Format

Send to

Choose Destination
See comment in PubMed Commons below
Appl Comput Harmon Anal. 2010 May;28(3):296-312.

Reference Free Structure Determination through Eigenvectors of Center of Mass Operators.

Author information

  • 1Department of Mathematics, Program in Applied Mathematics, Yale University, 10 Hillhouse Ave. PO Box 208283, New Haven, CT 06520-8283 USA. coifman-ronald@yale.edu.

Abstract

Recovering the three-dimensional structure of molecules is important for understanding their functionality. We describe a spectral graph algorithm for reconstructing the three-dimensional structure of molecules from their cryo-electron microscopy images taken at random unknown orientations.We first identify a one-to-one correspondence between radial lines in three-dimensional Fourier space of the molecule and points on the unit sphere. The problem is then reduced to determining the coordinates of points on the sphere given a subset of their pairwise geodesic distances. To recover those coordinates, we exploit the special geometry of the problem, as rendered by the Fourier projection-slice theorem, to construct a weighted graph whose vertices are the radial Fourier lines and whose edges are linked using the common line property. The graph organizes the radial lines on the sphere in a global manner that reveals the acquisition direction of each image. This organization is derived from a global computation of a few eigenvectors of the graph's sparse adjacency matrix. Once the directions are obtained, the molecule can be reconstructed using classical tomography methods.The presented algorithm is direct (as opposed to iterative refinement schemes), does not require any prior model for the reconstructed object, and is shown to have favorable computational and numerical properties. Moreover, the algorithm does not impose any assumption on the distribution of the projection orientations. Physically, this means that the algorithm is applicable to molecules that have unknown spatial preference.

PMID:
20436952
PMCID:
PMC2860334
DOI:
10.1016/j.acha.2009.11.003
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for PubMed Central
    Loading ...
    Support Center