Cryogenic electron microscopy (cryo-EM) has come into wide use in the past few years for finding the 3D structure of biomolecules and identifying their multiple conformational states as a set of 3D volumes, also called EM maps. I will present several recent methods and bioinformatic tools applied to cryo-EM data, which rely on various mathematical tools for shape analysis. I will first introduce a bioinformatic tool that interpolates and generates morphing trajectories joining two given EM maps. These interpolants are built using recent advances in computational optimal transport, to allow efficient evaluation of Wasserstein barycenters of 3D shapes. I will show how the method performs on experimental data–with significant improvement over existing methods–and how this transport-based approach can be applied for fast alignment of 3D EM maps and interpolation of cell-shape trajectory. In the context of biological shape analysis, I will also present two other geometrically based methods for Cryo-EM and cell image data: the application of Riemannian elastic shape metrics for cancer cell classification, and the development of variational auto-encoders with geometric inductive bias on the group of rotations SO(3) for single particle reconstruction.

This lecture will be delivered in person in LSK 306 and also streamed via Zoom. If you do not receive IAM seminar announcements by email, please RSVP here to receive the Zoom link.