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

Magnus Petersen, Roberto Covino

Keywords: MD, Rare Event Sampling, PINN, Neural Representation

TL;DR: A PINN approach that discovers minimum energy transition paths between protein conformations by optimizing a path representation against force fields.

Abstract: 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. Our approach reproduces the same conformational change captured in a landmark millisecond-scale explicit-solvent MD simulation (Shaw et al., 2010), while achieving remarkable computational efficiency, requiring only $\sim480,000$ force field evaluations compared to the approximately 412 billion evaluations in the original study. This represents a reduction of nearly six orders of magnitude, allowing us to generate the transition pathway in just 15 minutes on a standard GPU rather than weeks on specialized hardware.

Submission Number: 12