Jiří Komrska

S-layers on cell walls of cyanobacteria

S-layers are surface layers of bacterial cell walls. They are formed by two-dimensional, monomolecular crystalline arrays of identical units of protein or glycoprotein macromolecules (subunits). In general, each S-layer exhibits one of four possible 2-D lattice types: oblique (p1 or p2 symmetry), triangle (p3 symmetry), square (p4 symmetry) or hexagonal (p6 symmetry). The S-layer protein compasses up to 15% of the total protein of the bacterial cell and thus represents its major protein. Since 1972, S-layers have also been found in cyanobacteria. So far, they have been observed in 60 strains (isolates) of 23 species, belonging to 12 genera of unicellular Chroococcales and in just five strains or isolates (four species, four genera-only with p1 and p4 lattice symmetry) of filamentous Oscillatoriales; in further families of filamentous cyanobacteria (Nostocales, Stigonematales) they have not been detected, although filamentous cyanobacteria have been frequently studied in the electron microscope. In Chroococcales, relatively large cells of planktonic genera harbouring gas vesicles, S-layers are often present, while picoplanktonic species without gas vesicles usually do not have them. The p6 lattice symmetry appears to be the most common in cyanobacteria, having been found in 41 out of the 60 S-layers observed. All cells of a given strain, all strains capable of forming S-layers and all S-layer forming species of a given genus (as far as it is known) form S-layers of the same lattice type. Hence, the ability to form an S-layer appears to be useful as a supportive morphological marker for species classification. In 41 S-layer formers, the center-to-center spacing of their lattice unit arrays has been measured; the lattice constants range from 5 to 22nm, measured directly on surface of fixed cells. Coarse S-layers of p6 symmetry are the most frequent (with spacing of 15.0-22.0nm); p1 and p2 S-layers are the finest ones (with spacing of 5.0-10.0nm). Medium-spaced lattices (11.0-14.0nm) may be both of the p4 or p6 symmetry types. When measured on isolated S-layers, the spacings show a 10-60% higher value. All the hexagonal unit lattices have the same molecular architecture. Each S-layer unit resembles a truncated cone with an axial pore and with six protein subunits symmetrically placed around its opening. Adjoining units are interspaced by relatively fine channels. The fine detail of every S-layer of every individual strain is unique. Only the S-layer protein subunits of Synechococcus sp. strain GL24 have been analysed by electrophoresis. When incorporated into the S-layer units they confer a net neutral charge to the cell surface. This cyanobacterium induces mineralization of fine-grain gypsum and calcite in a saturated lake fresh water solution. This process is involved in the formation of stromatolites.

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures: errata

The Abbe transform is used to derive rigorous algebraic formulas for the wave function describing Fraunhofer diffraction at apertures in the form of arbitrary polygons. Two remarks bring the Abbe transform and the Abbe theorem into the context of the history of diffraction.

Scalar Diffraction Theory in Electron Optics

Publisher Summary This chapter discusses the interpretation of the phenomena appearing as a result of the electron scattering by the macroscopic obstacles. The invention of the electron microscope made it possible in principle to obtain perfect electron diffraction patterns by macroscopic obstacles. If the scattering objects are uncharged the diffraction integral may be simplified into the form currently used in optics. Because of the very small wavelength the conditions necessary for the simplification of the diffraction integral are well-satisfied in electron microscopy. A more complicated situation arises when the electrons are scattered by charged obstacles. In this case the diffraction integral has a form suitable for the description of the scattering in slightly nonuniform media. Moreover, even without numerical computations the scattering patterns can be discussed in remarkable detail by using the properties of the points in the integration region where the phase of the integrand is stationary.

Interpretation of medium-angle X-ray (neutron) scattering in amorphous solids by Fraunhofer diffraction of 2D-models

Abstract 2D-models of disordered structures are studied by optical (Fraunhofer) diffraction. It is shown that medium-angle scattering effects, e.g. the first sharp diffraction peak in chalcogenide glasses and the prepeak in metallic glasses, are evoked by clustering processes which can be identified with medium-range radial atomic density fluctuations.

Intensity Distributions in Electron Interference Phenomena Produced by an Electrostatic Bi-prism

The paper describes a model of electron interference obtained using an electrostatic bi-prism. The model is an approximation to the actual interference process, in which two diffracted waves, each representing the diffraction of electrons emerging from a single source by an opaque half-plane, are superposed in such a way that the half-planes are of opposite orientation and overlap by a distance equal to the width of the bi-prism filament. The intensity distribution in the interference pattern calculated according to the formula derived from this model is in an exact agreement with the intensity distribution found experimentally. This makes it possible to present a consistent quantitative explanation of all the special properties of the interference pattern, including intensity modulation of the fringes. The model may also serve for detailed interpretation of some interference phenomena in light optics, such as those observed with the help of Fresnel mirrors or a Fresnel bi-prism.

Quantitative-phase-contrast imaging of a two-level surface described as a 2D linear filtering process

The paper deals with quantitative phase imaging of two-height-level surface reliefs. The imaging is considered to be a linear system and, consequently, the Fourier transform of the image is the product of the Fourier transform of a 2D function characterizing the surface and a specific 2D coherent transfer function. The Fourier transform of functions specifying periodic surface reliefs is factorized into two functions similar to lattice and structure amplitudes in crystal structure analysis. The approach to the imaging process described in the paper enables us to examine the dependence of the phase image on the surface geometry. Theoretical results are verified experimentally by means of a digital holographic microscope.

Fraunhofer Diffraction at Apertures in the Form of Regular Polygons. II

In this second contribution the Fraunhofer diffraction patterns from apertures of the form of an equilateral triangle, a square, a regular pentagon, a hexagon and an octagon are compared with the calculated maps of the intensity distribution. For each shape of the aperture the first few maxima and minima of the intensity are tabulated and the formulae for the wave function are given characterizing the diffraction in the directions of the slowest and the steepest decrease of intensity.

Intensity and Phase in Fresnel Diffraction by a Plane Screen Consisting of Parallel Strips

Using the Huygens-Fresnel principle the expressions for the intensity and the phase in Fresnel diffraction phenomena have been derived. The cases of spherical, cylindrical and plane scalar waves incident upon the plane diffraction screen have been investigated. The diffraction screen may consist of any number of parallel strips of different transmissivities and different phase shifts, the width of the individual strips being large compared with the wave-length. As special cases of the general formulae, the intensity and phase distributions in the diffraction patterns for the following forms of the diffraction screen have been calculated: opaque and partially transparent half-plane, slit, strip and double slit. By means of the derived expressions, the validity of Babinets principle for Fresnel diffraction phenomena of this type has been verified.

Advances in S-Layer Research of Chroococcal Cyanobacteria

Cyanobacteria are among the most ancient residents of the Earth and were the first oxygenic organisms to provide oxygen to the Earth’s atmosphere by photosynthesis. Cyanobacteria appeared some 3.0–2.3 billion years ago, and have not evolved much since then. In today’s biosphere they are ubiquitous, inhabiting the most diverse and extreme ecological niches. Many of them possess crystalline S-layers on the surface of their cell walls.

Fresnel Diffraction of Electrons by a Filament

Expressions for calculating the electron diffraction phenomena by a filament and at half-plane have been derived using the Huygens-Fresnel principle. It is shown that approximations usual in light optics for the calculation of Fresnel diffraction phenomena are justified also for electron optics. The intensity distributions in the diffraction pattern for various filament diameters and a half-plane have been calculated. It is demonstrated to what extent at different filament diameters the approximation of the two symmetrical parts of the diffraction pattern by the diffraction at a half-plane is admissible. Also, the intensity distribution in the zone of geometrical shadow as approximated by the interference from two straight line sources placed at the edges of the filament is discussed. Experiments are in good agreement with the theory for both the diffraction by a filament and by a half-plane.