A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Unveiling the components of the signaling pathway between endosomes and the phagocytic uptake machinery in Dictyostelium discoideum

The soil amoebae Dictyostelium discoideum take up particles from their environment in order to obtain nutrition. The particle transits through the cell within a phagosome that fuses with organelles of different molecular compositions, undergoing a gradual degradation by different sets of hydrolytic enzymes. Griffiths’ concept of “phagosome individuality” predicts signaling from phagosomes into the cytoplasm, which might regulate many aspects of cell physiology. The finding that Dictyostelium cells depleted of the lysozyme AlyA or over-expressing the esterase Gp70 exhibit increased uptake of food particles, led to the postulation of a signaling cascade between endocytic compartments and the cytoskeletal uptake machinery at the plasma membrane. Assuming that Gp70 acts downstream of AlyA, gene-expression profiling of both mutants revealed different and overlapping sets of misregulated genes that might participate in this signaling cascade. Based on these results, we analyzed the effects of the artificial misregulation of six candidate genes by over-expression or negative genetic interference, in order to reconstruct at least part of the signaling pathway. SSB420 and SSL793 were chosen as candidates for the first signaling step, as they were up-regulated in AlyA-null cells and remained unaltered in the Gp70 over-expressing cells. The over-expression of SSB420 enhanced phagocytosis and raised the expression levels of Gp70, supporting its involvement in the signaling pathway between AlyA and Gp70 as a positive regulator of phagocytosis. However, this was not the case of cells over-expressing SSL793, as this mutation had no effects on phagocytosis. For the signaling downstream of Gp70, we studied four commonly misregulated genes in AlyA-depleted and Gp70 over-expressing cells. The expression levels of SLB350, SSB389 and TipD were lower in both mutants and therefore these were assumed as possible candidates for the negative regulation of phagocytosis. Cells depleted of SLB350 exhibited an increased phagocytic activity and no effect on Gp70 expression, proving its participation in the signaling pathway downstream of Gp70. Unlike SLB350, the disruption of the genes coding for SSB389 and TipD had no effects on particle uptake, excluding them from the pathway. The fourth candidate was Yipf1, the only gene that was commonly up-regulated in both mutants. Yet, the artificial over-expression of this protein had no effects on phagocytosis, so this candidate is also not included in the signaling pathway. Furthermore, localizing the products of the candidate genes within the cell helped unveiling several cellular organelles that receive signals from the phagosome and transduce them towards the uptake machinery.

Precision laser spectroscopy of the ground state hyperfine splitting of hydrogenlike ^209 Bi^82+

The first direct observation of a hyperfine splitting in the optical regime is reported. The wavelength of the M1 transition between the F = 4 and F = 5 hyperfine levels of the ground state of hydrogenlike ^209 Bi^82+ was measured to be \lamda_0 = 243.87(4) nm by detection of laser induced fluorescence at the heavy-ion storage ring ESR at GSI. In addition, the lifetime of the laser excited F = 5 sublevel was determined to be \tau_0 = 0.351(16) ms. The method can be applied to a number of other nuclei and should allow a novel test of QED corrections in the previously unexplored combination of strong magnetic and electric fields in highly charged ions.