Mathematics for cryo-electron microscopy

TL;DR

This paper discusses the mathematical principles behind algorithms used in cryo-electron microscopy, a high-resolution technique for determining biological macromolecular structures, highlighting its recent advancements and significance.

Contribution

It provides a comprehensive overview of the mathematical foundations underlying cryo-EM structure determination algorithms.

Findings

Cryo-EM has become a key method for high-resolution biological structure determination.

Mathematical principles are central to the development of cryo-EM algorithms.

Cryo-EM's significance is recognized by major awards and investments.

Abstract

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Methods as Method of the Year 2015, large scale investments in cryo-EM facilities are being made all over the world, and the Nobel Prize in Chemistry 2017 was awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM.