Analyze a 1-dimensional PMF from umbrella sampling

Erika McCarthy¹, Şölen Ekesan¹, and Darrin M. York¹

¹Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA

Learning objectives

• Analyze umbrella sampling for a 1-dimenional reaction using NDFES to generate a PMF

Relevant literature

• Catalytic mechanism and pH dependence of a methyltransferase ribozyme (MTR1) from computational enzymology

• Surface-Accelerated String Method for Locating Minimum Free Energy Paths

• Extension of the Variational Free Energy Profile and Multistate Bennett Acceptance Ratio Methods for High-Dimensional Potential of Mean Force Profile Analysis

Generating the PMF

Once the simulations are completed, take a look at the analyze_1.sh

#!/bin/bash

mkdir analysis
mkdir analysis/dumpaves

cd analysis

for i in $(seq 1 32); do

  base=$(printf "img%02i" ${i})
  ndfes-PrepareAmberData.py -d ../${base}.disang -i ../${base}.dumpave -o dumpaves/${base}.dumpave -r 1 >> metafile

done

ndfes_omp --mbar -w 0.15 --nboot 0 -c metafile.chk metafile

ndfes-path_omp --chk metafile.chk --ipath metafile --npathpts 32 --nsplpts 32 --opath path

This script will create an analysis directory and use the NDFES program to generate the potential of mean force. Each simulation generates a dumpave file that tracks the values of the restrained properties, including the reaction coordinate. For each dumpave file, the program ndfes-PrepareAmberData.py will extract just the data related to the reaction coordinate and output this to a new dumpave file in analysis/dumpaves. It will also generate a file called metafile that will indicate the index of the Hamiltonian (default is zero), the temperature (default is 298), the path to the dumpave file, the umbrella center, and the force constant.

Next, the program ndfes_omp is used to solve the MBAR equations with a bin width equal to 0.15. Setting the –nboot flag equal to zero means that we will perform no bootstrap resamples. If you wish to put error bars on your data points, nboot can be set to a nonzero number like 50, but this analysis will take longer with more resamples. The output of the program is an xml file called metafile.chk. This contains the value of the free energy in each sampled bin.

Finally, we use the ndfes-path_omp program to print the PMF information to a file called path. In this example, we are merely asking it to print the free energy along a path that is defined by the 32 control points in the metafile (ie. where we placed the umbrella windows). To create a smoother curve, one may increase the number of spline points to represent the path (–nsplpts). When using interpolation, the default setting is to use radial basis functions (rbf). Additional options will be discussed in upcoming exercises with more complex reaction paths.

Run the analysis script and take a look at the ouput.

[user@cluster] bash analyze_1.sh
[user@cluster] ls analysis
dumpaves  metafile  metafile.chk  path  path.rbf.0.dat  path.xml

Plot the PMF using xmgrace:

[user@cluster] cd analysis
[user@cluster] xmgrace -block path.rbf.0.dat -bxy 3:4