Cryo-Electron Microscopy (cryo-EM) is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules, cryo-electron microscopes produce images of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. "hyper-molecules," the mathematical formulation of truly continuously heterogeneous molecules, 2. Computational and numerical tools for expressing associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.
Roy Lederman is a postdoc at Princeton University, working with Amit Singer. Before joining Princeton, he spent a year as a Gibbs Assistant Professor at Yale University, where he had earned his PhD in Applied Mathematics, working with Vladimir Rokhlin and Ronald Coifman. He holds a BSc in Electrical Engineering and a BSc in Physics from Tel Aviv University. Roy is interested in methods for discovering hidden structures in data, and in mathematical, statistical, numerical, and computational aspects of data-science. He is interested in various applications in computational biology and structural biology.