ct0502864_si_002.zip (1.58 MB)
Use of the Weighted Histogram Analysis Method for the Analysis of Simulated and Parallel Tempering Simulations
dataset
posted on 2007-01-09, 00:00 authored by John D. Chodera, William C. Swope, Jed W. Pitera, Chaok Seok, Ken A. DillThe growing adoption of generalized-ensemble algorithms for biomolecular simulation
has resulted in a resurgence in the use of the weighted histogram analysis method (WHAM) to
make use of all data generated by these simulations. Unfortunately, the original presentation of
WHAM by Kumar et al. is not directly applicable to data generated by these methods. WHAM
was originally formulated to combine data from independent samplings of the canonical ensemble,
whereas many generalized-ensemble algorithms sample from mixtures of canonical ensembles
at different temperatures. Sorting configurations generated from a parallel tempering simulation
by temperature obscures the temporal correlation in the data and results in an improper treatment
of the statistical uncertainties used in constructing the estimate of the density of states. Here
we present variants of WHAM, STWHAM and PTWHAM, derived with the same set of
assumptions, that can be directly applied to several generalized ensemble algorithms, including
simulated tempering, parallel tempering (better known as replica-exchange among temperatures),
and replica-exchange simulated tempering. We present methods that explicitly capture the
considerable temporal correlation in sequentially generated configurations using autocorrelation
analysis. This allows estimation of the statistical uncertainty in WHAM estimates of expectations
for the canonical ensemble. We test the method with a one-dimensional model system and
then apply it to the estimation of potentials of mean force from parallel tempering simulations of
the alanine dipeptide in both implicit and explicit solvent.