Biomedical subjects

S Lanzavecchia

Publications and source records attributed to S Lanzavecchia.

23 records · Page 2Linked to original sources

PubMed1995

Three-dimensional reconstruction of helical structures with fast inversion of very large Fourier transforms.

A single projection of a helical distribution of matter allows one to obtain the complete three-dimensional reconstruction of the structure. This task is usually performed by a Fourier-Bessel algorithm, which is more efficient than a customary fast Fourier transform inversion. This article describes how to achieve such a result by a direct Fourier method in a reasonable time. Once the two-dimensional transform of the projection is obtained from the source image, it is possible to build up the three-dimensional transform array, in Cartesian coordinates, that yields the reconstruction by a straightforward Fourier inversion. Images of projected helices should be studied with high sampling rates to enhance the resolution, and the segments of helix should be long enough to give a satisfactory signal-to-noise ratio. These conditions result in three-dimensional transform arrays that would require one or more gigabytes of storage. The strategy proposed here requires much less storage and is fast enough to allow the reconstruction to be performed with different parameters and filters in a very short time without any sacrifice in resolution.

Algorithms↗

PubMed1993

FT3D: three-dimensional Fourier analysis on small Unix workstations for electron microscopy and tomographic studies.

FT3D is a self-contained package of tools for three-dimensional Fourier analysis, written in the C language for Unix workstations. It can evaluate direct transforms of three-dimensional real functions, inverse transforms, auto- and cross-correlations and spectra. The library has been developed to support three-dimensional reconstructions of biological structures from projections obtained in the electron microscope. This paper discusses some features of the library, which has been implemented in such a way as to profit from the resources of modern workstations. A table of elapsed times for jobs of different dimensions with different RAM buffers is reported for the particular hardware used in the authors' laboratory.

Algorithms↗

PubMed1991

A strategy for the reconstruction of structures possessing axial symmetry: sectioned axonemes in sperm flagella.

The images of complex biological structures seen in the electron microscope, possessing an n-fold rotational symmetry, can be enhanced by averaging the axially repeating motif in order to improve their signal-to-noise ratio; this requires that the slices with n-fold symmetry do not exhibit distortions relative to one another. A strategy is proposed to detect the relative distortions and to remove them in order to obtain reliable results from the averaging process. Extensive use is made of cross-correlation analysis and of interpolation; because the procedure involves iterated resampling of the image, it is essential to adopt interpolation algorithms which preserve the spectral power. The procedure is illustrated by the analysis of transverse sections of the sperm flagellum axoneme of a stick insect; it might be used for the reconstruction of microtubules, nuclear pore complexes, virus capsids, and other supramolecular aggregates. The reconstructed images of axoneme sections reveal new information about the interactions between adjacent doublets; in particular, a double conjunction connecting the inner dynein arm with the nearest B-tubule has been consistently observed.

Animals↗

PubMed1990

POLCA, a library running in a modern environment, implements a protocol for averaging randomly oriented images.

The library POLCA implements the averaging of biological structures whose images are recorded in digital form from electron micrographs. The averaging protocol is based upon a method developed about ten years ago, which allows one to operate on a sequence of objects oriented and displaced at random within their frame; the relative rotations and the displacements of the structures are detected with the use of correlation algorithms and modified to make all objects appear the same, apart from their noisy components. The average image is then obtained by a simple addition and the signal-to-noise ratio is improved by a factor equal to the square root of the number of objects used to calculate the average. With respect to the original implementation of the method, two novel features characterize the library: the first one deals with the functions that are cross-correlated to determine the relative rotations of the structures; the functions used here are the inverse transforms of the amplitude spectra (IAS functions), which give rise to sharp maxima when they are cross-correlated. The second peculiarity is the systematic adoption, in the transformations of coordinates and in other circumstances, of an interpolation technique based upon the Fourier series kernel. POLCA is written in C and runs on a VME machine under the UNIX V/68 operating system. A programming style has been adopted to exploit fully the machine resources.

Algorithms↗

PubMed1990

Microtubules and their protofilaments in the flagellum of an insect spermatozoon.

Spermatozoa of stick insects have nine accessory tubules, which surround the nine outer microtubular doublets and the two inner microtubular singlets. When fixed in a fixative that was designed to minimize protein denaturation (glutaraldehyde and tannic acid, no osmium post-fixation but block staining with uranyl acetate in water) the accessory tubules were seen to contain 17 protofilaments of the same type as those in the 9 + 2 microtubular doublets and singlets. The protofilaments in accessory tubules and other microtubules were roughly triangular. When studied by Markham's photographic method a somewhat different tilt of the two longer sides was seen; this makes it possible to distinguish a polarity in the microtubules, i.e. to differentiate between a microtubule that is viewed from its (-)end to its (+)end from one that is viewed in the opposite direction. The dynein arms of the doublets can be used as an independent type of marker for the polarity. In a computer-aided analysis of the fine structure of the tail axoneme, the A-subtubules of the outer doublets were seen to be not quite equidistant; rather, there were somewhat widened electron-dense interspaces in the ring of protofilaments in four places. The locations of these widened interspaces coincide with the attachment sites for the spoke, the inner dynein arm, the outer dynein arm, and the intertubular material. It is tentatively concluded that proteins of these structures, and perhaps also other microtubule-associated proteins, may be anchored deep within the wall of a microtubule rather than just superficially along it.

Animals↗