THEORETICAL STUDIES OF BILIPROTEIN CHROMOPHORES AND RELATED BILE PIGMENTS BY MOLECULAR ORBITAL AND RAMACHANDRAN TYPE CALCULATIONS

Ramachandran calculations have been used to gain insight into steric hindrance in bile pigments related to biliprotein chromophores. The high optical activity of denatured phycocyanin, as compared to phycoerythrin, has been related to the asymmetric substitution at ring A, which shifts the equilibrium towards the P-helical form of the chromophore. Geometric effects on the electronic structures and transitions have then been studied by molecular orbital calculations for several conjugation systems including the chromophores of phycocyanin. phytochrome P,, cations, cation radicals and tautomeric forms. For these different chromophores some general trends can be deduced. For instance, for a given change in the gross shape (e.g. either unfolding of the molecule from a cyclic-helical to a fully extended geometry, or upon out-of-plane twists of the pyrrole ring A) of the molecules under study, the predicted absorption spectra all change in a simikar way. Nonetheless, there are characteristic distinctions between the different n-systems, both in the transition energies and the charge distribution, which can be related to their known differences in spectroscopic properties and their reactivity

Infrared spectroscopy of phytochrome and model pigments

Fourier-transform infrared difference spectra between the red-absorbing and far-red-absorbing forms of oat phytochrome have been measured in H2O and 2H2O. The difference spectra are compared with infrared spectra of model compounds, i.e. the (5Z,10Z,15Z)- and (5Z,10Z,15E)-isomers of 2,3,7,8,12,13,17,18-octaethyl-bilindion (Et8-bilindion), 2,3-dihydro-2,3,7,8,12,13,17,18-octaethyl-bilindion (H2Et8-bilindion), and protonated H2Et8-bilindion in various solvents. The spectra of the model compounds show that only for the protonated forms can clear differences between the two isomers be detected. Since considerable differences are present between the spectra of Et8-bilindion and H2Et8-bilindion, it is concluded that only the latter compound can serve as a model system of phytochrome. The 2H2O effect on the difference spectrum of phytochrome supports the view that the chromophore in red-absorbing phytochrome is protonated and suggests, in addition, that it is also protonated in far-red-absorbing phytochrome. The spectra show that protonated carboxyl groups are influenced. The small amplitudes in the difference spectra exclude major changes of protein secondary structure

Comparison of two different approaches for computing the gravitational effect of a tesseroid

Forward modelling in the space domain is a very important task in geodesy and other geosciences. From topographical or isostatic information in the form of digital terrain model (DTM) and density model, the effects of these parameters or their derivatives on the gravity potential can be evaluated for different applications. In most cases, height or height-layer models are in use, which are gridded with respect to spherical coordinates. This holds for global as well as regional or even local applications. The definition of the spherical gridlines leads immediately to the spherical volume element, that is, the tesseroid. Only in the specific case that the observation point is located on the symmetry axis of the spherical coordinate system does the Newton integral have a closed analytical solution. More specifically, the effect of a tesseroid can be determined by evaluating the analytical solution of a segment of a spherical zonal band. To apply this aspect in practice, the DTM must be transformed into the local spherical azimuthal system of the observation point (UNIPOL approach). In the general case, the Newton integral can be solved, for example, using a Taylor series expansion of the integral kernel and a subsequently applied term-wise integration (GIK approach). Within this contribution, the two fundamentally different tesseroid approaches, namely, the GIK and the UNIPOL approach are compared. This comparison is performed, in particular, with regard to the required computational time and the approximation error under different test scenarios. The numerical studies show that both approaches are equivalent in terms of accuracy for both the gravitational potential and gravity; however, the UNIPOL approach is more time consuming because, for each observation point, the whole DTM must be transformed. Small numerical differences exist between the compared approaches for special constellations regarding the source point and the observation point