Great Restraining Wall in Multidimensional Collective Variable Space

Abstract

Enhanced sampling methods are pivotal for exploring rare events in molecular dynamics (MD), yet face challenges in high-dimensional collective variable (CV) spaces where exhaustive sampling becomes computationally prohibitive. While techniques like metadynamics (MetaD) and path-CV enable targeted free energy surface (FES) reconstruction, they often struggle with confinement stability, hyperparameter sensitivity, and geometric flexibility. This work introduces the Great Restraining Wall (GW) method, a robust framework for efficient FES sampling within predefined CV subspaces, addressing these limitations through a novel kernel density estimation (KDE)-derived restraining potential. GW operates by constructing a bias potential that confines sampling to user defined regions ranging from multidimensional masks to 1D pathways via asymptotically half-harmonic barriers. Unlike MetaD variants requiring iterative bias deposition, GW potential is derived from a cumulative distribution function, ensuring confinement without manual hyperparameter tuning. GW provides a versatile, stable, and efficient framework for targeted FES sampling, particularly beneficial for complex biomolecular systems with intricate CV landscapes. Its integration with existing enhanced sampling protocols opens avenues for studying ligand binding, conformational transitions, and other rare events with unprecedented precision. Future work will explore GW extension to adaptive regions and machine learning-guided CV discovery.