Replica state exchange metadynamics for improving the convergence of free energy estimates

Metadynamics (MTD) is a powerful enhanced sampling method for systems with rugged energy landscapes. It constructs a bias potential in a predefined collective variable (CV) space to overcome barriers between metastable states. In bias-exchange MTD (BE-MTD), multiple replicas approximate the CV space by exchanging bias potentials (replica conditions) with the Metropolis-Hastings (MH) algorithm. We demonstrate that the replica-exchange rates and the convergence of free energy estimates of BE-MTD are improved by introducing the infinite swapping (IS) or the Suwa-Todo (ST) algorithms. Conceptually, IS and ST perform transitions in a replica state space rather than exchanges in a replica condition space. To emphasize this, the proposed scheme is called the replica state exchange MTD (RSE-MTD). Benchmarks were performed with alanine polypeptides in vacuum and water. For the systems tested in this work, there is no significant performance difference between IS and ST.