Recent approaches to the study of biological molecules employ manifold learning to single-particle cryo-EM data sets to map the continuum of states of a molecule into a low-dimensional space spanned by eigenvectors or “conformational coordinates”. This is done separately for each projection direction (PD) on an angular grid. One important step in deriving a consolidated map of occupancies, from which the free energy landscape of the molecule can be derived, is to propagate the conformational coordinates from a given choice of “anchor PD” across the entire angular space. Even when one eigenvector dominates, its sign might invert from one PD to the next. The propagation of the second eigenvector is particularly challenging when eigenvalues of the second and third eigenvector are closely matched, leading to occasional inversions in their ranking as we move across the angular grid. In the absence of a computational approach, this propagation across the angular space has been done thus far “by hand” using visual clues, thus greatly limiting the general use of the technique. In this work we have developed a method that is able to solve the propagation problem computationally, by using optical flow and a probabilistic graphical model. We demonstrate its utility by selected examples.

中文翻译：

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通过流形嵌入从低温电磁数据映射状态连续体中的构象坐标在角空间中的传播。

研究生物分子的最新方法是利用流形学习对单粒子低温电磁数据集进行映射，以将分子状态的连续体映射到特征向量或“构象坐标”所跨越的低维空间中。对角网格上的每个投影方向（PD）分别完成此操作。得出占据率合并图的一个重要步骤，可以从其得出分子的自由能态图，是在整个角度空间中传播给定“锚定PD”的构象坐标。即使一个特征向量占主导地位，其符号也可能从一个PD转换为另一个PD。当第二和第三特征向量的特征值紧密匹配时，第二特征向量的传播特别具有挑战性，导致当我们在角度网格上移动时，它们的排名偶尔会反转。在没有计算方法的情况下，到目前为止，已经使用视觉线索“手动”完成了跨角度空间的这种传播，从而极大地限制了该技术的普遍使用。在这项工作中，我们开发了一种能够通过使用光流和概率图形模型来计算解决传播问题的方法。我们通过选定的示例演示其实用性。通过使用光流和概率图形模型。我们通过选定的示例演示其实用性。通过使用光流和概率图形模型。我们通过选定的示例演示其实用性。