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A theoretical model is presented, tested and applied for determining the rates of energy migration and distances within pairs of chemically identical fluorophores, so-called donors (D), which are exposed to different physical properties. The model is a general extension of the recently developed donor–donor energy migration (DDEM) model [J. Chem. Soc., Faraday Trans. 92 (1996)1563; J. Chem. Phys. 105 (1996) 10896] that applies to examining structure-function of biomacromolecules, such as proteins. Most fluorescent groups of the same kind incorporated at different positions (α and β) in a macromolecule exhibit shifts of the absorption and/or emission spectra, as well as different relaxation rates of the photophysics. As a consequence, the energy migration between the Dα and Dβ groups will be partially reversible. We refer to this case, as the partial donor–donor energy migration (PDDEM). The models of PPDEM presented can be used for analysing time-resolved fluorescence relaxation, as well as fluorescence depolarisation experiments. To explore the limitations of the PDDEM model, we have generated and re-analysed synthetic data that mimic time-correlated single photon counting (TCSPC) experiments. It was found that slow and fast rates of energy migration are most accurately recovered from the fluorescence relaxation and the depolarisation experiments, respectively. At comparable transfer and fluorescence rates, both kinds of experiments are equally useful. Real experiments on PDDEM were performed on an asymmetrically quenched bichromophoric molecule (1,32-dihydroxy-dotriacontane-bis-(Rhodamine 101) ester), that spans across the lipid bilayer of a vesicle. The depolarisation data were analysed by the PDDEM model and provide a distance between Rhodamine 101 groups, which agrees with independent studies

For distance measurements the fluorescence relaxation was explored within pairwise interacting chemically identical, but photophysically different fluorescent groups. The recently developed theory (Kalinin, S. V.; et al. Spectrochim. Acta, Part A 2002, 58, 1087-1097) of partial donor-donor energy migration (PDDEM) was tested on lipid vesicles as a model system, which, for example, enables arrangement of a pH gradient between the inside and outside of the lipid bilayer. Time-correlated single-photon counting and steady-state fluorescence experiments were performed on mono- and bis-lipid derivatives of fluorescein solubilized in lipid bilayers. The PDDEM approach was successfully applied in the analyses of the different experiments. The distances extracted between the fluorescein groups of bis-fluorescein derivatives in lipid vesicles composed 1,2-dioleoyl-sn-glycero-3-phosphocholine and 1,2-dimyristoyl-sn-glycero-3-phosphocholine were found to be in reasonable agreement with independent measurements of the bilayer thickness.

We show that the photophysics of chemically identical but photophysically non-identical fluorescent pairs can be used for measuring distances within proteins. For this purpose, the theory of partial donor-donor energy migration (PDDEM, S. Kalinin, J. G. Molotkovsky and L. B.-Angstrom. Johansson, Spectrochim. Acta, Part A, 2002, 58, 1057-1097) was applied for distance measurements between BODIPY groups covalently linked to cystein residues in plasminogen activator inhibitor of type 2 (PAI-2). Two sulfhydryl specific derivatives of BODIPY were used namely: N-(4,4-difluoro-1,3,5,7-tetramethyl-4-bora-3a,4a-diaza-s-indacene-2-yl) iodoacetamide and N-(4.4-difluoro-5.7-ditriethyl-4-bona-3a,4a-diaza-s-indacene-3-yl) methyl iodoacetamide. To determine distances, the time-resolved fluorescence relaxation for two singly labelled forms of PAI-2, as well as the corresponding doubly labelled protein were combined and analysed in a global manner. Fluorescence depolarisation experiments on the labelled mutants were also analysed. The distances determined by PDDEM were in good agreement to those obtained from donor-donor energy migration (DDEM) experiments and structural data on PAI-2. The PDDEM approach allows for the use of very different fluorescent probes, which enables wide range of distances to be measured. The PDDEM model also provides a rational explanation to why previous observations of polyfluorophore-labelled proteins exhibit a shorter average fluorescence lifetime compared to the arithmetic average of lifetimes obtained for the corresponding single labelled proteins.

Fluorescent groups typically exhibit nonexponential photophysics when incorporated into biomolecular structures, e.g., proteins and lipid membranes. Models assuming discrete and continuous distributions of lifetimes can each accurately describe the observed relaxation. In the analyses of energy transfer and PDDEM (partial donor-donor energy migration) experiments, one frequently needs to model the nonexponential decays of noninteracting donor and acceptor groups. The present paper aims at exploring whether calculated transfer/migration rates depend on modeling the photophysics' decay by discrete or continuous distributions of lifetimes. Discrete or continuous distribution models of the decay, generated synthetically, were analyzed as well as true experimental data. Two proteins were studied. In one of the systems, we examined energy transfer from Trp (donor) to BODIPY (acceptor) in ribosomal protein S6, obtained from Thermus thermophilus. In the second system, we examined PDDEM between different BODIPY derivatives that were pairwise specifically incorporated in mutant forms of plasminogen activator inhibitor type 2. Interestingly, the rates of electronic energy migration/transfer and distances determined within pairs of interacting chromophores reveal small or negligible influence on using discrete or continuous distributions of lifetimes.