ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Multiple state transition path sampling

Date: 08.01.2009
Place: Amsterdam Center for Multiscale Modeling - Symposium, Amsterdam, The Netherlands

Jutta Rogal

When investigating the dynamical properties of complex systems we are often challenged by the existence of several stable or metastable states that are separated by large free energy barriers (e.g. in protein folding). The resulting separation of time scales between the short time dynamics within each of the stable states and the long time dynamics describing the rare transitions in-between the stable states makes it unfeasible to study such a system with regular molecular dynamics simulations. One possibility to examine the dynamical behaviour of these systems on an extended time scale is to concentrate on the so-called rare events only and describe the time evolution within a Markovian state model (MSM). An essential ingredient to a MSM are the rate constants resp. transition probabilities that characterise the transitions between the different stable states. Here transition path sampling (TPS) and transition interface sampling (TIS) can e.g. be used to determine rate constants. However if in addition to the two defined stable states there are several intermediate states these methods become inefficient in sampling the path space since trajectories simply get stuck within the intermediate states. To overcome this problem we have extended the TPS method to include not only pathways between two defined stable states in the path ensemble but we can now sample pathways that connect any two stable or intermediate states within our system in one simulation. Combining this multiple state TPS with the idea of TIS we directly obtain an expression for the rate constants of all possible transitions between all of the stable or metastable states in the system. For a system with $N$ different states the number of required simulations is reduced from N (N-1) regular TIS simulations to N “partial” TIS simulations and only 1 multiple state TPS simulation.

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