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Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations

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Stelzl,  Lukas S.
Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max Planck Society;
Faculty of Biology, Johannes Gutenberg University Mainz, 55128 Mainz, Germany;
KOMET 1, Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany;
Institute of Molecular Biology, 55128 Mainz, Germany;

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Hummer,  Gerhard
Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max Planck Society;
Institute for Biophysics, Goethe University Frankfurt, 60438 Frankfurt am Main, Germany;

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Cossio,  Pilar
Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia, 050010 Medellín, Colombia;
Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max Planck Society;
Center for Computational Mathematics, Flatiron Institute, 10010 New York, United States;
Center for Computational Biology, Flatiron Institute, 10010 New York, United States;

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Citation

Palacio-Rodriguez, K., Vroylandt, H., Stelzl, L. S., Pietrucci, F., Hummer, G., & Cossio, P. (2022). Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations. The Journal of Physical Chemistry Letters, 13, 7490-7496. doi:10.1021/acs.jpclett.2c01807.


Cite as: https://hdl.handle.net/21.11116/0000-000A-D50E-7
Abstract
Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.