Is there anything left to say on enzyme kinetic constants and quasi-steady state approximation?

In this paper we re-examine the commonly accepted meaning of the two kinetic constants characterizing any enzymatic reaction, according to Michaelis-Menten kinetics. Expanding in terms of exponentials the solutions of the ODEs governing the reaction, we determine a new constant, which corrects some misinterpretations of current biochemical literature.     

Structural and Electrical Properties of Sol–Gel-processed CdTiO3 Powders and Films

Cadmium titanate, CdTiO₃, was prepared by the sol–gel technique in bulk and in thin film form. The thermal evolution of the gels and the phase changes were studied by thermo- gravimetric analysis (TGA), X-ray diffractometry (XRD) and Raman and energy-dispersive (EDS) spectroscopies. The morphology of the samples was observed using scanning electron microscopy (SEM). Gels heated to 800 °C gave rise to powders with only the ilmenite-like phase. The orthorhombic perovskite phase is the only crystalline phase observed after a 4 h heat-treatment at 1100 °C. With respect to the conventional preparation method by solid-state reaction, by the sol–gel method it is possible to prepare the ilmenite phase at lower temperatures and the perovskite phase in a shorter time. Clear, homogeneous thin films were obtained by the dip-coating method. The refraction index and the thickness of the films were measured using ellipsometry. The humidity-sensitive electrical properties were measured for thin films deposited on alumina substrates with comb-type gold electrodes, heated to 200 °C and 450 °C. The films heated to 200 °C, which still contained organics, showed a variation of the resistance of six orders of magnitude in the relative humidity (RH) range tested (4–87% RH). The films heated to 450 °C, made of ilmenite-type CdTiO₃, were nearly insensitive to RH. © 1997 by John Wiley & Sons, Ltd.     

Quasi steady-state approximations in complex intracellular signal transduction networks – a word of caution

Enzyme reactions play a pivotal role in intracellular signal transduction. Many enzymes are known to possess Michaelis–Menten (MM) kinetics and the MM approximation is often used when modeling enzyme reactions. However, it is known that the MM approximation is only valid at low enzyme concentrations, a condition not fulfilled in many in vivo situations. Recently the total quasi steady-state approximation (tQSSA) has been developed for enzymes with MM kinetics. This new approximation is valid not only whenever the MM approximation is, but moreover in a greatly extended parameter range. Starting from a single reaction and arriving at the mitogen activated protein kinase (MAPK) cascade, we give several examples of biologically realistic scenarios where the MM approximation leads to quantitatively as well as qualitatively wrong conclusions, and show that the tQSSA improves the accuracy of the simulations greatly.      

Dynamic secondary ion mass spectrometry and X-ray photoelectron spectroscopy on artistic bronze and copper artificial patinas

To prevent the natural processes of decay and to develop and improve the treatments of conservation and restoration of artistic bronzes meaning statues and sculptures, it is important understanding the patination processes and the knowledge of artificially corroded surfaces. Chemical and physical characterization of artificial patinas obtained on artistic bronzes and coppers by using the 19th century Western traditional patination techniques and recipes by means of SEM-EDS, light microscopy and ATR/FT-IR has been done in previous studies [I.Z. Balta, L. Robbiola, Characterization of artificial black patinas on artistic cast bronze and pure copper by using SEM-EDS and light microscopy, in: Proceedings of the 13th European Microscopy Congress, 22-27 August 2004, Antwerp, Belgium, EMC 2004 CD-Rom Conference Preprints; I.Z. Balta, L. Robbiola, Traditional artificial artistic bronze and copper patinas—an investigation by SEM-EDS and ATR/FT-IR, in: Proceedings of the 8th International Conference on Non Destructive Investigations and Microanalysis for the Diagnostics and Conservation of the Cultural and Environmental Heritage, 15-19 May 2005, Lecce, Italy, ART’05 CD-Rom Conference Preprints]. Differences in morphology (structure, thickness, porosity, adherence, compactity, uniformity, homogeneity) and also in composition, on both artistic cast bronze and pure copper patinas, were clearly evidenced. Further in-depth investigation is required to be carried out in order to better understand the patinas mechanisms of formation and the layers kinetics of growth. The elemental and chemical analysis, either on a surface monolayer or in a depth profile, by using the Secondary Ion Mass Spectrometry (SIMS) and X-ray Photoelectron Spectroscopy (XPS) techniques, can provide this kind of information, unique at trace-level sensitivity. SIMS has proved to be a suitable analytical technique for analyzing small amounts of material with high atomic sensitivity (ppm or even ppb) and high depth/lateral resolution in the micron and sub-micron range [R.G. Wilson, F.A. Stevie, C.W. Magee, Secondary Ion Mass Spectrometry: A Practical Handbook for Depth Profiling and Bulk Impurity Analysis, Wiley & Sons, New York, 1989; M. Dowsett, A. Adriaens, The role of SIMS in cultural heritage studies, Nucl. Instr. Meth. Phys. Res. B 226 (2004) 38-52]. XPS has the ability to provide detailed chemical information on virtually each kind of solid sample, and elemental identification is therefore possible due to the core level photoemission. The most important advantage is the high surface sensitivity of the chemical information (a few monolayers) [E. Ciliberto, G. Spoto, Modern Analytical Methods in Art and Archaeology, John Wiley & Sons, Inc., New York, 2000]. In addition elements’ relative abundance can be made semi-quantitative or quantitative and information on chemical bonds can be derived.The aim of the present work is to highlight the advantages and the limits of XPS and Dynamic SIMS surface analytical techniques for the characterization of artistic bronze and copper artificial patinas. The results obtained on the analyzed samples allowed the distribution of the main elements in the corrosion patinas layers and the contribution of each elements present in bronze matrix to the color of the resulting patinas to be precisely revealed. This information could be used for comparative studies between artificial and natural patinas, and also for provenience and authentication studies for artistic and archaeological bronzes.     

Buckling of an elastic hemispherical shell with an obstacle

We study the buckling of an axially symmetric elastic hemispherical shell, uniformly compressed, subject to a constraint to the radial shifting of the equatorial circumference. The static equilibrium equations, using tensorial notations, are obtained applying the virtual displacements principle to the energy functional. The presence of a constraint does not modify the field equations with respect to the case of a constraint-free buckling, but only influences the boundary conditions, so that, instead of a boundary value problem, we deal with a problem with complementarity conditions on the boundary. We revisit and improve some previously obtained mathematical results, adapting them for the subsequent numerical treatment. Finally, by suitably using a delicate quasi-static shooting technique, numerical results are obtained, which complete the theoretical analysis and give an interesting insight into the behavior of the bifurcation branches.