Single-particle electron cryomicroscopy (cryo-EM) and 2D NMR spectroscopy are methods for observing the three-dimensional structures of large and small macromolecules. respectively. We propose to develop and apply novel algorithms for solving the difficult mathematical problems posed by these techniques of structural biology. In cryo-EM the experimental data consist of noisy, random projection images of macromolecular "particles", and the problem is finding the 3D structure which is consistent with these images. Present reconstruction techniques rely on user input or ad hoc models to initiate a refinement cycle. We propose a new algorithm, "globally consistent angular reconstitution" (GCAR) that provides an unbiased and direct solution to the reconstruction problem. We further propose an extension to GCAR to handle heterogeneous particle populations. We also will pursue a powerful new approach to determining class averages, "triplet class averaging". This should allow GCAR to be used with data having very low signal-to-noise ratios, as is commonly obtained. The experimental data from NMR consist of estimates of local distances between atoms, and the goal is to find a globally consistent coordinate system. The same theory behind GCAR, involving the properties of sparse linear operators, can be applied to obtain a fast and direct solution to the distance geometry problem. We will develop and implement all of these algorithms and test them with experimental cryo-EM and NMR data.

Public Health Relevance

Determining the structures of proteins and other large molecules is an essential step in the basic understanding of biological processes, as well as the first step in rational drug design. We propose to develop new, faster and more reliable computer algorithms to increase the power of two structure-determination methods, cryo-EM and NMR.

National Institute of Health (NIH)
National Institute of General Medical Sciences (NIGMS)
Research Project (R01)
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Special Emphasis Panel (ZGM1-CBCB-5 (BM))
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Wehrle, Janna P
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Princeton University
Biostatistics & Other Math Sci
Schools of Arts and Sciences
United States
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Zhao, Zhizhen; Shkolnisky, Yoel; Singer, Amit (2016) Fast Steerable Principal Component Analysis. IEEE Trans Comput Imaging 2:1-12
Bandeira, Afonso S; Kennedy, Christopher; Singer, Amit (2016) Approximating the Little Grothendieck Problem over the Orthogonal and Unitary Groups. Math Program 160:433-475
Andén, Joakim; Katsevich, Eugene; Singer, Amit (2015) COVARIANCE ESTIMATION USING CONJUGATE GRADIENT FOR 3D CLASSIFICATION IN CRYO-EM. Proc IEEE Int Symp Biomed Imaging 2015:200-204
Katsevich, E; Katsevich, A; Singer, A (2015) Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem. SIAM J Imaging Sci 8:126-185
Bhamre, Tejal; Zhang, Teng; Singer, Amit (2015) Orthogonal Matrix Retrieval In Cryo-Electron Microscopy. Proc IEEE Int Symp Biomed Imaging 2015:1048-1052
Zhao, Zhizhen; Singer, Amit (2014) Rotationally invariant image representation for viewing direction classification in cryo-EM. J Struct Biol 186:153-66
Zhao, Zhizhen; Singer, Amit (2013) Fourier-Bessel rotational invariant eigenimages. J Opt Soc Am A Opt Image Sci Vis 30:871-7
Singer, A; Wu, H-T (2013) Two-Dimensional Tomography from Noisy Projections Taken at Unknown Random Directions. SIAM J Imaging Sci 6:136-175
Wang, Lanhui; Singer, Amit; Wen, Zaiwen (2013) Orientation Determination of Cryo-EM Images Using Least Unsquared Deviations. SIAM J Imaging Sci 6:2450-2483
Shkolnisky, Yoel; Singer, Amit (2012) Viewing Direction Estimation in Cryo-EM Using Synchronization. SIAM J Imaging Sci 5:

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