### AIMS Mathematics

2022, Issue 1: 986-999. doi: 10.3934/math.2022059
Research article Special Issues

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

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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