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Molecular dynamics (MD) simulations are essential for elucidating biomolecular function, yet the computational cost of all-atom models often limits their reach. Machine-learned coarse-grained (MLCG) models offer a solution by simplifying the representation while maintaining near-atomistic accuracy. However, the training of MLCG models currently requires vast amounts of force-labeled sample conformations from reference atomistic MD. Here, we overcome this limitation by unifying the training of MLCG models with the principles of generative diffusion models. We demonstrate that accurate high-dimensional distributions of molecular ensembles can be recovered by integrating traditional force-matching with denoising objectives. This framework enables the construction of physically consistent and stable force fields while reducing atomistic data requirements by up to two orders of magnitude. Validated across diverse protein folds and scales, our work establishes a bridge between molecular dynamics simulation and modern generative learning, substantially lowering the computational cost of constructing accurate MLCG models and broadening their applicability to large biomolecular systems. 

Graph Neural Networks (GNNs) are routinely used in molecular physics, social sciences, and economics to model many-body interactions in graph-like systems. However, GNNs are inherently local and can suffer from information flow bottlenecks. This is particularly problematic when modeling large molecular systems, where dispersion forces and local electric field variations drive collective structural changes. We introduce RANGE, a model-agnostic framework that employs an attention-based aggregation-broadcast mechanism that significantly reduces oversquashing effects, and achieves remarkable accuracy in capturing long-range interactions with linear scaling. Notably, RANGE integrates attention with positional encodings and regularization to dynamically expand virtual representations in virtual-node message-passing implementations. Across multiple state-of-the-art baselines, RANGE consistently restores long-range information, enabling the models to correctly predict electrostatic and dispersion-driven behavior even in out-of-distribution extrapolation tasks, where other unmodified baselines fail. Compared with other long-range paradigms, RANGE achieves the highest accuracy while requiring significantly less computational overhead, and it enables stable and scalable molecular dynamic simulations. RANGE offers accurate and efficient modeling of long-range interactions for simulating large molecular systems. 

Machine learned potentials based on artificial neural networks are becoming a popular tool to define an effective energy model for complex systems, either incorporating electronic structure effects at the atomistic resolution, or effectively renormalizing part of the atomistic degrees of freedom at a coarse-grained resolution. One main criticism regarding neural network potentials is that their inferred energy is less interpretable than in traditional approaches, which use simpler and more transparent functional forms. Here we address this problem by extending tools recently proposed in the nascent field of explainable artificial intelligence to coarse-grained potentials based on graph neural networks. With these tools, neural network potentials can be practically decomposed into n-body interactions, providing a human understandable interpretation without compromising predictive power. We demonstrate the approach on three different coarse-grained systems including two fluids (methane and water) and the protein NTL9. The obtained interpretations suggest that well-trained neural network potentials learn physical interactions, which are consistent with fundamental principles. 

Hydrogen bonded electrolytes that exhibit accelerated proton transport via sequential reactive hops have drawn interest for their promise in clean energy applications. Molecular dynamics simulations of these electrolytes offer the opportunity to uncover microscopic mechanistic details that could be used to design and tune the properties of candidate electrolyte technologies. However, accurately modeling the proton transfer reactions and transport properties that give rise to high charge conductivites in these electrolytes proves computationally challenging because of the need to perform lengthy condensed phase simulations, treating both the electronic and nuclear degrees of freedom quantum mechanically. In this paper, we demonstrate that such a modeling task can be efficiently achieved with the use of density functional theory (DFT)-trained machine learning potentials (MLP) to accelerate path integral molecular dynamics (PIMD) simulations. We highlight the practical utility of this approach by using it to benchmark how closely PIMD simulations employing different DFT exchange–correlation functionals reproduce the composition-dependent densities, diffusion coefficients, and electrical conductivities of mixtures consisting of imidazole and levulinic acid. Even with the speedup afforded by our MLPs, PIMD simulations remain quite expensive. In order to render PIMD more computationally tractable, we introduce and benchmark the accuracy of a ring polymer contraction approach that leverages a computationally efficient short-range MLP to accelerate our PIMD simulations by an additional factor of four. 

Coarse-grained (CG) molecular dynamics simulations extend the length and time scales of atomistic simulations by replacing groups of correlated atoms with CG beads. Machine-learned coarse-graining (MLCG) has recently emerged as a promising approach to construct highly accurate force fields for CG molecular dynamics. However, the calibration of MLCG force fields typically hinges on force matching, which demands extensive reference atomistic trajectories with corresponding force labels. In practice, atomistic forces are often not recorded, making traditional force matching infeasible on pre-existing datasets. Recently, noise-based kernels have been introduced to adapt force matching to the low-data regime, including situations in which reference atomistic forces are not present. While this approach produces force fields that recapitulate slow collective motion, it introduces significant local distortions due to the corrupting effects of the noise-based kernel. In this work, we introduce more general kernels based on normalizing flows that substantially reduce these local distortions while preserving global conformational accuracy. We demonstrate our method on small proteins, showing that flow-based kernels can generate high-quality CG forces solely from configurational samples. 

The contribution of nuclear quantum effects (NQEs) to the properties of various hydrogen-bound systems, including biomolecules, is increasingly recognized. Despite the development of many acceleration techniques, the computational overhead of incorporating NQEs in complex systems is sizable, particularly at low temperatures. In this work, we leverage deep learning and multiscale coarse-graining techniques to mitigate the computational burden of path integral molecular dynamics (PIMD). In particular, we employ a machine-learned potential to accurately represent corrections to classical potentials, thereby significantly reducing the computational cost of simulating NQEs. We validate our approach using four distinct systems: Morse potential, Zundel cation, single water molecule, and bulk water. Our framework allows us to accurately compute position-dependent static properties, as demonstrated by the excellent agreement obtained between the machine-learned potential and computationally intensive PIMD calculations, even in the presence of strong NQEs. This approach opens the way to the development of transferable machine-learned potentials capable of accurately reproducing NQEs in a wide range of molecular systems. 

Coarse-grained models allow computational investigation of biomolecular processes occurring on long time and length scales, intractable with atomistic simulation. Traditionally, many coarse-grained models rely mostly on pairwise interaction potentials. However, the decimation of degrees of freedom should, in principle, lead to a complex many-body effective interaction potential. In this work, we use experimental data on mutant stability to parametrize coarse-grained models for two proteins with and without many-body terms. We demonstrate that many-body terms are necessary to reproduce quantitatively the effects of point mutations on protein stability, particularly to implicitly take into account the effect of the solvent. 

Abstract A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.