Hummer Gerhard, Köfinger Jürgen
Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue Str. 3, 60438 Frankfurt am Main, Germany.
J Chem Phys. 2015 Dec 28;143(24):243150. doi: 10.1063/1.4937786.
We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.
我们描述了不同的贝叶斯系综优化方法，研究了它们之间的相互关系，并讨论了它们的实际应用。通过系综优化，可以通过整合广泛的实验数据（包括系综平均可观测量的测量值）来表征动态和部分无序（生物）分子结构的性质。我们从一个贝叶斯公式出发，其中后验是一个对不同构型空间分布进行排序的泛函。通过最大化这个后验，我们推导出一个最优的贝叶斯系综分布。对于离散构型，这个最优分布与通过最大熵“小角X射线散射的系综优化”（EROS）公式得到的分布相同。贝叶斯复制系综优化通过在耦合复制分子动力学模拟中对可观测量的平均值施加约束，增强了相关构型的采样。我们表明，约束的强度应与复制的数量成线性比例，以确保在无限多个复制的极限情况下收敛到最优的贝叶斯结果。在“系综的贝叶斯推断”方法中，我们结合了复制和EROS方法来加速收敛。可以使用自适应算法直接从最优系综中采样，而无需复制。我们讨论了单分子测量和动态可观测量（如弛豫参数）的纳入。对不同贝叶斯系综优化方法的理论分析为实际应用提供了基础，并为进一步研究提供了起点。
