An adaptive weighted ensemble procedure for efficient computation of free energies and first passage rates

By Divesh Bhatt and Ivet Bahar.

Published in Journal of Chemical Physics 137(10):104101 on September 14, 2012. PMID: 22979844. PMCID: PMC3460967. Link to publication page.

Core Facility: Computational Modeling

Figure 1. A schematic of division of the relevant configuration space into smaller regions. The two known crystal structures are labeled A and B, with the corresponding regions depicted in yellow. Any point inside region i is closer to the structure defining region i (represented by a solid circle) than to the structure defining any other region. Transition probabilities between two such regions are explicitly labeled. Also shown are the bins within one of the regions, and the minimum flux boundary delimiting the two states is shown by the red line. In this paper, these regions are based on Voronoi tessellation.


We introduce an adaptive weighted-ensemble procedure (aWEP) for efficient and accurate evaluation of first-passage rates between states for two-state systems. The basic idea that distinguishes aWEP from conventional weighted-ensemble (WE) methodology is the division of the configuration space into smaller regions and equilibration of the trajectories within each region upon adaptive partitioning of the regions themselves into small grids. The equilibrated conditional∕transition probabilities between each pair of regions lead to the determination of populations of the regions and the first-passage times between regions, which in turn are combined to evaluate the first passage times for the forward and backward transitions between the two states. The application of the procedure to a non-trivial coarse-grained model of a 70-residue calcium binding domain of calmodulin is shown to efficiently yield information on the equilibrium probabilities of the two states as well as their first passage times. Notably, the new procedure is significantly more efficient than the canonical implementation of the WE procedure, and this improvement becomes even more significant at low temperatures.


Figure 2. Structures used to construct Voronoi regions along a putative transition pathway between two states of the calcium binding domain of calmodulin.

Figure 5. Transition probabilities between pairs of regions.