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Simulations with an adaptive time-dependent bias, such as metadynamics,enable an efficient exploration of the conformational space of a system.However, the dynamic information of the system is altered by the bias. Withinfrequent metadynamics it is possible to recover the transition rate ofcrossing a barrier, if the collective variables are ideal and there is no biasdeposition near the transition state. Unfortunately, for simulations of complexmolecules, these conditions are not always fulfilled. To overcome theselimitations, and inspired by single-molecule force spectroscopy, we developed amethod based on Kramers' theory for calculating the barrier-crossing rate whena time-dependent bias is added to the system. We assess the quality of the biasparameter by measuring how efficiently the bias accelerates the transitionscompared to ideal behavior. We present approximate analytical expressions ofthe survival probability that accurately reproduce the barrier-crossing timestatistics, and enable the extraction of the unbiased transition rate even forchallenging cases, where previous methods fail.

Transition rates, survival probabilities, and quality of bias from time-dependent biased simulations