Roy Lederman - CS-Lecture
Sunday, 26.11.2017, 10:30
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
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 together, cryo-EM produces measurements 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, and I will briefly discuss convex optimization approaches
and non-convex optimization approaches for this problem. I will then discuss
components which we are introducing in order to address the problem of
continuous heterogeneity in cryo-EM: 1. "hyper-molecules," the first
mathematical formulation of truly continuously heterogeneous molecules, 2.
The optimal representation of objects that are highly concentrated in both
the spatial domain and the frequency domain using high-dimensional Prolate
spheroidal functions, and 3. Bayesian algorithms for inverse problems with
an unsupervised-learning component for recovering such hyper-molecules in
Roy Lederman is a postdoc at the Program in Applied and Computational
Mathematics at Princeton University, working with Amit Singer. Before
joining Princeton, he was a postdoc at Yale University, where he also
completed his PhD in applied mathematics, working with Vladimir Rokhlin and
Ronald Coifman. Roy holds a BSc in Electrical Engineering and a BSc in
Physics from Tel Aviv University.