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; 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, Amit; Wu, Hau-Tieng (2011) Orientability and Diffusion Maps. Appl Comput Harmon Anal 31:44-58
Singer, A (2011) Angular Synchronization by Eigenvectors and Semidefinite Programming. Appl Comput Harmon Anal 30:20-36
Ponce, Colin; Singer, Amit (2011) Computing steerable principal components of a large set of images and their rotations. IEEE Trans Image Process 20:3051-62
Singer, Amit; Coifman, Ronald R; Sigworth, Fred J et al. (2010) Detecting consistent common lines in cryo-EM by voting. J Struct Biol 169:312-22
Coifman, Ronald R; Shkolnisky, Yoel; Sigworth, Fred J et al. (2010) Reference Free Structure Determination through Eigenvectors of Center of Mass Operators. Appl Comput Harmon Anal 28:296-312