### Abstract

A pre-condition for the ab initio assignment of Euler angles to a set of projections from an asymmetric object is that at least three of the available projections correspond to rotations about different axes. For symmetric objects this condition may be relaxed. There are some applications of single-particle electron microscopy, such as the reconstruction of filamentous macromolecular assemblies, where all available projections more-or-less correspond to rotations about a common rotation axis making it difficult to satisfy this condition. Here, a method has been developed to overcome this problem, based on the fact that the correlation between two central sections of the Fourier transform of a compact object will not be limited to an infinitesimal central line but will have a finite extent, which is related to the angle between the corresponding projections. Projections from model filaments, with different degrees of rotational symmetry about the long axis, have been used to test the methodology. The results show that angle determination is robust down to signal-to-noise ratios as low as 2 and that, in general, the error decreases as the degree of symmetry increases. The method has been used to assign angles to a set of negatively stained muscle thick filament projections to obtain an initial 3D reconstruction. The main features of the projections are seen to be faithfully reproduced in the reprojections from the reconstruction. A real-space adaptation of this method is also discussed.

Original language | English |
---|---|

Pages (from-to) | 707-724 |

Number of pages | 18 |

Journal | Journal of Molecular Biology |

Volume | 344 |

Issue number | 3 |

DOIs | |

Publication status | Published - 26 Nov 2004 |

Externally published | Yes |

### Fingerprint

### Keywords

- 3D reconstruction
- angular reconstitution
- electron microscopy
- myosin
- single particle analysis

### ASJC Scopus subject areas

- Virology

### Cite this

*Journal of Molecular Biology*,

*344*(3), 707-724. https://doi.org/10.1016/j.jmb.2004.09.068

**A measure for the angle between projections based on the extent of correlation between corresponding central sections.** / Patwardhan, Ardan; Paul, Danielle; AL-Khayat, Hind A.; Morris, Edward P.

Research output: Contribution to journal › Article

*Journal of Molecular Biology*, vol. 344, no. 3, pp. 707-724. https://doi.org/10.1016/j.jmb.2004.09.068

}

TY - JOUR

T1 - A measure for the angle between projections based on the extent of correlation between corresponding central sections

AU - Patwardhan, Ardan

AU - Paul, Danielle

AU - AL-Khayat, Hind A.

AU - Morris, Edward P.

PY - 2004/11/26

Y1 - 2004/11/26

N2 - A pre-condition for the ab initio assignment of Euler angles to a set of projections from an asymmetric object is that at least three of the available projections correspond to rotations about different axes. For symmetric objects this condition may be relaxed. There are some applications of single-particle electron microscopy, such as the reconstruction of filamentous macromolecular assemblies, where all available projections more-or-less correspond to rotations about a common rotation axis making it difficult to satisfy this condition. Here, a method has been developed to overcome this problem, based on the fact that the correlation between two central sections of the Fourier transform of a compact object will not be limited to an infinitesimal central line but will have a finite extent, which is related to the angle between the corresponding projections. Projections from model filaments, with different degrees of rotational symmetry about the long axis, have been used to test the methodology. The results show that angle determination is robust down to signal-to-noise ratios as low as 2 and that, in general, the error decreases as the degree of symmetry increases. The method has been used to assign angles to a set of negatively stained muscle thick filament projections to obtain an initial 3D reconstruction. The main features of the projections are seen to be faithfully reproduced in the reprojections from the reconstruction. A real-space adaptation of this method is also discussed.

AB - A pre-condition for the ab initio assignment of Euler angles to a set of projections from an asymmetric object is that at least three of the available projections correspond to rotations about different axes. For symmetric objects this condition may be relaxed. There are some applications of single-particle electron microscopy, such as the reconstruction of filamentous macromolecular assemblies, where all available projections more-or-less correspond to rotations about a common rotation axis making it difficult to satisfy this condition. Here, a method has been developed to overcome this problem, based on the fact that the correlation between two central sections of the Fourier transform of a compact object will not be limited to an infinitesimal central line but will have a finite extent, which is related to the angle between the corresponding projections. Projections from model filaments, with different degrees of rotational symmetry about the long axis, have been used to test the methodology. The results show that angle determination is robust down to signal-to-noise ratios as low as 2 and that, in general, the error decreases as the degree of symmetry increases. The method has been used to assign angles to a set of negatively stained muscle thick filament projections to obtain an initial 3D reconstruction. The main features of the projections are seen to be faithfully reproduced in the reprojections from the reconstruction. A real-space adaptation of this method is also discussed.

KW - 3D reconstruction

KW - angular reconstitution

KW - electron microscopy

KW - myosin

KW - single particle analysis

UR - http://www.scopus.com/inward/record.url?scp=5144221713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5144221713&partnerID=8YFLogxK

U2 - 10.1016/j.jmb.2004.09.068

DO - 10.1016/j.jmb.2004.09.068

M3 - Article

C2 - 15533440

AN - SCOPUS:5144221713

VL - 344

SP - 707

EP - 724

JO - Journal of Molecular Biology

JF - Journal of Molecular Biology

SN - 0022-2836

IS - 3

ER -