Transition-Tempered Metadynamics: Robust, Convergent Metadynamics via On-the-Fly Transition Barrier Estimation

Well-tempered metadynamics has proven to be a practical and efficient adaptive enhanced sampling method for the computational study of biomolecular and materials systems. However, choosing its tunable parameter can be challenging and requires balancing a trade-off between fast escape from local metastable states and fast convergence of an overall free energy estimate. In this article, we present a new smoothly convergent variant of metadynamics, transition-tempered metadynamics, that removes that trade-off and is more robust to changes in its own single tunable parameter, resulting in substantial speed and accuracy improvements. The new method is specifically designed to study state-to-state transitions in which the states of greatest interest are known ahead of time, but transition mechanisms are not. The design is guided by a picture of adaptive enhanced sampling as a means to increase dynamical connectivity of a model's state space until percolation between all points of interest is reached, and it uses the degree of dynamical percolation to automatically tune the convergence rate. We apply the new method to Brownian dynamics on 48 random 1D surfaces, blocked alanine dipeptide in vacuo, and aqueous myoglobin, finding that transition-tempered metadynamics substantially and reproducibly improves upon well-tempered metadynamics in terms of first barrier crossing rate, convergence rate, and robustness to the choice of tuning parameter. Moreover, the trade-off between first barrier crossing rate and convergence rate is eliminated: the new method drives escape from an initial metastable state as fast as metadynamics without tempering, regardless of tuning.