ParseFEP Plugin, Version 1.9
ParseFEP consists of a set of tools for the analysis of freeenergy perturbation (FEP) calculations carried out within NAMD. FEP estimator. Based on the output file of an FEP calculation, i.e. the alchOutFile file, ParseFEP computes the freeenergy difference and provides an estimate of the statistical error. Bidirectional FEP calculations. If the transformation is performed bidirectionally (1), the results of the forward and the backward simulations can be combined in the form of the simpleoverlap sampling (SOS) estimator, or the Bennett acceptanceratio (BAR) estimator (2) of the free energy. For each approach, an estimator of the statistical error is supplied. Because combination of the statistical data accrued in bidirectional FEP calculations reduces the variance, it is recommended to carry out the simulation in both the forward and the backward directions. The BAR estimator corresponds to the maximumlikelihood value of the free energy and is obtained selfconsistently, using as an initial guess the result of the FEP calculation. Pictorial representation. For unidirectional FEP calculations, ParseFEP provides a graphical representation of the underlying probability distribution, the Boltzmann weight, and the product of the two. For bidirectional FEP calculations, ParseFEP displays the probability distributions characterizing the forward and the backward transformations. These distibutions are shown for all the windows, or strata, found in the alchOutFile file. It is, therefore, assumed that the output files for the FEP calculations performed in the two directions contain the same number of intermediate states. Comprehensive error analysis. The error associated to freeenergy estimates embraces contributions of different nature, a statistical component, namely the variance of the freeenergy estimator, and a systematic component, that is, the bias arising from the finite length of the simulation. ParseFEP computes the variance for the three, i.e. FEP, SOS and BAR, freeenergy estimators, thereby providing an assessment of the precision of the calculation. In addition, it estimates the bias as the relative inaccuracy of the freeenergy calculation, based on the degree of overlap of the underlying probability distributions (3). Monitoring the convergence. ParseFEP plots the evolution of the free energy as a function of the number of moleculardynamics steps. Only the information utilized towards the estimation of the freeenergy difference, i.e. past alchEquilSteps, is displayed. In the case of bidirectional FEP calculations, the evolution of the free energy is shown for both the forward and the backward transformations. GramCharlier interpolation. The statistical information accumulated in the alchOutFile file can be employed to model the underlying probability distribution. The latter can be described in terms of a product of a Gaussian distribution by a series of Hermite polynomials, i.e. a GramCharlier expansion (3). Convergence of the GramCharlier expansion at a given order represents a relevant measure of how welldefined the probability distribution is. Enthalpies and entropies. The perturbation formalism used to infer freeenergy differences can be generalized for the determination of enthalpy and entropy differences (3). These estimates are inherently less accurate than those of the free energy, because they involve averages of the total energy and the computation of a difference of two, independently measured large numbers, subject to large fluctuations. Commandline user interface. ParseFEP can now be run in text mode, that is without its GUI, which may be useful for batch analyses of FEP calculations. This version of the plugin uses the very intuitive syntax — parsefep <option 1> <option 2> ..., with the following options: forward <file name>: FEP alchOutFile file for the forward transformation, entropy: Compute enthaply and entropy differences, gc <max order>: GramCharlier expansion at a given order, gauss: Gaussian approximation to model the underlying probability distribution, backward <file name>: FEP alchOutFile file for the backward transformation, <sosbar>: use the SOS or BAR estimator. References (1) Pohorille, A.; Jarzynski, C.; Chipot, C. Good practices in freeenergy calculations. J. Phys. Chem. B 2010, 114, 1023510253. (2) Bennett, C. H. Efficient estimation of free energy differences from Monte Carlo data. J. Comp. Phys. 1976, 22, 245268. (3) Chipot, C.; Pohorille, A. (Eds.) Free energy calculations. Theory and applications in chemistry and biology. Springer Verlag, 2007. Note. On platforms running a Unixlike operating system, it is assumed that XMGrace and ImageMagick (display) are installed for visualization purposes. On Windows platforms, use is made of the Multiplot plotting program. How to cite ParseFEP. Liu, P.; Dehez, F.; Cai, W.; Chipot, C. A toolkit for the analysis of freeenergy perturbation calculations, J. Chem. Theor. Comput. 2012, 8, 26062616. Contributors. Chris Chipot (chipot@illinois.edu) and Liu Peng (superdirac@gmail.com). 
Figure 1. ParseFEP graphical user interface
Figure 2. Probability distributions for a bidirectional calculation.
Figure 3. Evolution of the free energy in a bidirectional calculation.
Figure 4. Error analysis based on overlapping distributions.
