Structure and Dynamics of Coil-like Molecules by Residual Dipolar Couplings

Nuclear magnetic resonance (NMR) spectroscopy provides us with many means to study biological macromolecules in solution. Proteins in particular are the most intriguing targets for NMR studies. Protein functions are usually ascribed to specific three-dimensional structures but more recently tails, long loops and non-structural polypeptides have also been shown to be biologically active. Examples include prions, -synuclein, amylin and the NEF HIV-protein. However, conformational preferences in coil-like molecules are difficult to study by traditional methods. Residual dipolar couplings (RDCs) have opened up new opportunities; however their analysis is not trivial. Here we show how to interpret RDCs from these weakly structured molecules. The most notable residual dipolar couplings arise from steric obstruction effects. In dilute liquid crystalline media as well as in anisotropic gels polypeptides encounter nematogens. The shape of a polypeptide conformation limits the encounter with the nematogen. The most elongated conformations may come closest whereas the most compact remain furthest away. As a result there is slightly more room in the solution for the extended than for the compact conformations. This conformation-dependent concentration effect leads to a bias in the measured data. The measured values are not arithmetic averages but essentially weighted averages over conformations. The overall effect can be calculated for random flight chains and simulated for more realistic molecular models. Earlier there was an implicit thought that weakly structured or non-structural molecules would not yield to any observable residual dipolar couplings. However, in the pioneering study by Shortle and Ackerman RDCs were clearly observed. We repeated the study for urea-denatured protein at high temperature and also observed indisputably RDCs. This was very convincing to us but we could not possibly accept the proposed reason for the non-zero RDCs, namely that there would be some residual structure left in the protein that to our understanding was fully denatured. We proceeded to gain understanding via simulations and elementary experiments. In measurements we used simple homopolymers with only two labelled residues and we simulated the data to learn more about the origin of RDCs. We realized that RDCs depend on the position of the residue as well as on the length of the polypeptide. Investigations resulted in a theoretical model for RDCs from coil-like molecules. Later we extended the studies by molecular dynamics. Somewhat surprisingly the effects are small for non-structured molecules whereas the bias may be large for a small compact protein. All in all the work gave clear and unambiguous results on how to interpret RDCs as structural and dynamic parameters of weakly structured proteins.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}