We present a multiscale method for the determination of collective reaction coordinates for macromolecular dynamics based on two recently developed mathematical techniques: diffusion map and the determination of local intrinsic dimensionality of large datasets. Our method accounts for the local variation of molecular configuration space, and the resulting global coordinates are correlated with the time scales of the molecular motion. To illustrate the approach, we present results for two model systems: all-atom alanine dipeptide and coarse-grained src homology 3 protein domain. We provide clear physical interpretation for the emerging coordinates and use them to calculate transition rates. The technique is general enough to be applied to any system for which a Boltzmann-sampled set of molecular configurations is available.
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As in Hummer's work, we also perform Metropolis Monte Carlo on Pi, the probability of being in the ith cell. The elements of R and P are related through detailed balance: Ri + 1, i/Ri, i + 1 = Pi + 1/Pi. While the Bayesian analysis method provides estimates of the free-energy, we use the more finely sampled free-energy directly from our simulation for the evaluation of the Kramers' integrals.
© 2011 American Institute of Physics.
2011
American Institute of Physics
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