Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis
Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis
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DOI：
10.1016/j.bpj.2015.07.028
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发表时间：
2015-09-01
影响因子：
3.4
通讯作者：
Chou, Tom
中科院分区：
文献类型：
--
作者：
Chang, Joshua C.;Fok, Pak-Wing;Chou, Tom
动态单分子力谱经常被用来扭曲键。以断裂力、施加的功和位移轨迹的形式得到的响应被用来重建键势。这种方法通常依赖于一维键势的简单参数化，平衡起始状态的假设，和/或大量的轨迹数据。参数方法在推断具有多个极小值的复杂键势时通常失败，而分段估计可能不能保证在大距离具有适当行为的平滑结果。现有的技术，特别是那些基于功定理的技术，也没有解决由于空间不均匀耦合到大分子中的其他自由度而可能引起的扩散率的空间变化。为了应对这些挑战，我们开发了一种全面的经验贝叶斯方法，将数据和正则化项直接合并到路径积分中。我们方法中的所有实验和统计参数都是直接从数据中估计的。在模拟数据上测试我们的方法，我们的正则化方法需要更少的数据，并允许同时推断复杂的键势和扩散系数分布。重要的是，我们证明了重建的键势的精度对空间变化的扩散系数很敏感，只有当两者同时被推断时，才能期望准确的重建。此外，在提供了一种从数据中自洽地选择正则化参数的方法之后，我们得到了允许不确定性量化的后验概率分布。
Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification.