Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

PROTEIN STRUCI'URE MODELLING OF THE BACTERIAL LIGHT-HARVESTING COMPLEX

Abstract Protein structure modelling offers a method of obtaining 3-dimensional information that can be tested and used to plan mutagenesis experiments when a crystallographically determined structure is not available. At its simplest a model may consist of little more than a secondary structure prediction coupled with a determination of the likely regions of transmembrane/membrane surface/globular configuration. These methods can yield an interesting topology map of the protein, which places the residues in their likely positions with respect to, for example, the membrane interface. If it is a member of a large family of related proteins then aligned protein sequences can be used to predict the residues that have an important function as these. will be largely conserved in the alignments. Using all these methods a model can be constructed (using for example, the Nicholson Molecular Modelling Kit) to visualize the proposed structure in three dimensions following the premise of good design, that is, avoiding obvious steric clashes, packing of helices in a realistic manner, observing the correct H-bond lengths, etc . In this latter exercise the review of Chothia ( Annu. Rev. Biochem . 53 , 537–572, 1984) of the principles of protein structure is particularly helpful as it clearly sets out how proteins pack and their preferred configuration. There is a wealth of information about individual amino acid conformational preferences and observed frequencies of occurrence in known protein structures, which can help decide how the residues in the model can be oriented.
In this article we have collated the various protein models of the bacterial light-harvesting complexes and present our own model, which is a synthesis of the available biophysical data and theoretical predictions, and show its performance in explaining recent results of site-directed mutants of the LHI and LH2 light-harvesting complexes of Rhodobacter sphaeroides .     

The molecular structure of beryllocene, (C5H5)2Be. A reinvestigation by gas phase electron diffraction

The electron scattering pattern of gaseous dicyclopentadienylberyllium, Cp₂Be, has been recorded from s = 2.00 to 39.00 Å⁻¹ with a nozzle temperature of about 120°C. Molecular models of D_5d symmetry or models containing one π-bonded and one σ-bonded Cp ring are not compatible with the data. The possibility the gaseous Cp₂Be consists fo a mixture D_5d and π-Cp, σ-Cp conformers is considered and rejected. A model of C_5v symmetry can be brought into satisfactory agreement with the data. It is also found that a slip sandwich model obtained from the C_5v model by moving sideways the ring which is at the greatest distance from Be, while keeping the two rings essentially parallel is compatible with the electron diffraction data. The best fit between experimental and calculated intensity curves is obtained with a model with a sideways slip of 0.8(1) Å. This model is similar to that indicated by the X-ray diffraction investigations by Wong and coworkers [4,5]. It is suggested that the potential energy of the molecule does not change much as the magnitude of the slip changes and that the molecule thus undergoes large amplitude vibration.     

Chiroptical properties of α-substituted succinic acids : Conformation and absolute configuration

The effect of conformational preference on the chiroptical properties of α-substituted succinic acids and esters 2 has been investigated using variable-temperature CD in solvents of different polarity. All available evidence indicates that when R' in 2 is alkyl or halogen, the preferred conformation is 1e with the -CH₂COOR group eclipsed by the CO bond, while when R' in 2 is hydroxy, methoxy or amino, the major conformer is 1d in which the heteroatom is eclipsed by the CO bond. In both cases, conformation 1f appears to be the least favored, mainly on steric grounds. The results when R' = chloro or bromo do not support previously proposed conclusions and an alternative explanation is advanced. In the resultant octant projection (Fig, 2) it is shown that the sign of the Cotton effect for 1 will be determined by the position of the groups X and Y in the back octants, and since one of these is always H in the two favored conformations, the sign is actually determined by the position of the other group. This octant projection predicts successfully the sign of the ellipticity of the n→π^* transition for any α-substituted succinic acid or ester with the appropriate substituent R', and appears to apply also to simple alkanoic acids and esters with the same substituents.