Unbiased Enhanced Sampling in Molecular Dynamics via Simultaneously Accelerating Diffusion in Multiple Low-Dimensional Collective Variable Spaces

Molecular dynamics (MD) simulations face significant challenges in capturing rare events hindered by high energy barriers. While traditional enhanced sampling methods─whether biased or unbiased─typically rely on collective variables (CVs) for guidance, identifying optimal CVs for complex systems remains a formidable task. Here we propose a novel unbiased enhanced sampling methodology that circumvents the CV-related challenge through an iterative approach: projecting unbiased sampling data onto multiple low-dimensional CV spaces to calculate their sampling density distributions, integrating these distributions to guide subsequent sampling, and repeating the cycle. Conceptualizing MD-based conformational sampling as diffusion in high-dimensional space implies that our methodology accelerates diffusive exploration in all relevant CV spaces simultaneously. This method overcomes the exponential efficiency decay in high-dimensional CV spaces while offering several key advantages over existing methods: (1) it applies all CV guidance to the same unbiased ensemble, eliminating the need for replica exchange; (2) it accelerates diffusion in multiple CV spaces simultaneously, rather than being confined to one-dimensional “tube”-like pathway-based CVs, thus making it applicable to general multibasin systems. In addition, the method’s ability to dynamically adjust CV spaces during sampling, along with its provision of well-classified, high-quality unbiased ensembles, greatly facilitates on-the-fly CV generation. In summary, this method provides a new paradigm for addressing CV-related challenges by leveraging the synergistic interplay between unbiased sampling and CV algorithms: On one hand, unbiased sampling enables simultaneous utilization of multiple CVs and enhances the effectiveness of CV generation methods while preserving the primary advantage─low CV dependence (yielding accurate results even with imperfect CVs). On the other hand, the optimized CV guidance effectively resolves the CV-related efficiency problems of unbiased sampling. As an additional benefit, the method provides weighted trajectory ensembles that retain complete system information. Validations through high-dimensional/multibasin model potentials and a coarse-grained protein system demonstrate the method’s capability to accurately extract both thermodynamic properties (e.g., free energy landscapes) and kinetic properties (e.g., transition rates) with remarkable sampling efficiency.