Advancing Force Fields Parameterization: A Directed Graph Attention Networks Approach.

Force fields (FFs) are an established tool for simulating large and complex molecular systems. However, parametrizing FFs is a challenging and time-consuming task that relies on empirical heuristics, experimental data, and computational data. Recent efforts aim to automate the assignment of FF parameters using pre-existing databases and on-the-fly ab initio data. In this study, we propose a graph-based force field (GB-FFs) model to directly derive parameters for the Generalized Amber Force Field (GAFF) from chemical environments and research into the influence of functional forms. Our end-to-end parametrization approach predicts parameters by aggregating the basic information in directed molecular graphs, eliminating the need for expert-defined procedures and enhances the accuracy and transferability of GAFF across a broader range of molecular complexes. Simulation results are compared to the original GAFF parametrization. In practice, our results demonstrate an improved transferability of the model, showcasing its improved accuracy in modeling intermolecular and torsional interactions, as well as improved solvation free energies. The optimization approach developed in this work is fully applicable to other nonpolarizable FFs as well as to polarizable ones.

Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation.

We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.

Sparse Quantum State Preparation for Strongly Correlated Systems.

Quantum computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialization of the qubits to a high-quality approximation of the sought-after ground state. Quantum state preparation enables the generation of approximate eigenstates derived from classical computations but is frequently treated as an oracle in quantum information. In this study, we investigate the quantum state preparation of prototypical strongly correlated systems' ground state, up to 28 qubits, using the Hyperion-1 GPU-accelerated state-vector emulator. Various variational and nonvariational methods are compared in terms of their circuit depth and classical complexity. Our results indicate that the recently developed Overlap-ADAPT-VQE algorithm offers the most advantageous performance for near-term applications.

Incorporating Neural Networks into the AMOEBA Polarizable Force Field.

Neural network potentials (NNPs) offer significant promise to bridge the gap between the accuracy of quantum mechanics and the efficiency of molecular mechanics in molecular simulation. Most NNPs rely on the locality assumption that ensures the model's transferability and scalability and thus lack the treatment of long-range interactions, which are essential for molecular systems in the condensed phase. Here we present an integrated hybrid model, AMOEBA+NN, which combines the AMOEBA potential for the short- and long-range noncovalent atomic interactions and an NNP to capture the remaining local covalent contributions. The AMOEBA+NN model was trained on the conformational energy of the ANI-1x data set and tested on several external data sets ranging from small molecules to tetrapeptides. The hybrid model demonstrated substantial improvements over the baseline models in term of accuracy as the molecule size increased, suggesting its potential as a next-generation approach for chemically accurate molecular simulations.

Enforcing Local DNA Kinks by Sequence-Selective Trisintercalating Oligopeptides of a Tricationic Porphyrin: A Polarizable Molecular Dynamics Study.

Bisacridinyl-bisarginyl porphyrin (BABAP) is a trisintercalating derivative of a tricationic porphyrin, formerly designed and synthesized in order to selectively target and photosensitize the ten-base pair palindromic sequence d(CGGGCGCCCG)2 . We resorted to the previously derived (Far et al., 2004) lowest energy-minimized (EM) structure of the BABAP complex with this sequence as a starting point. We performed polarizable molecular dynamics (MD) on this complex. It showed, over a 150 ns duration, the persistent binding of the Arg side-chain on each BABAP arm to the two G bases upstream from the central porphyrin intercalation site. We subsequently performed progressive shortenings of the connector chain linking the Arg-Gly backbone to the acridine, from n=6 methylenes to 4, followed by removal of the Gly backbone and further connector shortenings, from n=4 to n=1. These resulted into progressive deformations ('kinks') of the DNA backbone. In its most accented kinked structure, the DNA backbone was found to have a close overlap with that of DNA bound to Cre recombinase, with, at the level of one acridine intercalation site, negative roll and positive tilt values consistent with those experimentally found for this DNA at its own kinked dinucleotide sequence. Thus, in addition to their photosensitizing properties, some BABAP derivatives could induce sequence-selective, controlled DNA deformations, which are targets for cleavage by endonucleases or for repair enzymes.

Force-field-enhanced neural network interactions: from local equivariant embedding to atom-in-molecule properties and long-range effects.

We introduce FENNIX (Force-Field-Enhanced Neural Network InteraXions), a hybrid approach between machine-learning and force-fields. We leverage state-of-the-art equivariant neural networks to predict local energy contributions and multiple atom-in-molecule properties that are then used as geometry-dependent parameters for physically-motivated energy terms which account for long-range electrostatics and dispersion. Using high-accuracy ab initio data (small organic molecules/dimers), we trained a first version of the model. Exhibiting accurate gas-phase energy predictions, FENNIX is transferable to the condensed phase. It is able to produce stable Molecular Dynamics simulations, including nuclear quantum effects, for water predicting accurate liquid properties. The extrapolating power of the hybrid physically-driven machine learning FENNIX approach is exemplified by computing: (i) the solvated alanine dipeptide free energy landscape; (ii) the reactive dissociation of small molecules.

Cooperativity and Frustration Effects (or Lack Thereof) in Polarizable and Non-polarizable Force Fields.

Understanding cooperativity and frustration is crucial for studying biological processes such as molecular recognition and protein aggregation. Force fields have been extensively utilized to explore cooperativity in the formation of protein secondary structures and self-assembled systems. Multiple studies have demonstrated that polarizable force fields provide more accurate descriptions of this phenomenon compared to fixed-charge pairwise nonpolarizable force fields, thanks to the incorporation of polarization effects. In this study, we assess the performance of the AMOEBA polarizable force field and the AMBER and OPLS nonpolarizable pairwise force fields in capturing positive and negative cooperativity recently explored in neutral and charged molecular clusters using density functional theory. Our findings show that polarizable and nonpolarizable force fields qualitatively reproduce the relative cooperativity observed in electron structure calculations. However, AMBER and OPLS fail to describe absolute cooperativity. In contrast, AMOEBA accounts for the absolute cooperativity by considering interactions beyond pairwise interactions. According to the energy decomposition analysis, it is observed that the electrostatic interactions calculated with the AMBER and OPLS force fields seem to play an important and counterintuitive role in reproducing the adiabatic interaction energies calculated with density functional theory. However, it is important to note that these force fields, due to their nature, do not explicitly incorporate many-body effects, which limits their ability to accurately describe cooperativity. On the other hand, frustration in polarizable and nonpolarizable force fields is caused by changes in bond stretching and angle bending terms of the building blocks when they are forming a complex.

Smooth particle mesh Ewald-integrated stochastic Lanczos many-body dispersion algorithm.

We derive and implement an alternative formulation of the Stochastic Lanczos algorithm to be employed in connection with the Many-Body Dispersion model (MBD). Indeed, this formulation, which is only possible due to the Stochastic Lanczos' reliance on matrix-vector products, introduces generalized dipoles and fields. These key quantities allow for a state-of-the-art treatment of periodic boundary conditions via the O(Nlog(N)) Smooth Particle Mesh Ewald (SPME) approach which uses efficient fast Fourier transforms. This SPME-Lanczos algorithm drastically outperforms the standard replica method which is affected by a slow and conditionally convergence rate that limits an efficient and reliable inclusion of long-range periodic boundary conditions interactions in many-body dispersion modelling. The proposed algorithm inherits the embarrassingly parallelism of the original Stochastic Lanczos scheme, thus opening up for a fully converged and efficient periodic boundary conditions treatment of MBD approaches.

ANKH: A Generalized O(N) Interpolated Ewald Strategy for Molecular Dynamics Simulations.

To evaluate electrostatics interactions, molecular dynamics (MD) simulations rely on Particle Mesh Ewald (PME), an O(Nlog(N)) algorithm that uses Fast Fourier Transforms (FFTs) or, alternatively, on O(N) Fast Multipole Methods (FMM) approaches. However, the FFTs low scalability remains a strong bottleneck for large-scale PME simulations on supercomputers. On the opposite, FFT-free FMM techniques are able to deal efficiently with such systems but they fail to reach PME performances for small- to medium-size systems, limiting their real-life applicability. We propose ANKH, a strategy grounded on interpolated Ewald summations and designed to remain efficient/scalable for any size of systems. The method is generalized for distributed point multipoles, and so for induced dipoles, which makes it suitable for high performance simulations using new generation polarizable force fields toward exascale computing.

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.

Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations.

The Trotterized Unitary Coupled Cluster Single and Double (UCCSD) ansatz has recently attracted interest due to its use in Variation Quantum Eigensolver (VQE) molecular simulations on quantum computers. However, when the size of molecules increases, UCCSD becomes less interesting as it cannot achieve sufficient accuracy. Including higher-order excitations is therefore mandatory to recover the UCC's missing correlation effects. Here, we extend the Trotterized UCC approach via the addition of (true) Triple T excitations introducing UCCSDT. We also include both spin and orbital symmetries. Indeed, in practice, the latter help to reduce unnecessary circuit excitations and thus accelerate the optimization process enabling researchers to tackle larger molecules. Our initial numerical tests (12-14 qubits) show that UCCSDT improves the overall accuracy by at least two orders of magnitude with respect to standard UCCSD. Overall, the UCCSDT ansatz is shown to reach chemical accuracy and to be competitive with the CCSD(T) gold-standard classical method of quantum chemistry.

Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: From Force Fields to Machine Learning Potentials.

We report the implementation of a multi-CPU and multi-GPU massively parallel platform dedicated to the explicit inclusion of nuclear quantum effects (NQEs) in the Tinker-HP molecular dynamics (MD) package. The platform, denoted Quantum-HP, exploits two simulation strategies: the Ring-Polymer Molecular Dynamics (RPMD) that provides exact structural properties at the cost of a MD simulation in an extended space of multiple replicas and the adaptive Quantum Thermal Bath (adQTB) that imposes the quantum distribution of energy on a classical system via a generalized Langevin thermostat and provides computationally affordable and accurate (though approximate) NQEs. We discuss some implementation details, efficient numerical schemes, and parallelization strategies and quickly review the GPU acceleration of our code. Our implementation allows an efficient inclusion of NQEs in MD simulations for very large systems, as demonstrated by scaling tests on water boxes with more than 200,000 atoms (simulated using the AMOEBA polarizable force field). We test the compatibility of the approach with Tinker-HP's recently introduced Deep-HP machine learning potentials module by computing water properties using the DeePMD potential with adQTB thermostatting. Finally, we show that the platform is also compatible with the alchemical free energy estimation capabilities of Tinker-HP and fast enough to perform simulations. Therefore, we study how NQEs affect the hydration free energy of small molecules solvated with the recently developed Q-AMOEBA water force field. Overall, the Quantum-HP platform allows users to perform routine quantum MD simulations of large condensed-phase systems and will help to shed new light on the quantum nature of important interactions in biological matter.

Generalized Many-Body Dispersion Correction through Random-Phase Approximation for Chemically Accurate Density Functional Theory.

We extend our recently proposed Deep Learning-aided many-body dispersion (DNN-MBD) model to quadrupole polarizability (Q) terms using a generalized Random Phase Approximation (RPA) formalism, thus enabling the inclusion of van der Waals contributions beyond dipole. The resulting DNN-MBDQ model only relies on ab initio-derived quantities as the introduced quadrupole polarizabilities are recursively retrieved from dipole ones, in turn modeled via the Tkatchenko-Scheffler method. A transferable and efficient deep-neuronal network (DNN) provides atom-in-molecule volumes, while a single range-separation parameter is used to couple the model to Density Functional Theory (DFT). Since it can be computed at a negligible cost, the DNN-MBDQ approach can be coupled with DFT functionals, such as PBE, PBE0, and B86bPBE (dispersionless). The DNN-MBQ-corrected functionals reach chemical accuracy while exhibiting lower errors compared to their dipole-only counterparts.

Improving Condensed-Phase Water Dynamics with Explicit Nuclear Quantum Effects: The Polarizable Q-AMOEBA Force Field.

We introduce a new parametrization of the AMOEBA polarizable force field for water denoted Q-AMOEBA, for use in simulations that explicitly account for nuclear quantum effects (NQEs). This study is made possible thanks to the recently introduced adaptive Quantum Thermal Bath (adQTB) simulation technique which computational cost is comparable to classical molecular dynamics. The flexible Q-AMOEBA model conserves the initial AMOEBA functional form, with an intermolecular potential including an atomic multipole description of electrostatic interactions (up to quadrupole), a polarization contribution based on the Thole interaction model and a buffered 14-7 potential to model van der Waals interactions. It has been obtained by using a ForceBalance fitting strategy including high-level quantum chemistry reference energies and selected condensed-phase properties targets. The final Q-AMOEBA model is shown to accurately reproduce both gas-phase and condensed-phase properties, notably improving the original AMOEBA water model. This development allows the fine study of NQEs on water liquid phase properties such as the average H-O-H angle compared to its gas-phase equilibrium value, isotope effects, and so on. Q-AMOEBA also provides improved infrared spectroscopy prediction capabilities compared to AMOEBA03. Overall, we show that the impact of NQEs depends on the underlying model functional form and on the associated strength of hydrogen bonds. Since adQTB simulations can be performed at near classical computational cost using the Tinker-HP package, Q-AMOEBA can be extended to organic molecules, proteins, and nucleic acids opening the possibility for the large-scale study of the importance of NQEs in biophysics.

Targeting the Major Groove of the Palindromic d(GGCGCC)2 Sequence by Oligopeptide Derivatives of Anthraquinone Intercalators.

GC-rich sequences are recurring motifs in oncogenes and retroviruses and could be targeted by noncovalent major-groove therapeutic ligands. We considered the palindromic sequence d(G1G2C3G4C5C6)2, and designed several oligopeptide derivatives of the anticancer intercalator mitoxantrone. The stability of their complexes with an 18-mer oligonucleotide encompassing this sequence in its center was validated using polarizable molecular dynamics. We report the most salient structural features of two novel compounds, having a dialkylammonium group as a side chain on both arms. The anthraquinone ring is intercalated in the central d(CpG)2 sequence with its long axis perpendicular to that of the two base pairs. On each strand, this enables each ammonium group to bind in-register to O6/N7 of the two facing G bases upstream. We subsequently designed tris-intercalating derivatives, each dialkylammonium substituted with a connector to an N9-aminoacridine intercalator extending our target range from a six- to a ten-base-pair palindromic sequence, d(C1G2G3G4C5G6C7C8C9G10)2. The structural features of the complex of the most promising derivative are reported. The present design strategy paves the way for designing intercalator-oligopeptide derivatives with even higher selectivity, targeting an increased number of DNA bases, going beyond ten.

Efficient and Accurate Description of Diels-Alder Reactions Using Density Functional Theory.

Modeling chemical reactions using Quantum Chemistry is a widely used predictive strategy capable to complement experiments in order to understand the intrinsic mechanisms guiding the chemicals towards the most favorable reaction products. However, at this purpose, it is mandatory to use reliable and computationally tractable theoretical methods. In this work, we focus on six Diels-Alder reactions of increasing complexity and perform an extensive benchmark of middle- to low-cost computational approaches to predict the characteristic reactions energy barriers. We found that Density Functional Theory, using the ωB97XD, LC-ωPBE, CAM-B3LYP, M11 and MN12SX functionals, with empirical dispersion corrections coupled to an affordable 6-31G basis set, provides quality results for this class of reactions, at a small computational effort. Such efficient and reliable simulation protocol opens perspectives for hybrid QM/MM molecular dynamics simulations of Diels-Alder reactions including explicit solvation.

Development of the Quantum-Inspired SIBFA Many-Body Polarizable Force Field: Enabling Condensed-Phase Molecular Dynamics Simulations.

We present the extension of the Sum of Interactions Between Fragments Ab initio Computed (SIBFA) many-body polarizable force field to condensed-phase molecular dynamics (MD) simulations. The quantum-inspired SIBFA procedure is grounded on simplified integrals obtained from localized molecular orbital theory and achieves full separability of its intermolecular potential. It embodies long-range multipolar electrostatics (up to quadrupole) coupled to a short-range penetration correction (up to charge-quadrupole), exchange repulsion, many-body polarization, many-body charge transfer/delocalization, exchange dispersion, and dispersion (up to C10). This enables the reproduction of all energy contributions of ab initio symmetry-adapted perturbation theory (SAPT(DFT)) gas-phase reference computations. The SIBFA approach has been integrated within the Tinker-HP massively parallel MD package. To do so, all SIBFA energy gradients have been derived and the approach has been extended to enable periodic boundary conditions simulations using smooth particle mesh Ewald. This novel implementation also notably includes a computationally tractable simplification of the many-body charge transfer/delocalization contribution. As a proof of concept, we perform a first computational experiment defining a water model fitted on a limited set of SAPT(DFT) data. SIBFA is shown to enable a satisfactory reproduction of both gas-phase energetic contributions and condensed-phase properties highlighting the importance of its physically motivated functional form.

Accurate Deep Learning-Aided Density-Free Strategy for Many-Body Dispersion-Corrected Density Functional Theory.

Using a deep neuronal network (DNN) model trained on the large ANI-1 data set of small organic molecules, we propose a transferable density-free many-body dispersion (DNN-MBD) model. The DNN strategy bypasses the explicit Hirshfeld partitioning of the Kohn-Sham electron density required by MBD models to obtain the atom-in-molecules volumes used by the Tkatchenko-Scheffler polarizability rescaling. The resulting DNN-MBD model is trained with minimal basis iterative Stockholder atomic volumes and, coupled to density functional theory (DFT), exhibits comparable (if not greater) accuracy to other approaches based on different partitioning schemes. Implemented in the Tinker-HP package, the DNN-MBD model decreases the overall computational cost compared to MBD models where the explicit density partitioning is performed. Its coupling with the recently introduced Stochastic formulation of the MBD equations (J. Chem. Theory Comput. 2022, 18 (3), 1633-1645) enables large routine dispersion-corrected DFT calculations at preserved accuracy. Furthermore, the DNN electron density-free features extend the MBD model's applicability beyond electronic structure theory within methodologies such as force fields and neural networks.

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.

O(N) Stochastic Evaluation of Many-Body van der Waals Energies in Large Complex Systems.

We propose a new strategy to solve the key equations of the many-body dispersion (MBD) model by Tkatchenko, DiStasio Jr., and Ambrosetti. Our approach overcomes the original O(N3) computational complexity that limits its applicability to large molecular systems within the context of O(N) density functional theory. First, to generate the required frequency-dependent screened polarizabilities, we introduce an efficient solution to the Dyson-like self-consistent screening equations. The scheme reduces the number of variables and, coupled to a direct inversion of the iterative subspace extrapolation, exhibits linear-scaling performances. Second, we apply a stochastic Lanczos trace estimator resolution to the equations evaluating the many-body interaction energy of coupled quantum harmonic oscillators. While scaling linearly, it also enables communication-free pleasingly parallel implementations. As the resulting O(N) stochastic massively parallel MBD approach is found to exhibit minimal memory requirements, it opens up the possibility of computing accurate many-body van der Waals interactions of millions-atoms' complex materials and solvated biosystems with computational times in the range of minutes.