PINN-MEP: Continuous Neural Representations for Minimum-Energy Path Discovery in Molecular Systems

Characterizing conformational transitions in physical systems remains a fundamental challenge in the computational sciences. Traditional sampling methods like molecular dynamics (MD) or MCMC often struggle with the high-dimensional nature of molecular systems and the high energy barriers of transitions between stable states. While these transitions are rare events in simulation timescales, they often represent the most biologically significant processes - for example, the conformational change of an ion channel protein from its closed to open state, which controls cellular ion flow and is crucial for neural signaling. Such transitions in real systems may take milliseconds to seconds but could require months or years of continuous simulation to observe even once. We present a method that reformulates transition path generation as a continuous optimization problem solved through physics-informed neural networks (PINNs) inspired by string methods for minimum-energy path (MEP) generation. By representing transition paths as implicit neural functions and leveraging automatic differentiation with differentiable molecular dynamics force fields, our method enables the efficient discovery of physically realistic transition pathways without requiring expensive path sampling. We demonstrate our method's effectiveness on two proteins, including an explicitly hydrated bovine pancreatic trypsin inhibitor (BPTI) system with over 8,300 atoms.