IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Reference free cryo-EM algorithms using self-consistent data fusion

  • Feb. 26, 2009, 2 p.m. Sumwalt 102
  • Feb. 26, 2009, 3 p.m. Sumwalt 102


The goal in Cryo-EM structure determination is to reconstruct 3D macromolecular structures from their noisy projections taken at unknown random orientations by an electron microscope. Resolving the Cryo-EM problem is of great scientific importance, as the method is applicable to essentially all macromolecules, as opposed to other existing methods such as crystallography. Since almost all large proteins have not yet been crystallized for 3D X-ray crystallography, Cryo-EM seems the most promising alternative, once its associated mathematical challenges are solved.

In the first part of the talk, we present an extremely efficient and robust algorithm that successfully recovers the projection angles in a globally consistent manner. The simple algorithm combines ideas and principles from spectral graph theory, nonlinear dimensionality reduction, geometry, and computed tomography. The heart of the algorithm is a unique construction of a sparse graph followed by a fast computation of its eigenvectors. In order to provide better insight into the algorithm, we apply the exact same concept to the problem of sensor-network localization. The simpler setup of the sensor-network problem reveals the generality and power of the suggested approach.

In the second part of the talk, we describe a set of classic challenges in cryo-EM, as well as our new approach to their solution. Overcoming these challenges is essential for any reconstruction algorithm to achieve its maximum potential. These challenges include common-lines detection in the presence of noise, projection alignment, class averaging techniques, and a glimpse into the notorious heterogeneity problem.

Joint work with Ronald Coifman and Fred Sigworth.

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