Weighted Histogram Analysis Method (WHAM)

This is an fast implementation of the weighted histogram analysis method written in Rust. It allows the calculation of multidimensional free energy profiles from umbrella sampling simulations. For more details on the method, I suggest Roux, B. (1995). The calculation of the potential of mena force using computer simulations, CPC, 91(1), 275-282.

Features

• Fast, especially for small systems
• Multidimensional
• Error analysis
• Unit tested

Usage

wham has a convenient command line interface. You can see all options with wham -h:

To run the two dimensional example (simulation of dialanine phi and psi angle): ```bash wham --max 3.14,3.14 --min -3.14,-3.14 -T 300 --bins 100,100 --cyclic -f example/2d/metadata.dat

Supplied WHAM options: Metadata=example/2d/metadata.dat, histmin=[-3.14, -3.14], histmax=[3.14, 3.14], bins=[100, 100] verbose=false, tolerance=0.000001, iterations=100000, temperature=300, cyclic=true Reading input files. 625 windows, 624262 datapoints Iteration 10: dF=0.389367172324539 Iteration 20: dF=0.21450559607810152 (...) Iteration 620: dF=0.0000005800554892309461 Iteration 630: dF=0.00000047424278621817084 Finished. Dumping final PMF (... pmf dump ...)

``` After convergence, final bias offsets (F) and the free energy will be dumped to stdout and the output file is written.

The output file contains the free energy and probability for each bin. Probabilities are normalized to sum to P=1.0 and the smallest free energy is set to 0 (with other free energies based on that). ```

coord1 coord2 Free Energy +/- Probability +/-

-3.108600 -3.108600 10.331716 0.000000 0.000095 0.000000 -3.045800 -3.108600 8.893231 0.000000 0.000170 0.000000 -2.983000 -3.108600 7.372765 0.000000 0.000312 0.000000 -2.920200 -3.108600 6.207354 0.000000 0.000498 0.000000 -2.857400 -3.108600 4.915298 0.000000 0.000836 0.000000 -2.794600 -3.108600 3.644738 0.000000 0.001392 0.000000 -2.731800 -3.108600 3.021743 0.000000 0.001787 0.000000 -2.669000 -3.108600 2.827463 0.000000 0.001932 0.000000 -2.606200 -3.108600 2.647531 0.000000 0.002076 0.000000 (...) ```

Error analysis

WHAM can perform error analysis using the bayesian bootstrapping method. Every simulation window is assumed to be an individual set of data point. By calculating probabilities N times with randomly assigned weights for each window, one can estimate the error as standard deviation between the N bootstrapping runs. For more details see van der Spoel, D. et al. (2010). g_wham—A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates, JCTC, 6(12), 3713-3720.

To perform bayesian bootstrapping in WHAM, use the -bt <RUNS> flag to perform individual bootstrapping runs. The error estimates of bin probabilities and free energy will be given as separate column (+/-) in the output file. If no error analysis is performed, these columns are set to 0.0.

Examples

The example folder contains input and output files for two simple test systems:

• 1d: Phi torsion angle of dialanine in vaccum
• 2d: Phi and psi torsion angles of the same system

TODO

• Multithreading (?)
• Autocorrelation
• Replica exchange

License

WHAM is licensed under the GPL-3.0 license. Please read the LICENSE file in this repository for more information.

Parts of this work, especially some perfomance optimizations and the I/O format, are inspired by the implementation of A. Grossfield (A. Grossfield, "WHAM: the weighted histogram analysis method", http://membrane.urmc.rochester.edu/content/wham).