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.
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.
| 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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