Abstract

In a cryo-electron microscopy (cryo-EM) experiment, many identical copies of a protein are prepared in solution, flash frozen, and imaged. After processing, each image is a noisy 2D projection of a copy of the 3D biomolecule in a particular shape. This 3D shape can be reconstructed from the images to atomic accuracy. With advances in microscopes and algorithms, the cryo-EM community has shifted from 3D reconstruction to the much more ambitious task of "heterogeneity analysis": from the images, estimating the probability distribution of the protein’s arrangements. These arrangements and their relative frequencies of each arrangement determine understanding cellular processes, with direct impact in drug discovery and disease studies. The significance and difficulty of the heterogeneity problem has drawn much popularity among applied mathematicians and computer scientists, with many classical numerical methods to new machine learning approaches. Here, I will focus on two aspects of the problem: my work on (1) illuminating a statistical fallacy common in heterogeneity analysis, and (2) a non-parametric maximum likelihood approach which can be used to post-process many existing heterogeneity methods. I will highlight the noise robustness and numerical simplicity of our approach, and outline future opportunities of numerical methods for this inverse problem.