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.

鉴于利用分子模拟估算生物系统自由能所伴随的极高计算成本，本研究进一步拓展了对现有“信念传播”（BP）算法在固定骨架肽和蛋白质系统中的应用研究。通过预先计算离散化侧链构象库之间的成对相互作用，并将蛋白质侧链表示为图模型中的节点，实现了BP方法的直接应用，该方法的预计算阶段之后仅需约1秒的单处理器运行时间。本研究采用了一种“循环BP”算法，该算法可视作对高度连接（即循环）图（如Transformer）的传递矩阵方法的近似推广，并且之前已被应用于蛋白质计算。本研究考察了循环BP在数种肽以及T4溶菌酶L99A突变体的结合位点上的应用。本研究报告了以下内容：（i）将近似BP结果与基于Amber99SB力场的无偏估计值进行比较；（ii）研究了库大小变化对BP预测的影响；（iii）对BP计算中可能出现的离散化效应进行了理论探讨。数据表明，尽管BP自由能估算具有近似性质，但其准确性极高——实际上，它们从未超出独立结果可获得系统的无偏估计值的置信区间。此外，我们发现，大多数情况下，可以通过标准计算资源获得足够精细的离散化库（这降低了库大小敏感性）。总的来说，极低的计算时间和准确的结果表明，BP方法值得进一步研究。