Ecoffet Arthur, Woollard Geoffrey, Kushner Artem, Poitevin Frédéric, Duc Khanh Dao
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T1Z4, Canada.
Department of Computer Science, University of British Columbia, 2366 Main Mall #201, Vancouver, BC V6T1Z4, Canada.
AIMS Math. 2022;7(1):986-999. doi: 10.3934/math.2022059. Epub 2021 Oct 19.
Cryogenic electron microscopy (cryo-EM) has become widely used for the past few years in structural biology, to collect single images of macromolecules "frozen in time". As this technique facilitates the identification of multiple conformational states adopted by the same molecule, a direct product of it is a set of 3D volumes, also called EM maps. To gain more insights on the possible mechanisms that govern transitions between different states, and hence the mode of action of a molecule, we recently introduced a bioinformatic tool that interpolates and generates morphing trajectories joining two given EM maps. This tool is based on recent advances made in optimal transport, that allow efficient evaluation of Wasserstein barycenters of 3D shapes. As the overall performance of the method depends on various key parameters, including the sensitivity of the regularization parameter, we performed various numerical experiments to demonstrate how MorphOT can be applied in different contexts and settings. Finally, we discuss current limitations and further potential connections between other optimal transport theories and the conformational heterogeneity problem inherent with cryo-EM data.
在过去几年中，低温电子显微镜（cryo-EM）在结构生物学领域得到了广泛应用，用于采集“瞬间冻结”的大分子单张图像。由于该技术有助于识别同一分子所采取的多种构象状态，其直接产物是一组三维体积数据，也称为电子显微镜图谱（EM图谱）。为了更深入地了解控制不同状态之间转变的可能机制，进而了解分子的作用模式，我们最近引入了一种生物信息学工具，该工具可以对连接两个给定EM图谱的形态变化轨迹进行插值和生成。此工具基于最优传输领域的最新进展，这些进展使得能够高效评估三维形状的瓦瑟斯坦重心。由于该方法的整体性能取决于各种关键参数，包括正则化参数的灵敏度，我们进行了各种数值实验，以展示MorphOT如何应用于不同的背景和设置。最后，我们讨论了当前的局限性以及其他最优传输理论与低温电子显微镜数据固有的构象异质性问题之间进一步的潜在联系。
