A new and general procedure is described for a detailed analysis of time-resolved fluorescence depolarisation data in the presence of electronic energy migration. An isotropic ensemble of bifluorophoric molecules (D1-R-D2) has been studied to demonstrate its utility. Intramolecular donor-donor energy migration occurs between the two donor groups (D), which are covalently connected to a rigid linker group (R). These groups undergo restricted reorientational motions with respect to the R group. The analysis of depolarisation data basically involves the search for best-fit parameters which describe the local reorienting motions, the interfluorophore D1-D2 distance, as well as the mutual orientations of the donors. For this, the analysis is partly performed in the Fourier domain and the best-fit parameters are determined by using an approach based on a Genetic Algorithm. The energy migration process has been described by using Monte Carlo simulations and an extended Förster theory. It is found that this theory provides the least time-consuming computational method. Since one-photon and two-photon excited fluorescence experiments can be applied for energy migration studies, a general and unified theoretical formulation is given. To exemplify the developed quantitative approach the depolarisation of the fluorescence in the presence of electronic energy migration within a bis-(9-anthrylmethylphosphonate) bisteroid molecule has been studied by time-resolved two-photon excited fluorescence depolarisation experiments. To solely obtain information about local reorientations of the 9-anthrylmethyl group, also the mono-(9-anthrylmethylphosphonate) bisteroid was studied, which enabled modelling of the ordering potential of the donor. Values of the two-photon absorption tensor components were obtained. To describe the discrepancy between the measured values of the initial anisotropy and fundamental anisotropy predicted by theory the distribution of absorption tensor caused by fast processes have been introduced. An angular parameter of absorption tensor was determined. Reasonable values of the distance between the 9-anthrylmethyl groups, as well as for their mutual orientation were obtained.

<p>We have studied fundamental aspects of time-resolved two-photon excited fluorescence depolarisation. The thesis presents experimental as well as theoretical progress. We show that a multi-photon induced instrumental response function obtained from a suspension of gold nanoparticles is appropriate for the analysis of two-photon excited fluorescence decays obtained using time-correlated single photon counting detection. Theoretical expressions have been derived for the fluorescence anisotropy decay obtained upon two-photon excitation of various molecular systems in liquid solutions: a) an anisotropic rigid rotor that undergoes rotational diffusion in the presence of ultrafast unresolved restricted reorientations, e.g. librations. b) a molecular group covalently attached to a stationary macromolecule, and undergoing local reorientation in a uniaxial ordering potential. A new approach to the analysis of two-photon excited fluorescence depolarisation experiments was developed, which combines data obtained by using linearly and circularly polarised excitation light, in a global manner. In the analysis, knowledge about unresolved reorientations was obtained from one-photon excitation studies of the corresponding systems. By means of this procedure it has been possible to obtain quantitative information about the molecular two-photon absorption tensor for perylene and two of its derivatives. Thereby the symmetry of the final excited and intermediate vibronic states could be assigned. The analysis reveals that the two-photon transition studied with the 800 nm laser exhibits mixed character. An important finding from the experiments was that the two-photon absorption tensor appears to be solvent dependent. Furthermore, the thesis presents the first theoretical treatment of two-photon excited donor-donor energy migration in the presence of molecular reorientation and which applies the extended Förster theory. Explicit expressions for molecules that belong to the point groups D_2h, D₂ and C_2v are given. Preliminary experiments are finally also reported on a two-photon excited donor-donor energy migration system consisting of a bisanthryl-bisteroid. </p>

We have studied fundamental aspects of time-resolved two-photon excited fluorescence depolarisation. The thesis presents experimental as well as theoretical progress. We show that a multi-photon induced instrumental response function obtained from a suspension of gold nanoparticles is appropriate for the analysis of two-photon excited fluorescence decays obtained using time-correlated single photon counting detection. Theoretical expressions have been derived for the fluorescence anisotropy decay obtained upon two-photon excitation of various molecular systems in liquid solutions: a) an anisotropic rigid rotor that undergoes rotational diffusion in the presence of ultrafast unresolved restricted reorientations, e.g. librations. b) a molecular group covalently attached to a stationary macromolecule, and undergoing local reorientation in a uniaxial ordering potential. A new approach to the analysis of two-photon excited fluorescence depolarisation experiments was developed, which combines data obtained by using linearly and circularly polarised excitation light, in a global manner. In the analysis, knowledge about unresolved reorientations was obtained from one-photon excitation studies of the corresponding systems. By means of this procedure it has been possible to obtain quantitative information about the molecular two-photon absorption tensor for perylene and two of its derivatives. Thereby the symmetry of the final excited and intermediate vibronic states could be assigned. The analysis reveals that the two-photon transition studied with the 800 nm laser exhibits mixed character. An important finding from the experiments was that the two-photon absorption tensor appears to be solvent dependent. Furthermore, the thesis presents the first theoretical treatment of two-photon excited donor-donor energy migration in the presence of molecular reorientation and which applies the extended Förster theory. Explicit expressions for molecules that belong to the point groups D2h, D2 and C2v are given. Preliminary experiments are finally also reported on a two-photon excited donor-donor energy migration system consisting of a bisanthryl-bisteroid.

A kinetic model of electronic energy migration within pairs of photophysically non-identical fluorophores has been developed. The model applies to fluorescent groups that exhibit different photophysical and spectral properties when attached to different positions in a macromolecule. The energy migration within such asymmetric pairs is partially reversible, which leads to the case of partial donor-donor energy migration (PDDEM). The model of PDDEM is an extension of the recently developed donor-donor energy migration model (DDEM, F. Bergström et al, PNAS 96 (1999) 12477), and applies to quantitative measurements of energy migration rates and distances within macromolecules. One important distinction from the DDEM model is that the distances can be obtained from fluorescence lifetime measurements. A model of fluorescence depolarisation in the presence of PDDEM is also presented. To experimentally test the PDDEM approach, different model systems were studied. The model was applied to measure distances between rhodamine and fluorescein groups within on-purpose synthesised molecules that were solubilised in lipid bilayers. Moreover, distances were measured between BODIPY groups in mutant forms of the plasminogen activator inhibitor of type 2 (PAI-2). Measurements of both the fluorescence intensity decays and the time-resolved depolarisation were performed. The obtained distances were in good agreement with independent determinations. Finally, the PDDEM within pairs of donors is considered, for which both donors exhibit a nonexponential fluorescence decay. In this case it turns out that the fluorescence relaxation of a coupled system contains distance information even if the photophysics of the donors is identical. It is also demonstrated that the choice of relaxation model has a negligible effect on the obtained distances. The latter conclusion holds also for the case of donor-acceptor energy transfer.

The homo and hetero dimerisation of two spectroscopically different chromophores were studied, namely: 4,4-difluoro-4-bora-3a,4a-diazas-indacene (g-BODIPY) and its 5-styryl-derivative (r-BODIPY). Various spectroscopic properties of the r-BODIPY in different common solvents were determined. It was shown that g- and r-BODIPY in the ground state can form homo- as well as hetero dimers. We demonstrate that the ganglioside GM1 in lipid bilayers of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) exhibits a non-uniform lateral distribution, which is an argument in favour of self-aggregation of GM1 being an intrinsic property of the GM1. This was concluded from energy transfer/migration studies of BODIPY-labelled gangliosides. An algorithm is presented that quantitatively accounts for donor–donor energy migration (DDEM) among fluorophore-labelled proteins forming regular non-covalent polymers. The DDEM algorithm is based on Monte Carlo (MC) and Brownian dynamics (BD) simulations and applies to the calculation of fluorescence depolarisation data, such as the fluorescence anisotropy. Thereby local orientations, as well as reorienting motions of the fluorescent groups are considered in the absence and presence of DDEM among them. A new method, in which a genetic algorithm (GA) was combined with BD and MC simulations, was developed to analyse fluorescence depolarisation data collected by the time-correlated single photon counting technique. It was applied to study g-BODIPY-labelled filamentous actin (F-actin). The technique registered the local order and reorienting motions of the fluorophores, which were covalently coupled to cysteine 374 (C374) in actin and interacted by means of electronic energy migration within the polymer. Analyses of F-actin samples composed of different fractions of labelled actin molecules revealed the known helical organiszation of F-actin, and demonstrated the usefulness of this technique for structure determination of complex protein polymers. The distance from the filament axis to the fluorophore was found to be considerably less than expected from the proposed position of C374 at a high filament radius. In addition, polymerisation experiments with BODIPY-actin suggest a 25-fold more efficient signal for filament formation than pyrene-actin.