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.
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.
| Andén, Joakim; Singer, Amit (2018) Structural Variability from Noisy Tomographic Projections. SIAM J Imaging Sci 11:1441-1492 |
| Bendory, Tamir; Boumal, Nicolas; Ma, Chao et al. (2018) Bispectrum Inversion with Application to Multireference Alignment. IEEE Trans Signal Process 66:1037-1050 |
| Heimowitz, Ayelet; Andén, Joakim; Singer, Amit (2018) APPLE picker: Automatic particle picking, a low-effort cryo-EM framework. J Struct Biol 204:215-227 |
| Greenberg, Ido; Shkolnisky, Yoel (2017) Common lines modeling for reference free Ab-initio reconstruction in cryo-EM. J Struct Biol 200:106-117 |
| Abbe, Emmanuel; Pereira, João M; Singer, Amit (2017) Sample Complexity of the Boolean Multireference Alignment Problem. Proc IEEE Int Symp Info Theory 2017:1316-1320 |
| Bhamre, Tejal; Zhao, Zhizhen; Singer, Amit (2017) MAHALANOBIS DISTANCE FOR CLASS AVERAGING OF CRYO-EM IMAGES. Proc IEEE Int Symp Biomed Imaging 2017:654-658 |
| Zhang, Teng; Singer, Amit (2017) Disentangling orthogonal matrices. Linear Algebra Appl 524:159-181 |
| Landa, Boris; Shkolnisky, Yoel (2017) Steerable Principal Components for Space-Frequency Localized Images. SIAM J Imaging Sci 10:508-534 |
| 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 |
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