SPARK, a kernel of software programs for spatial reconstruction in electron microscopy

SPARK, an acronym for ‘SPAtial Reconstruction Kernel’, is the nucleus of a software library being developed for the three‐dimensional (3‐D) reconstruction of objects observed by the electron microscope. A unifying concept is used: the Fourier transform, known in several central sections, is resampled to obtain a 3‐D Cartesian grid, which is inverted by a fast Fourier transform. This technique is used for both single‐axis tilting (of 2‐D periodic layers or of isolated objects) and for the random conical‐tilt technique. The principles that make it possible to recover Cartesian grids in the two different geometries are illustrated and some preliminary results are reported. SPARK resamples the Cartesian grids with the use of a fast and efficient algorithm of Shannon interpolation developed by the authors.

[1]  D. J. De Rosier,et al.  Reconstruction of Three Dimensional Structures from Electron Micrographs , 1968, Nature.

[2]  Richard Henderson,et al.  A model for the structure of bacteriorhodopsin based on high resolution electron cryomicroscopy , 1990 .

[3]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[4]  J. Lepault,et al.  Structure of purple membrane from halobacterium halobium: recording, measurement and evaluation of electron micrographs at 3.5 Å resolution , 1986 .

[5]  R. Hegerl,et al.  The molecular architecture of the extracellular hemoglobin of Ophelia bicornis: Analysis of individual molecules , 1992 .

[6]  R. Hegerl,et al.  Three-Dimensional Structure Determination by Electron Microscopy (Nonperiodic Specimens) , 1980 .

[7]  M. Radermacher,et al.  Three-dimensional reconstruction of single particles from random and nonrandom tilt series. , 1988, Journal of electron microscopy technique.

[8]  P L Bellon,et al.  A strategy for the reconstruction of structures possessing axial symmetry: sectioned axonemes in sperm flagella , 1991, Journal of microscopy.

[9]  R A Crowther,et al.  The structure of Nudaurelia capensis beta virus: the first example of a capsid with icosahedral surface symmetry T-4. , 1974, The Journal of general virology.

[10]  L. Norton-Wayne.  Computer Techniques for Image Processing in Electron Microscopy , 1979, Advances in Imaging and Electron Physics.

[11]  S. Lanzavecchia,et al.  CFFT: a package of tools for Fourier analysis, written in C for UNIX machines , 1989 .

[12]  Salvatore Lanzavecchia,et al.  POLCA, a library running in a modern environment, implements a protocol for averaging randomly oriented images , 1990, Comput. Appl. Biosci..

[13]  A Klug,et al.  Structure of viruses of the papilloma-polyoma type. IV. Analysis of tilting experiments in the electron microscope. , 1968, Journal of molecular biology.

[14]  R. M. Mersereau,et al.  Digital reconstruction of multidimensional signals from their projections , 1974 .

[15]  A. Papoulis,et al.  Error analysis in sampling theory , 1966 .

[16]  J M Carazo,et al.  Bacteriophage T3 gene 8 product oligomer structure. , 1986, Journal of ultrastructure and molecular structure research.

[17]  M van Heel,et al.  Molecular shape of Lumbricus terrestris erythrocruorin studied by electron microscopy and image analysis. , 1988, Biochimica et biophysica acta.

[18]  J Frank,et al.  Three-dimensional reconstruction of single particles embedded in ice. , 1992, Ultramicroscopy.

[19]  P R Smith,et al.  A study of the structure of the T-layer of Bacillus brevis. , 1973, Journal of supramolecular structure.

[20]  K. Gehring,et al.  Structural architecture of an outer membrane channel as determined by electron crystallography , 1991, Nature.

[21]  I Bajla,et al.  A high-speed reconstruction from projections using direct Fourier method with optimized parameters-an experimental analysis. , 1990, IEEE transactions on medical imaging.

[22]  E. Dubois,et al.  Digital picture processing , 1985, Proceedings of the IEEE.

[23]  P. Gilbert.  The reconstruction of three-dimensional structure from projections and its application to electron microscopy II. Direct methods , 1972, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[24]  Giuseppe Tognon,et al.  The molecular architecture of the extracellular hemoglobin of Ophelia bicornis: Analysis of two-dimensional crystalline arrays , 1991 .

[25]  R. Keys.  Cubic convolution interpolation for digital image processing , 1981 .

[26]  José María Carazo,et al.  Study of the direct Fourier method for the three‐dimensional reconstruction of objects in the case of a missing angular data range , 1986 .

[27]  M. Heel,et al.  Exact filters for general geometry three dimensional reconstruction , 1986 .

[28]  R. Hingorani,et al.  An Investigation of Computerized Tomography by Direct Fourier Inversion and Optimum Interpolation , 1981, IEEE Transactions on Biomedical Engineering.

[29]  Salvatore Lanzavecchia,et al.  Pattern reconstruction in ultrastructural morphology , 1992 .

[30]  U Aebi,et al.  Electron microscopy and image processing applied to the study of protein structure and protein-protein interactions. , 1984, Journal of ultrastructure research.

[31]  J. Frank,et al.  Three‐dimensional reconstruction from a single‐exposure, random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli , 1987, Journal of microscopy.

[32]  R A Crowther,et al.  An analysis of the fine structure of the surface layers from two strains of Clostridia, including correction for distorted images. , 1977, Journal of ultrastructure research.

[33]  A. Cormack.  Representation of a Function by Its Line Integrals, with Some Radiological Applications , 1963 .

[34]  J F Deatherage,et al.  Three-dimensional reconstruction of the Z disk of sectioned bee flight muscle , 1989, The Journal of cell biology.

[35]  D. DeRosier,et al.  The reconstruction of a three-dimensional structure from projections and its application to electron microscopy , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[36]  Ronald A. Milligan,et al.  Architecture and design of the nuclear pore complex , 1992, Cell.

[37]  Marin van Heel.  A fast algorithm for transposing large multidimensional image data sets , 1991 .

[38]  Salvatore Lanzavecchia,et al.  A Moving Window Shannon Reconstruction Algorithm for Image Interpolation , 1994, J. Vis. Commun. Image Represent..

[39]  Giuseppe Zanotti,et al.  The molecular architecture of the extracellular haemoglobin of Ophelia bicornis , 1985 .

[40]  R. Henderson,et al.  Model for the structure of bacteriorhodopsin based on high-resolution electron cryo-microscopy. , 1990, Journal of molecular biology.

[41]  J M Carazo,et al.  Three-dimensional reconstruction of the connector of bacteriophage phi 29 at 1.8 nm resolution. , 1986, Journal of molecular biology.

[42]  J Frank,et al.  Tomographic three-dimensional reconstruction of cilia ultrastructure from thick sections. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[43]  Hsieh Hou,et al.  Cubic splines for image interpolation and digital filtering , 1978 .

[44]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[45]  Salvatore Lanzavecchia,et al.  The sperm tail of a gall midge and its microtubular arrangement studied by two strategies of image analysis (cecidomyiidae, diptera, insecta) , 1991 .

[46]  R. Henderson,et al.  Three-dimensional structure determination by electron microscopy of two-dimensional crystals. , 1982, Progress in biophysics and molecular biology.