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

journal contribution

posted on 10.04.2012 by Jorge Numata, Ernst-Walter Knapp#### journal contribution

Any type of content formally published in an academic journal, usually following a peer-review process.

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.