submerged TS and a pre-TS structure lower in energy. The different solvation between endo and exo pre-TS is revealed as the driving force pushing the reaction toward a much higher preference for the endo product at high pressure.

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.

Cost-Effective Potential for Accurate Polarizable Embedding Calculations in Protein Environments

The fragment-based polarizable embedding (PE) model combined with an appropriate electronic structure method constitutes a highly efficient and accurate multiscale approach for computing spectroscopic properties of a central moiety including effects from its molecular environment through an embedding potential. There is, however, a comparatively high computational overhead associated with the computation of the embedding potential, which is derived from first-principles calculations on individual fragments of the environment. To reduce the computational cost associated with the calculation of embedding potential parameters, we developed a set of amino acid-specific transferable parameters tailored for large-scale PE-based calculations that include proteins. The amino acid-based parameters are obtained by simultaneously fitting to a set of reference electric potentials based on structures derived from a backbone-dependent rotamer library. The developed cost-effective polarizable protein potential (CP³) consists of atom-centered charges and isotropic dipole-dipole polarizabilities of the standard amino acids. In terms of reproduction of electric potentials, the CP³ is shown to perform consistently and with acceptable accuracy across both small tripeptide test systems and larger proteins. We show, through applications on realistic protein systems, that acceptable accuracy can be obtained by using a pure CP³ representation of the protein environment, thus altogether omitting the cost associated with the calculation of embedding potential parameters. High accuracy comparable to that of the full fragment-based approach can be achieved through a mixed description where the CP³ is used only to describe amino acids beyond a threshold distance from the central quantum part.

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

Accurate Biomolecular Simulations Account for Electronic Polarization

In this perspective, we discuss where and how accounting for electronic many-body polarization affects the accuracy of classical molecular dynamics simulations of biomolecules. While the effects of electronic polarization are highly pronounced for molecules with an opposite total charge, they are also non-negligible for interactions with overall neutral molecules. For instance, neglecting these effects in important biomolecules like amino acids and phospholipids affects the structure of proteins and membranes having a large impact on interpreting experimental data as well as building coarse grained models. With the combined advances in theory, algorithms and computational power it is currently realistic to perform simulations with explicit polarizable dipoles on systems with relevant sizes and complexity. Alternatively, the effects of electronic polarization can also be included at zero additional computational cost compared to standard fixed-charge force fields using the electronic continuum correction, as was recently demonstrated for several classes of biomolecules.

General Linear Scaling Implementation of Polarizable Embedding Schemes

A general framework to treat polarizable embedding schemes in the context of QM/MM calculations is presented. Such a framework is completely general, as it allows in principle one to treat any electrostatic distribution and polarization model with minimal modifications and achieves linear scaling in computational cost and memory requirements. The performances and scaling of the new implementation are demonstrated with benchmark calculations on water clusters including up to 1146240 atoms.