Numerical analysis of the rotational relaxation time of spectrin segments and spectrin heterodimer in dilute aqueous solution

The rotational relaxation time for different models of the spectrin αβ-heterodimer and spectrin subunits were obtained through numerical simulation making use of the so-called rigid-body approximation. Based on information on the helix structure of the 106 aminoacids in the repeating motif of spectrin, three different models with varying degree of refinement were set up to represent the spectrin subunits: the two-bead, the many-bead and the shell model. For one- and two-subunit spectrin the relaxation time was found to be 20 ± 4 ns and 92 ± 5 ns, respectively. The last result conforms well with available experimental data from transient electric birefringence measurements. For the αβ-heterodimer two different models were applied: a chain of beads (pearl necklace model) and a more refined so-called San necklace model. Using the San necklace model, the relaxation time was found to be in the range of 9 to 18 μs (depending on the flexibility of the joint), which is in accordance with what has been obtained from intrinsic viscosity measurements, but considerably higher than experimental data from measurements of transient electric birefringence.     

Multicenter bonding within the AIM theory

This study reports the incorporation of recently proposed formalism for the detection and localization of multicenter bonding in molecules, the so-called generalized population analysis, into the framework of the atoms in molecules (AIM) theory. The reliability of this new approach is tested by direct numerical comparison of the values of multicenter bond indices derived from both the original and the AIM-generalized forms of the population analysis. Received: 1 June 2000 / Accepted: 11 October 2000 / Published online: 23 January 2001     

Midisuperspace Models of Canonical Quantum Gravity

A midisuperspace model is a field theoryobtained by symmetry reduction of a parent gravitationaltheory. Such models have proven useful for exploring theclassical and quantum dynamics of the gravitational field. I present three recent classes ofresults pertinent to canonical quantization of vacuumgeneral relativity in the context of midisuperspacemodels. (1) I give necessary and sufficient conditions such that a given symmetry reduction can beperformed at the level of the Lagrangian or Hamiltonian.(2) I discuss the Hamiltonian formulation of modelsbased upon cylindrical and toroidal symmetry. In particular, I explain how these models can beidentified with parametrized field theories of wavemaps; thus a natural strategy for canonical quantizationis available. (3) The quantization of a parametrized field theory, such as the midisuperspace modelsconsidered in (2), requires construction of a quantumfield theory on a fixed (flat) spacetime that allows fortime evolution along arbitrary foliations of spacetime. I discuss some recent results on thepossibility of finding such a quantum fieldtheory.     

Changing shapes: adiabatic dynamics of composite solitary waves

We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite nonlinear non-dispersive waves points to variations in shape.     

Conventional and modified Schwarzschild objective for EUV lithography: design relations

The design criteria of a Schwarzschild-type optical system are reviewed in relation to its use as an imaging system in an extreme ultraviolet lithography setup. Both the conventional and the modified reductor imaging configurations are considered, and the respective performances, as far as the geometrical resolution in the image plane is concerned, are compared. In this connection, a formal relation defining the modified configuration is elaborated, refining a rather naïve definition presented in an earlier work. The dependence of the geometrical resolution on the image-space numerical aperture for a given magnification is investigated in detail for both configurations. So, the advantages of the modified configuration with respect to the conventional one are clearly evidenced. The results of a semi-analytical procedure are compared with those obtained from a numerical simulation performed by an optical design program. The Schwarzschild objective based system under implementation at the ENEA Frascati Center within the context of the Italian FIRB project for EUV lithography has been used as a model. Best-fit functions accounting for the behaviour of the system parameters vs. the numerical aperture are reported; they can be a useful guide for the design of Schwarzschild objective type optical systems.     

Synthesis, structural characterization and ex vivo biological properties of a new complex [Cu(propranolol)2]·2H2O, a potential beta-blocker

The synthesis and spectroscopic characterization (UV–Vis, IR, EPR) of a new copper complex with a beta-blocker propranolol (1-(isopropylamino)-3-(1-naphthyloxy)-2-propanol) are presented. Besides, the X-ray crystal structure of [Cu(propranolol)₂]·2H₂O is determined, showing two different copper ions, one coordinated through two S propranolol isomers and the other through two R isomers. The effect on the heart contraction force and on the heart rate plus the block of response to adrenaline of the complex and the free ligand, were studied. The effect of [Cu(propranolol)₂]·2H₂O on contractility was very similar to that of the free propranolol while the reduction on the heart rate is approximately 30% of the reduction obtained with the free ligand. This is an encouraging result since the search of new beta-blocker drugs that have lesser effect on heart rate is one of the important topics in cardiac pharmacology. The block of the response to adrenaline is at least similar for both ligand and complex.     

Weighted and Ergodic Theorems for Series of Differences of Convolutions

We extend some results of C. Demeter about the boundedness of series of difference of convolutions to the setting of one-sided A _p weights. We need to use a different approach. To be precise, we prove that the kernel of the associated operator satisfies a generalized Hörmander condition. The weighted inequalities allow us to transfer the result to the ergodic case, when the operator is induced by a mean bounded, invertible, positive groups.     

Further comparisons between the conventional and the modified Schwarzschild objectives

The performance of the modified Schwarzschild objective configuration in comparison with the ordinary configuration is further investigated, completing the analysis presented in a previous work, which was concerned with the trend of the image-plane resolution against the numerical aperture. Here, we compare the third-order aberration coefficients in both configurations, illustrating the dependence of each coefficient on both the on-axis object position and the numerical aperture. This conveys the tolerances of the two configurations to lateral and mirrors’ axial misalignments. Also, the nonconcentric mirror configuration is considered and the relative performance confronted with that of the modified configuration. PACS 42.15.Eq; 42.82.Cr     

Diversity oriented synthesis of hispanane-like terpene derivatives from (R)-(+)-sclareolide

(R)-(+)-Sclareolide 1 has been used as a starting material to develop a diversity oriented methodology to access hispanane 28 a, and hispanane-like derivatives 27 b-27 e. This methodology is based on the intramolecular Friedel-Crafts acylation of the corresponding 12-desoxylabdanoic-like acids 27, for the construction of the cycloheptane ring which is characteristic of the hispananes. Acids 27 are obtained from alcohols 20, available by addition of the lithium or magnesium reagents to amide 12 (followed by Luche reduction), or to aldehyde 21. This sequence has resulted in the preparation of hispanane framework 27 a. The versatility of this methodology therefore allows a structural diversity oriented synthesis, since it allows the access to a wide variety of hispanane-like derivatives.