Software for 3-D Reconstruction from Images of Oblique Sections through 3-D Crystals HANSPETER WINKLER 1,2 AND KENNETH A. TAYLOR 2 Department of Cell Biology, Duke University Medical Center, Durham, North Carolina 27710 Received May 15, 1995, and in revised form August 18, 1995 Oblique section reconstruction can produce a 3-D image from electron micrographs of a sectioned crystal when the orientation of the section plane is not aligned with the principal planes of the unit cell. We describe here the reconstruction protocol and the specialized computer software for a Fourier space method that can extract 3-D information from 2-D projection images of oblique sections. The pro- tocol encompasses correction for image defects and image distortions, determination and refinement of reciprocal lattices, calculation of the crystal orien- tation in 3-D space, extraction of periodic informa- tion, alignment in Fourier space, determination and deconvolution of section thickness, and calculation of structure factors of the original crystal. A 3-D map of the unit cell can then be computed by stan- dard crystallographic procedures. Oblique section reconstruction provides an alternative to tomogra- phy for 3-D imaging of crystalline objects with large unit cells. The method provides an excellent means of obtaining a 3-D transform using electron micros- copy for comparison with X-ray diffraction data from native specimens. © 1996 Academic Press, Inc. INTRODUCTION Oblique section 3-D reconstruction (OSR) is a method for calculating a 3-D image from electron micrographs of a section through a 3-D crystal (Crowther, 1984; Crowther et al., 1990). OSR takes advantage of the fact that the majority of thin sec- tions through a crystal are oblique and that it takes considerable effort to obtain sections parallel to the principal planes of the unit cell. OSR is particularly well adapted to the 3-D imaging of muscle speci- mens which typically have large unit cells that are heterogeneous in character, i.e., M-band, Z-disk, and A-band. The first OSRs were done on images of the fish muscle M-band (Crowther and Luther, 1984). Most recently, OSR methods have been used to vi- sualize the A-band structure of insect flight muscle (Taylor et al., 1993; Schmitz et al., 1994). OSRs can be computed by two different methods, either in real space by crystallographic serial section reconstruction, or CSSR (Taylor and Crowther, 1991), or in Fourier space with the superlattice re- construction, or SLR (Taylor and Crowther, 1992; Winkler and Taylor, 1994). The term CSSR was cho- sen to emphasize the similarity with serial section reconstruction. However, CSSR uses the crystal pe- riodicity to build a 3-D density matrix from a single image of a section, whereas serial section recon- struction builds the 3-D matrix from aligned images of successive sections cut through the specimen. CSSR methods can currently be applied to only a limited range of section orientations, whereas the SLR method is much less restricted with respect to section orientation. Under favorable circumstances, a single image of an oblique section is sufficient to reconstruct the full unit cell by SLR. OSR requires that sections be thin relative to the unit cell dimensions. Thin sections are needed be- cause projection of the density along the direction normal to the section plane smears fine specimen detail, thereby reducing the resolution in that di- rection. Deconvolution of the section thickness can partially overcome the resolution limit, but even with deconvolution, some spatial frequencies are weighted to zero resulting in loss of information in the reconstruction. However, combining OSRs from sections of different thickness and orientation can help restore information missing in any one recon- struction. Since the whole 3-D transform can be measured with the methods described below, struc- ture factors can be readily compared to data from other sources, such as X-ray diffraction. The SLR method is the more generally applicable of the OSR methods and is thus the focus of the following dis- cussion. 1 To whom correspondence should be addressed. Fax: 1-904- 561-1406; e-mail: winkler@sb.fsu.edu. 2 Current address: Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306-3015. JOURNAL OF STRUCTURAL BIOLOGY 116, 241–247 (1996) ARTICLE NO. 0037 241 1047-8477/96 $18.00 Copyright © 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.