College of Engineering
University of Wisconsin - Madison

WEB Dynamics on the Web

A new method, weighted-ensemble Brownian (WEB) dynamics, is being used by Dr. Kim's research group at the Rheology Research Center for the simulation of protein-association reactions and other events whose frequencies of outcomes are constricted by free energy barriers. The method features a weighted ensemble of trajectories in configuration space with energy levels dictating the proper correspondence between "particles" and probability. Instead of waiting a very long time for an unlikely event to occur, the probability packets are split, and small packets of probability are allowed to diffuse almost immediately into regions of configuration space that are less likely to be sampled. Because the method is essentially a variant of standard Brownian dynamics algorithms, it is anticipated that weighted-ensemble Brownian dynamics can be used to enhance the efficiency of the stochastic simulation of polymers as well.

A copy of our transparencies presented at AIChE 1996 annual meeting at Chicago: IRIS. Showcase or PostScript format.

Professor Kim acknowledges the support of the National Science Foundation and of the Office of Naval Research to develop these rheological animations.

Video Clips

Huber, G. A. and S. Kim. 1996. Weighted-Ensemble Brownian Dynamics Simulations for Protein Association Reactions. Biophysical Journal 70:97-110.

Click on image to play MPEG clip.

A point in configuration space with 2-D energy surface.
Stochastic simulation shows very low probability of crossing the energy barrier.
Many trajectories must be run to obtain accurate statistics to estimate reaction rate constant.

Embarrasingly parallel algorithm helps, but not much.
We see a few particles at higher energy levels, but crossing probability is still very low.

In the WE method, the space is subdivided into bins. The particles in each bin are split or merged to keep an equal number in each bin.
Here we have 10 bins. Now particles carry different weights (low/high), and we get good statistics on crossing the barrier.

The stochastic simulation can be merged with the solution of the associated Fokker-Planck equation.
We see particles emerge under the blanket representing the probability density function.

The Northrup-Erickson model (PNAS, 89, 3338, 1992). The little spheres on each molecule must align to react.
Stochastic simulation shows very few eventual reactions.

Northrup-Erickson model with WE method merged with numerical solutions of FPE. One reactant is shrunked for clarity.
Many reactions are observed during stochastic simulation.

Last Modified: Tuesday, 10-Jun-2008 12:57:57 CDT
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Address comments to rheology@engr.wisc.edu

	A point in configuration space with 2-D energy surface. Stochastic simulation shows very low probability of crossing the energy barrier. Many trajectories must be run to obtain accurate statistics to estimate reaction rate constant.
	Embarrasingly parallel algorithm helps, but not much. We see a few particles at higher energy levels, but crossing probability is still very low.
	In the WE method, the space is subdivided into bins. The particles in each bin are split or merged to keep an equal number in each bin. Here we have 10 bins. Now particles carry different weights (low/high), and we get good statistics on crossing the barrier.
	The stochastic simulation can be merged with the solution of the associated Fokker-Planck equation. We see particles emerge under the blanket representing the probability density function.
	The Northrup-Erickson model (PNAS, 89, 3338, 1992). The little spheres on each molecule must align to react. Stochastic simulation shows very few eventual reactions.
	Northrup-Erickson model with WE method merged with numerical solutions of FPE. One reactant is shrunked for clarity. Many reactions are observed during stochastic simulation.