Systematic Testing of Belief-Propagation Estimates for Absolute Free Energies in Atomistic Peptides and Proteins

Motivated by the extremely high computing
costs associated with
estimates of free energies for biological systems using molecular
simulations, we further the exploration of existing “belief
propagation” (BP) algorithms for fixed-backbone peptide and
protein systems. The precalculation of pairwise interactions among
discretized libraries of side-chain conformations, along with representation
of protein side chains as nodes in a graphical model, enables direct
application of the BP approach, which requires only ∼1 s of
single-processor run time after the precalculation stage. We use a
“loopy BP” algorithm, which can be seen as an approximate
generalization of the transfer-matrix approach to highly connected
(i.e., loopy) graphs, and it has previously been applied to protein
calculations. We examine the application of loopy BP to several peptides
as well as the binding site of the T4 lysozyme L99A mutant. The present
study reports on (i) the comparison of the approximate BP results
with estimates from unbiased estimators based on the Amber99SB force
field; (ii) investigation of the effects of varying library size on
BP predictions; and (iii) a theoretical discussion of the discretization
effects that can arise in BP calculations. The data suggest that,
despite their approximate nature, BP free-energy estimates are highly
accurateindeed, they never fall outside confidence intervals
from unbiased estimators for the systems where independent results
could be obtained. Furthermore, we find that libraries of sufficiently
fine discretization (which diminish library-size sensitivity) can
be obtained with standard computing resources in most cases. Altogether,
the extremely low computing times and accurate results suggest the
BP approach warrants further study.