Computer processing of electron microscope cross sections of multilayer mirrors.

A method is developed for determining interface profiles of extreme ultraviolet- (EUV-) layered synthetic microstructures (LSM's). It is based on computer processing digitized LSM electron micrographs. This study was carried out on a tungsten/carbon multilayer. Interfacial roughness has been characterized by means of two statistical parameters, i.e., the root mean square (rms) roughness height and the autocorrelation length varsigma. Additionally, knowledge of interface profiles should enable one to study more accurately the structural behavior of the stack, from the substrate to the top, and, in turn, help one better understand its EUV optical properties.

Influence of the Number of Bilayers on the Optical Performances of X-UV Multilayer Interferential Mirrors.

The influence of the number of bilayers on the optical performances of actual X-UV multilayer interferential mirrors (MIMs) has been studied in order to emphasize the experimental restrictions in the designing of "thick" mirrors used for the development of etched multilayer gratings. Several sets of samples (W/C, Mo/Si) with increasing number of bilayers have been manufactured in the very same conditions by means of a sputtering technique. X-ray diffraction characterization at Cu-Kα radiation (λ = 1.54018 Å) exhibits technical constraints in the achievement of multilayer structures with large number of bilayers. We obtain a gradual loss of reflectivity for deposition times greater than 1h 30 min to 2h without significant drift of the MIM's geometrical parameters (period and division parameter). In the same time, absolute reflectivity measurements at Cu-Lα radiation (λ = 1.333 nm) emphasize satisfying optical and spectroscopic performances of W/C thick samples ( 150 bilayers).

Distribution of zero crossings for the profile of random rough surfaces.

The distribution of zero crossings for the profile of a statistically rough surface of a silver thin film is determined and compared with a Poisson distribution. It is shown that the density of zero crossings may be related to the autocorrelation length and might be a useful parameter for characterizing spatial information of statistically rough surfaces.

Electron micrography and x-ray study of dip-lacquered LiF (220).

It has been proposed to use the 220 reflection of LiF with a multilayer deposited upon the top for simultaneous spectroscopy near Fe-k and O-k and below the C-k absorption edge (284 eV) in x-ray astronomy. We demonstrate that a substantial reduction of surface roughness is obtained by dip lacquering state-of-the-art polished LiF(220) surfaces. Using a microdensitometer analysis of electron micrographs of surface replicas and x-ray reflection, we have measured approximately 10-A rms roughness of Au-coated dip-lacquered LiF(220) crystals, as opposed to approximately 60 A measured on the bare LiF(220) crystal surface.

Abortive intermediates in transcription by wheat-germ RNA polymerase II. Dynamic aspects of enzyme/template interactions in selection of the enzyme synthetic mode.

At constant enzyme concentration and with the full set of nucleotide substrates dictated by template sequence, the chain-length distribution of polymeric product varies with template concentration in reactions catalysed by wheat-germ RNA polymerase II. Under the same conditions, but in the presence of a single ribonucleoside triphosphate, the rate of condensation of the triphosphate substrate to a dinucleotide primer also exhibits a complex dependence with the template concentration. This effect is observed using poly[d(A-T)] as a template. For both reactions there are two extreme types of behaviour in each of which transcription appears to involve a single enzyme synthetic mode, characterized by either a high (at low template concentration) or a low (at high template concentration) probability of releasing the transcripts. A strong correlation is found between these two pathways, such that conditions favouring the abortive release of trinucleotide products in the single-step addition reaction are associated with the synthesis of short-length RNA species in productive elongation, and reciprocally. A model previously developed by Papanicolaou, Lecomte & Ninio [(1986) J. Mol. Biol. 189, 435-448] to account for the kinetics of polymerization/excision ratios with Escherichia coli DNA polymerase I, and by Job, Soulié, Job & Shire [(1988) J. Theor. Biol. 134, 273-289] for kinetics of RNA-chain elongation by wheat-germ RNA polymerase II provides an explanation for the observed behaviour with the plant transcriptase. The basic requirement of this model is a slow equilibrium between two states of the polymerization complex with distinct probabilities of releasing the product. In the presence of Mn2+, and under conditions allowing the synthesis of poly[r(A-U)], one of these states is involved in the formation of oligonucleotides shorter than 15 bases, whereas the other catalyses the polymerization of chains longer than 40 bases.

Molecular organization and clustering of cell-wall-bound enzymes as a source of kinetic apparent co-operativity.

When fixed charges and enzyme molecules are not homogeneously distributed in a matrix, the degree of organization of charges, of enzyme molecules and of charges with respect to enzyme molecules modulate the enzyme reaction rate. The overall reaction velocity of the bound enzyme system may be expressed in terms of monovariate moments of the charge density distribution and of the bivariate moments of the charge and enzyme density distributions. With respect to the situation where fixed charges and enzyme molecules are randomly distributed in the matrix, the molecular organization, as expressed by the monovariate and bivariate moments results in an increase or a decrease, of the overall reaction rate, as well as in the appearance of a kinetic cooperativity. The degree of spatial organization of objects may be expressed quantitatively through the concept of minimal spanning tree. This concept may thus be applied to the quantification of the degree of order that may exist in the bidimensional distribution of enzyme molecules in a charged matrix. Primary walls of isolated plant cells in sterile culture behave as a polyanion and contain different enzymes. The spatial distribution in sycamore cell walls of an acid phosphatase has been studied through the concept of minimal spanning tree and shown to be non-randomly distributed in the polyanionic matrix, but clustered in that matrix. This spatial organization results in a modulation of the reaction rate of the cell-wall-bound phosphatase reaction. Both the theoretical and experimental results presented in this study leave little doubt as to the validity of the idea that in situ the organization of fixed charges and enzyme molecules modulate the overall dynamics of enzyme reactions.

Toward a new approach in tumor cell heterogeneity studies using the concept of order.

A new methodology was developed to study dynamic processes topographically in biological systems by means of a graph-theoretical method. It is based upon order parameters obtained from a minimal spanning tree analysis coupled with computer simulations. The method was used to analyse the heterogeneous behavior of two neoplastic cell lines after treatment with laminin. The laminin-induced cell detachment was quantitated and shown to be inversely related to cell population density and thus to cellular interactions. Our statistical analysis is a very powerful tool to obtain information from seemingly disorderly heterogeneous biological models.

Statistical parameters for rough surfaces of thin films of CaF(2) and Ag/CaF(2).

Statistical parameters, rms roughness delta and autocovariance length sigma, are determined both for rough surfaces of CaF(2) deposits and for surfaces of silver films deposited on these CaF(2) underlayers. The dependence of delta and sigma on the CaF(2) film thickness d is investigated. It is shown that the silver films do not replicate well the CaF(2) underlayers. A review of the relationships between delta, sigma and d when seeking control of the roughness of a silver film by controlling d is proposed. It is also shown that CaF(2) is a good underlayer compared with LiF.

Extreme UV and x-ray scattering measurements from a rough LiF crystal surface characterized by electron micrography.

XUV and x-ray scattering by a LiF crystal is measured. The angular distribution of the scattered radiation (ADSR) reveals characteristic features, side peaks or asymmetry. The surface of the sample is statistically characterized by a microdensitometer analysis of electron micrographs resolving the short spatial wavelengths of the surface roughness. This analysis shows that the surface has a large microroughness with an autocovariance function which is Gaussian in its initial portion. The first-order perturbation vector theory of the roughness-induced scattering leads to an interpretation of the ADSR features in terms of the modulation of the surface power spectral density function associated with the microroughness by an optical factor. The possibility of obtaining short scale roughness characterization from XUV or x-ray measurements is discussed.

Quantization of directional properties in biological structures using the Minimal Spanning Tree.

A method that uses the Minimal Spanning Tree graph has previously been developed (Dussert et al., 1987, J. theor. Biol. 125, 317) in order to analyse the degree of order in biological structures. This graph is shown here to be very powerful in bringing out directional properties of biological structures which cannot be revealed by a simple visual examination. The method is illustrated by means of various computer simulations.

Minimal spanning tree analysis of biological structures.

A new approach to study order and disorder in biological membranes and more generally in biological structures is developed. It is based on a graph constructed on the set points representing the position of particles. From this graph, which is called the minimal spanning tree, it is possible to deduce two parameters, namely the average length m and the standard deviation sigma which are characteristic of the repartition to be studied. The use of a diagram involving both m and sigma makes it possible to determine the degree of order by taking a simple reading in the (m, sigma) plane.

Comparative efficiency of natural crystals and multilayers as dispersing devices in the copper L(2,3) range.

Recent sputtering techniques have been used to produce layered synthetic microstructures (LSMs) as dispersing devices for varied applications in x-ray optics and spectroscopy. These analyzers, specially suited for synchrotron radiation, have been mounted in a two-parallel crystal monochromator. In this paper we show the first experimental results obtained with beryl crystals and multilayers for analyzing x-ray spectral distributions transmitted through screens or reflected on mirrors of copper near the L(2) and L(3) absorption edges. The significance of these findings is discussed in terms of comparison with natural and synthetic crystals and of designing a useful dispersing device for x-ray spectroscopy.

Quantitative characterization of a biological membrane by means of its spatial autocovariance.

Profiles for the exoplasmic face (EF) of the freeze-fractured plasma membrane from the root storage tissue of red beets are reconstructed by microdensitometry of micrographs of surface-shadowed-platinum carbon replicas. Autocovariance functions (ACFs) are computed from those profiles. The initial portions of the ACFs have a Gaussian form whose parameters (root mean square surface roughness and autocovariance length) are estimated. The parameter estimates are used to show that the pits on the EF faces are in good complementarity with the intramembrane particles seen on the complementary protoplasmic fracture faces.

Characterization of layered synthetic microstructure by transmission electron microscopy and diffraction.

Transmission electron diffraction patterns related to the cross section of layered synthetic microstructures (LSM's) are obtained. By depositing the multilayers onto (111) orientation silicon single-crystal substrates, it is possible to obtain on the same plate both the LSM diffraction pattern and a calibrated one and thus to measure the LSM mean period accurately. Results concerning tungsten-carbon LSM's are presented.

Height and slope distributions for surfaces of rough metallic deposits.

This paper deals with the accurate determination of height and slope distributions for surfaces of rough metallic deposits (magnesium, copper, silver, and gold). These distributions are computed using a microdensitometer analysis of electron micrographs of surface replicas. It is shown that most of the surfaces examined have reasonable Gaussian height and slope distributions. Apart from magnesium surfaces, the rms roughnesses determined from these distributions agree (within the accuracy range of their measurements) with rms roughnesses deduced from the autocovariance functions computed previously. Within the framework of scalar scattering theory, some emphasis is laid on the value of slopes to draw certain conclusions about the validity of the assumptions under which the scalar scattering theory is derived.