Geometric shape matching for recovering protein conformations from single-particle Cryo-EM data

TL;DR

This paper introduces a shape analysis-based method for reconstructing 3D protein backbone structures from noisy cryo-EM data by modeling deformations as matrix Lie group actions and optimizing deformation energies.

Contribution

It presents a novel approach that treats cryo-EM reconstruction as an indirect shape matching problem using Lie group deformations and develops algorithms for optimal deformations.

Findings

Successfully recovers 3D backbone structure from synthetic cryo-EM data.

Demonstrates the effectiveness of shape analysis in protein structure recovery.

Provides computational algorithms for optimal deformations based on energy minimization.

Abstract

We address recovery of the three-dimensional backbone structure of single polypeptide proteins from single-particle cryo-electron microscopy (Cryo-SPA) data. Cryo-SPA produces noisy tomographic projections of electrostatic potentials of macromolecules. From these projections, we use methods from shape analysis to recover the three-dimensional backbone structure. Thus, we view the reconstruction problem as an indirect matching problem, where a point cloud representation of the protein backbone is deformed to match 2D tomography data. The deformations are obtained via the action of a matrix Lie group. By selecting a deformation energy, the optimality conditions are obtained, which lead to computational algorithms for optimal deformations. We showcase our approach on synthetic data, for which we recover the three-dimensional structure of the backbone.