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 mean force using computer simulations, CPC, 91(1), 275-282.

Features

• Fast, especially for small systems
• Multithreaded (automatically runs on all available cores)
• Multidimensional (any number of collective variables are possible)
• Autocorrelation to remove correlated samples
• Error analysis via bootstrapping
• Unit tested

Installation

Installation from source via cargo: ```bash

cargo installation

curl -sSf https://static.rust-lang.org/rustup.sh | sh

cargo install wham ```

Usage

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

``` wham 1.1.0 D. Bauer bauer@cbs.tu-darmstadt.de wham is a fast implementation of the weighted histogram analysis method (WHAM) written in Rust. It currently supports potential of mean force (PMF) calculations in multiple dimensions at constant temperature.

Metadata file format: /path/to/timeseriesfile1 x1 x2 xN fc1 fc2 fcN /path/to/timeseriesfile2 x1 x2 xN fc1 fc2 fcN /path/to/timeseriesfile3 x1 x2 xN fc1 fc2 fcN The first column is a path to a timeseries file _relative to the metadata file (see below). This is followed by the position of the umbrella potential x in N dimensions and the force constant fc in each dimension. Lines starting with a

are treated as comments and will not be parsed.

Timeseries file format: time x1 x2 xN time x1 x2 xN time x1 x2 x_N The first column will be ignored and is followed by N reaction coordinates x.

Shipped under the GPLv3 license.

USAGE: wham [FLAGS] [OPTIONS] --bins --max --file --min --temperature

FLAGS: -c, --cyclic For periodic reaction coordinates. If this is set, the first and last coordinate bin in each dimension are treated as neighbors for the bias calculation. -h, --help Prints help information -g, --uncorr Estimates statistical inefficiency of each timeseries via autocorrelation and removes correlated samples (default is off). -V, --version Prints version information -v, --verbose Enables verbose output.

OPTIONS: -b, --bins Number of histogram bins (comma separated). --bt Number of bayesian bootstrapping runs for error analysis by assigning random weights (defaults to 0). --seed Random seed for bootstrapping runs. --convdt Performs WHAM for slices with the given delta in time and returns an output file for each slice. THis is useful to check the result for convergence. Example: with --convdt 100 and a timeseries ranging from 0-300, free energy surfaces for slices 0-100, 0-200 and 0-300 will be given returned. --end Skip rows in timeseries with an index larger than this value (defaults to 1e+20) -i, --iterations Stop WHAM after this many iterations without convergence (defaults to 100,000). --max Histogram maxima (comma separated). Also accepts "pi". -f, --file Path to the metadata file. --min Histogram minima (comma separated for multiple dimensions). Also accepts "pi". -o, --output

Free energy output file (defaults to wham.out). --start Skip rows in timeseries with an index smaller than this value (defaults to 0) -T, --temperature WHAM temperature in Kelvin. -t, --tolerance Abortion criteria for WHAM calculation. WHAM stops if abs(Fnew - Fold) < tolerance (defaults to 0.000001). ```

Examples

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

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

The command below will run the two dimensional example (simulation of dialanine phi and psi angle) and calculate the free energy based on the two collective variables in the range of -3.14 to 3.14, with 100 bins in each dimension and periodic collective variables:

```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 points. 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 standard error (SE) in a separate column (+/-) in the output file. If no error analysis is performed, these columns are set to 0.0.

Autocorrelation analysis

With the --uncorr flag, WHAM calculates the autocorrelation time tau for all timeseries and all collective variables. Timeseries are then filtered based on their highest autocorrelation time to remove correlated samples from the dataset. This reduces the number of data points but can improve the accuracy of the result.

For filtering, the statistical inefficiency g is calculated: g = 1 + 2*tau, and only every gth element of the timeseries is used for unbiasing. A more detailed description of the method can be found in Chodera, J.D. et al. (2007). Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations, JCTC 3(1):26-41

License & Citing

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

There's no publication for this WHAM implementation. However, there is a citeabe DOI. If you use this software for your work, please consider citing it: Bauer, D., WHAM - An efficient weighted histogram analysis implementation written in Rust, Zenodo. https://doi.org/10.5281/zenodo.1488597

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