A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics

In drug discovery, molecular dynamics (MD) simulation for protein-ligand binding provides a powerful tool for predicting binding affinities, estimating transport properties, and exploring pocket sites. There has been a long history of improving the efficiency of MD simulations through better numerical methods and, more recently, by utilizing machine learning (ML) methods. Yet, challenges remain, such as accurate modeling of extended-timescale simulations. To address this issue, we propose NeuralMD, the first ML surrogate that can facilitate numerical MD and provide accurate simulations in protein-ligand binding dynamics. We propose a principled approach that incorporates a novel physics-informed multi-grained group symmetric framework. Specifically, we propose (1) the BindingNet model that satisfies group symmetry using vector frames and captures the multi-level protein-ligand interactions, and (2) an augmented neural differential equation solver that learns the trajectory under Newtonian mechanics. For the experiment, we design ten single-trajectory and three multi-trajectory binding simulation tasks. We demonstrate the efficiency and effectiveness of NeuralMD, achieving over 1K$\times$ speedup compared to standard numerical MD simulations. NeuralMD also outperforms all other ML approaches, achieving up to 15$\times$ reduction in reconstruction error and 70% increase in validity. Additionally, we qualitatively illustrate that the oscillations in the predicted trajectories align more closely with ground-truth dynamics than those of other machine-learning methods. We believe NeuralMD paves the foundation for a new research paradigm in simulating protein-ligand dynamics.