Application of transport-based metric for continuous interpolation between cryo-EM density maps

Arthur Ecoffet; Geoffrey Woollard; Artem Kushner; Frédéric Poitevin; Khanh Dao Duc; Arthur Ecoffet; Geoffrey Woollard; Artem Kushner; Frédéric Poitevin; Khanh Dao Duc

doi:10.3934/math.2022059

AIMS Mathematics

2022, Volume 7, Issue 1: 986-999. doi: 10.3934/math.2022059

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Application of transport-based metric for continuous interpolation between cryo-EM density maps

1.
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T1Z4, Canada
2.
Department of Computer Science, University of British Columbia, 2366 Main Mall #201, Vancouver, BC V6T1Z4, Canada
3.
SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
4.
Department of Zoology, University of British Columbia, 4200 - 6270 University Blvd., Vancouver, BC V6T1Z4, Canada

Received: 21 December 2020 Accepted: 24 September 2021 Published: 19 October 2021
MSC : Primary 92C40, 65D05; Secondary 49Q10

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.
- optimal transport,
- interpolation,
- 3D shapes,
- cryo-EM,
- conformational heterogeneity
Citation: Arthur Ecoffet, Geoffrey Woollard, Artem Kushner, Frédéric Poitevin, Khanh Dao Duc. Application of transport-based metric for continuous interpolation between cryo-EM density maps[J]. AIMS Mathematics, 2022, 7(1): 986-999. doi: 10.3934/math.2022059

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Abstract

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.

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