Sparse approximations of protein structure from noisy random projections. (English) Zbl 1234.62147

Panaretos, Victor M.; Konis, Kjell

Ann. Appl. Stat. 5, No. 4, 2572-2602 (2011).

Summary: Single-particle electron microscopy is a modern technique that biophysicists employ to learn the structure of proteins. It yields data that consist of noisy random projections of the protein structure in random directions, with the added complication that the projection angles cannot be observed. In order to reconstruct a three-dimensional model, the projection directions need to be estimated by use of an ad-hoc starting estimate of the unknown particle. We propose a methodology that does not rely on knowledge of the projection angles, to construct an objective data-dependent low-resolution approximation of the unknown structure that can serve as such a starting estimate. The approach assumes that the protein admits a suitable sparse representation, and employs discrete \(L^{1}\)-regularization (LASSO) as well as notions from shape theory to tackle the peculiar challenges involved in the associated inverse problem. We illustrate the approach by application to the reconstruction of an E. coli protein component called the Klenow fragment.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
92C55	Biomedical imaging and signal processing
62H35	Image analysis in multivariate analysis
92C40	Biochemistry, molecular biology

Keywords:

statistical tomography; electron microscopy; single particles; nearly black object; LASSO; deconvolution; Roman surface

Software:

ElemStatLearn; R; lars

References:

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