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.

中文翻译：

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原子肽和蛋白质中绝对自由能的置信度估计值的系统测试

由于使用分子模拟估算生物系统的自由能会产生极高的计算成本，因此，我们对固定骨架肽和蛋白质系统的现有“信度传播”（BP）算法进行了进一步的探索。对离散化的侧链构象文库之间的成对相互作用进行预先计算，以及将蛋白质侧链表示为图形模型中的节点，可以直接应用BP方法，该方法仅需约1 s的单处理器运行时间即可。预计算阶段。我们使用“ loopy BP”算法，该算法可以看作是传递矩阵方法对高度连接（即loopy）图的近似概括，并且以前已应用于蛋白质计算。我们检查of回血压对几种肽的应用以及T4溶菌酶L99A突变体的结合位点。本研究报告（i）将近似BP结果与基于Amber99SB力场的无偏估计量的估计值进行比较；（ii）研究不同库大小对BP预测的影响；（iii）关于在BP计算中可能出现的离散化影响的理论讨论。数据表明，尽管BP自由能估计具有近似性质，但实际上是非常准确的-实际上，它们从未落在可获取独立结果的系统的无偏估计量的置信区间之外。此外，我们发现，在大多数情况下，可以使用标准计算资源来获得足够精细的离散化库（这会减小库大小的敏感性）。总之，极短的计算时间和准确的结果表明BP方法值得进一步研究。