Efficient Extraction of Free Energy Profiles From Nonequilibrium Experiments

Hummer and Szabo recently presented a method based on the Jarzynski equality to calculate Helmholtz free energy profiles from nonequilibrium pathways obtained in simulations or experiments. In their approach, the free energy is reconstructed from weighted histograms. Here, we give a systematic derivation of the optimum weight, which-in principle-minimizes the statistical errors in the resulting free energy profiles. We then compare this optimum weight to Hummer and Szabo's original weight and several others by means of simulations of two one-dimensional models, for which the free energy profile is analytically known. In addition, we carry out simulations of a deca-alanine molecule pulled by a harmonic trap to assess the efficiency of the weights in a more realistic situation. In all cases, the weight of Hummer and Szabo performs very well leading to errors approximately equal to those obtained with a simplified version of the optimum weight. The performance of the optimum weight itself is unsatisfying due to statistical errors arising in the weight calculation. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 30: 1726-1736, 2009