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.

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.

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.

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.

An Efficient Gaussian-Accelerated Molecular Dynamics (GaMD) Multilevel Enhanced Sampling Strategy: Application to Polarizable Force Fields Simulations of Large Biological Systems.

We introduce a novel multilevel enhanced sampling strategy grounded on Gaussian-accelerated Molecular Dynamics (GaMD). First, we propose a GaMD multi-GPUs-accelerated implementation within the Tinker-HP molecular dynamics package. We introduce the new "dual-water" mode and its use with the flexible AMOEBA polarizable force field. By adding harmonic boosts to the water stretching and bonding terms, it accelerates the solvent-solute interactions while enabling speedups, thanks to the use of fast multiple-time step integrators. To further reduce the time-to-solution, we couple GaMD to Umbrella Sampling (US). The GaMD─US/dual-water approach is tested on the 1D Potential of Mean Force (PMF) of the solvated CD2-CD58 system (168 000 atoms), allowing the AMOEBA PMF to converge within 1 kcal/mol of the experimental value. Finally, Adaptive Sampling (AS) is added, enabling AS-GaMD capabilities but also the introduction of the new Adaptive Sampling-US-GaMD (ASUS-GaMD) scheme. The highly parallel ASUS-GaMD setup decreases time to convergence by, respectively, 10 and 20 times, compared to GaMD-US and US. Overall, beside the acceleration of PMF computations, Tinker-HP now allows for the simultaneous use of Adaptive Sampling and GaMD-"dual water" enhanced sampling approaches increasing the applicability of polarizable force fields to large-scale simulations of biological systems.

Interfacial Water Many-Body Effects Drive Structural Dynamics and Allosteric Interactions in SARS-CoV-2 Main Protease Dimerization Interface.

Following our previous work ( Chem. Sci. 2021, 12, 4889-4907), we study the structural dynamics of the SARS-CoV-2 Main Protease dimerization interface (apo dimer) by means of microsecond adaptive sampling molecular dynamics simulations (50 µs) using the AMOEBA polarizable force field (PFF). This interface is structured by a complex H-bond network that is stable only at physiological pH. Structural correlations analysis between its residues and the catalytic site confirms the presence of a buried allosteric site. However, noticeable differences in allosteric connectivity are observed between PFFs and non-PFFs. Interfacial polarizable water molecules are shown to appear at the heart of this discrepancy because they are connected to the global interface H-bond network and able to adapt their dipole moment (and dynamics) to their diverse local physicochemical microenvironments. The water-interface many-body interactions appear to drive the interface volume fluctuations and to therefore mediate the allosteric interactions with the catalytic cavity.

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.

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.

Tinker-HP: Accelerating Molecular Dynamics Simulations of Large Complex Systems with Advanced Point Dipole Polarizable Force Fields Using GPUs and Multi-GPU Systems.

We present the extension of the Tinker-HP package (Lagardère, Chem. Sci. 2018, 9, 956-972) to the use of Graphics Processing Unit (GPU) cards to accelerate molecular dynamics simulations using polarizable many-body force fields. The new high-performance module allows for an efficient use of single- and multiple-GPU architectures ranging from research laboratories to modern supercomputer centers. After detailing an analysis of our general scalable strategy that relies on OpenACC and CUDA, we discuss the various capabilities of the package. Among them, the multiprecision possibilities of the code are discussed. If an efficient double precision implementation is provided to preserve the possibility of fast reference computations, we show that a lower precision arithmetic is preferred providing a similar accuracy for molecular dynamics while exhibiting superior performances. As Tinker-HP is mainly dedicated to accelerate simulations using new generation point dipole polarizable force field, we focus our study on the implementation of the AMOEBA model. Testing various NVIDIA platforms including 2080Ti, 3090, V100, and A100 cards, we provide illustrative benchmarks of the code for single- and multicards simulations on large biosystems encompassing up to millions of atoms. The new code strongly reduces time to solution and offers the best performances to date obtained using the AMOEBA polarizable force field. Perspectives toward the strong-scaling performance of our multinode massive parallelization strategy, unsupervised adaptive sampling and large scale applicability of the Tinker-HP code in biophysics are discussed. The present software has been released in phase advance on GitHub in link with the High Performance Computing community COVID-19 research efforts and is free for Academics (see https://github.com/TinkerTools/tinker-hp).

Tinker-HP : Accelerating Molecular Dynamics Simulations of Large Complex Systems with Advanced Point Dipole Polarizable Force Fields using GPUs and Multi-GPUs systems.

We present the extension of the Tinker-HP package (Lagard\`ere et al., Chem. Sci., 2018,9, 956-972) to the use of Graphics Processing Unit (GPU) cards to accelerate molecular dynamics simulations using polarizable many-body force fields. The new high-performance module allows for an efficient use of single- and multi-GPU architectures ranging from research laboratories to modern supercomputer centers. After detailing an analysis of our general scalable strategy that relies on OpenACC and CUDA, we discuss the various capabilities of the package. Among them, the multi-precision possibilities of the code are discussed. If an efficient double precision implementation is provided to preserve the possibility of fast reference computations, we show that a lower precision arithmetic is preferred providing a similar accuracy for molecular dynamics while exhibiting superior performances. As Tinker-HP is mainly dedicated to accelerate simulations using new generation point dipole polarizable force field, we focus our study on the implementation of the AMOEBA model. Testing various NVIDIA platforms including 2080Ti, 3090, V100 and A100 cards, we provide illustrative benchmarks of the code for single- and multi-cards simulations on large biosystems encompassing up to millions of atoms. The new code strongly reduces time to solution and offers the best performances to date obtained using the AMOEBA polarizable force field. Perspectives toward the strong-scaling performance of our multi-node massive parallelization strategy, unsupervised adaptive sampling and large scale applicability of the Tinker-HP code in biophysics are discussed. The present software has been released in phase advance on GitHub in link with the High Performance Computing community COVID-19 research efforts and is free for Academics (see https://github.com/TinkerTools/tinker-hp).

Reduced-order modeling of hemodynamics across macroscopic through mesoscopic circulation scales.

We propose a hemodynamic reduced-order model bridging macroscopic and mesoscopic blood flow circulation scales from arteries to capillaries. In silico tree-like vascular geometries, mathematically described by graphs, are synthetically generated by means of stochastic growth algorithms constrained by statistical morphological and topological principles. Scale-specific pruning gradation of the tree is then proposed in order to fit computational budget requirement. Different compliant structural models with respect to pressure loads are used depending on vessel walls thicknesses and structures, which vary considerably from macroscopic to mesoscopic circulation scales. Nonlinear rheological properties of blood are also included, and microcirculation network responses are computed for different rheologies. Numerical results are in very good agreement with available experimental measurements. The computational model captures the dynamic transition between large- to small-scale flow pulsatility speeds and magnitudes and wall shear stresses, which have wide-ranging physiological influences.