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.

Cryo-em images are intrinsically low dimensional

Simulation-based inference provides a powerful framework for cryo-electron microscopy, employing neural networks in methods like CryoSBI to infer biomolecular conformations via learned latent representations. This latent space represents a rich opportunity, encoding valuable information about the physical system and the inference process. Harnessing this potential hinges on understanding the underlying geometric structure of these representations. We investigate this structure by applying manifold learning techniques to CryoSBI representations of hemagglutinin (simulated and experimental). We reveal that these high-dimensional data inherently populate low-dimensional, smooth manifolds, with simulated data effectively covering the experimental counterpart. By characterizing the manifold's geometry using Diffusion Maps and identifying its principal axes of variation via coordinate interpretation methods, we establish a direct link between the latent structure and key physical parameters. Discovering this intrinsic low-dimensionality and interpretable geometric organization not only validates the CryoSBI approach but enables us to learn more from the data structure and provides opportunities for improving future inference strategies by exploiting this revealed manifold geometry.