Balanced and Bias-Corrected Computation of Conformational Entropy Differences for Molecular Trajectories

The mutual information (MI) expansion is applied to two molecular systems to probe algorithms that serve to estimate conformational entropy differences more precisely. The individual terms of the MI expansion are evaluated with a histogram method. Internal coordinates are used to avoid spurious correlations, which would require higher order terms in the MI expansion. Two approaches are applied that compensate for systematic errors that occur with a histogram method: (1) Simulation data are balanced by using the same number of coordinate sets (frames) for both conformer domains considered for the entropy difference computation. Balancing puts fluctuations of the histogram bin contents on the same level for both conformer domains, allowing efficient error cancellation. (2) Bias correction compensates for systematic deviations due to a finite number of frames per bin. Applying both corrections improves the precision of entropy differences drastically. Estimates of entropy differences are compared to thermodynamic benchmarks of a simple polymer model and trialanine, where excellent agreement was found. For trialanine, the average error for the estimated conformational entropy difference is only 0.3 J/(mol K), which is 100 times smaller than without applying the two corrections. Guidelines are provided for efficiently estimating conformational entropies. The program ENTROPICAL, used for the computations, is made available, which can be used for molecular dynamics or Monte Carlo simulation data on macromolecules like oligopeptides, polymers, proteins, and ligands.