Conformational changes in proteins (e.g. folding) can exhibit a rough free energy landscape involving multiple (meta)stable states. If there is a separation of time scales between the residence time in these stable states and the molecular crossing time, transitions between stable states can be considered rare events. Markovian state models can describe the long time kinetics of such systems, provided one has access to the hopping rates. For the unbiased study of the dynamics, rate constants, and mechanism of such rare events, transition path sampling has proven to be an effective method. However, in case there are multiple states, only one pair of states can be handled simultaneously. In this work, we present an efficient extension of the path ensemble that includes trajectories connecting two arbitrary stable states within the system. Combining this approach with transition interface sampling we directly obtain an expression for the rate constants of all possible transitions. We show the efficiency of this approach for several model systems. We find that the path switching behavior is the key ingredient. If some of the transitions become much more likely than others, we can use a biasing approach. We show that such a biasing method is effective in some cases, but fails in other.
Authors : Jutta Rogal and Peter Bolhuis
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