Single-particle electron cryomicroscopy (cryo-EM) is a method for observing the three- dimensional structures of large macromolecules. 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. The proposal aims to develop and apply to experimental data novel algorithms for solving two difficult mathematical problems posed by this technique of structural biology. First, classical cryo-EM reconstruction techniques assume that the particles are identical. However, in many datasets this assumption does not hold. Some molecules of interest have more than one conformational state. These structural variations are of great interest to biologists, as they provide insight int the functioning of the molecule. The first area of investigation in this project is the development of algorithmic and mathematical framework for determining structures associated with heterogeneous particle populations. The proposed algorithm is not only faster than existing techniques but is also mathematically provable to reveal the different conformations if the number of images is sufficiently large. Second, a major limiting factor for present cryo-EM studies is the particle size. Images of small particles are often too noisy for existing methods to provide valid three-dimensional reconstructions;although the images contain structural information, the assignment of orientations to the individual particles is unreliable. The second area of investigation focuses on developing a radical new approach for reconstruction of small particles without the need for determining particle orientations.

Public Health Relevance

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

National Institute of Health (NIH)
Research Project (R01)
Project #
Application #
Study Section
Macromolecular Structure and Function D Study Section (MSFD)
Program Officer
Flicker, Paula F
Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
Princeton University
Biostatistics & Other Math Sci
Schools of Arts and Sciences
United States
Zip Code
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