Weighted Ensemble¶
Weighted ensemble (WE) is an enhanced sampling method for molecular dynamics that accelerates the observation of rare events -- such as protein folding or ligand binding -- without biasing the dynamics.
How It Works¶
Instead of running a single long trajectory, WE maintains an ensemble of short simulations (called walkers) that are periodically pruned and replicated based on their progress toward a target state.
Each iteration of the WE algorithm proceeds in three stages:
graph LR
S["Simulate"] --> B["Bin & Recycle"] --> R["Resample"]
R -->|next iteration| S1. Simulate¶
Each walker runs a short MD segment (e.g., 10 ps) starting from its current restart file. At the end of the segment, a progress coordinate (pcoord) is computed -- typically RMSD to a reference structure -- that measures how close the walker is to the target state.
2. Bin and Recycle¶
Walkers are sorted into bins along the progress coordinate. Walkers that reach the target state (e.g., RMSD < 1.0 A) are recycled: their statistical weight is recorded and they are reset to a basis (starting) state. This allows the ensemble to continuously generate new transition events.
3. Resample¶
Within each bin, walkers are split (replicated) or merged (combined) to maintain a target number of walkers per bin. Splitting focuses computational effort on under-sampled regions of progress coordinate space, while merging avoids wasting resources on over-represented regions.
Important
Resampling preserves the statistical weights of walkers so that ensemble averages remain unbiased. This is a key advantage of WE over other enhanced sampling methods.
Key Concepts¶
Walker : A single simulation trajectory, characterized by its statistical weight, progress coordinate, and restart file.
Progress Coordinate (pcoord) : A low-dimensional measure of progress toward the target state. Common choices include RMSD, fraction of native contacts, or distance to a binding site.
Bin : A partition of progress coordinate space. Walkers within the same bin compete for computational resources during resampling.
Basis State : An initial (typically unfolded or unbound) configuration from which walkers start or are recycled to.
Target State : The desired end state (e.g., folded protein). Walkers that reach the target state are recycled.
Algorithms in DeepDriveWE¶
DeepDriveWE provides several pluggable components:
| Component | Options |
|---|---|
| Binners | RectilinearBinner, MultiRectilinearBinner |
| Recyclers | LowRecycler, HighRecycler |
| Resamplers | HuberKimResampler, SplitLowResampler, SplitHighResampler, LOFLowResampler |
The Huber-Kim resampler is the default and implements the algorithm described in Huber & Kim (1996), which maintains a fixed number of walkers per bin by balancing split and merge operations.
Further Reading¶
- Zwier, M. C. et al. "WESTPA: An Interoperable, Highly Scalable Software Package for Weighted Ensemble Simulation and Analysis." J. Chem. Theory Comput. 2015, 11 (2), 800--809.
- Zuckerman, D. M. & Chong, L. T. "Weighted Ensemble Simulation: Review of Methodology, Applications, and Software." Annu. Rev. Biophys. (2017).
- Leung, J. M. G. et al. "Unsupervised Learning of Progress Coordinates during Weighted Ensemble Simulations: Application to NTL9 Protein Folding." J. Chem. Theory Comput. 2025, 21 (7), 3691--3699.