Theory of two-photon induced fluorescence anisotropy decay in membranes

We report the first theoretical description for the time-dependent fluorescence anisotropy decay resulted from two-photon excitation (r([2])(t)) for fluorophores in macroscopically isotropic and oriented membranes. In case of two-photon excitation, the initial value of the fluorescence anisotropy r([2])(0) immediately after excitation by a flash of polarized light is a function of the components of the two-photon absorption transition tensor [unk]S and the projections of the emission transition moment to the principal axes of [unk]S. The components of [unk]S depend on the symmetries of all molecular states relevant to the two-photon absorption process. The maximal value of r([2])(0) is proven to be as large as 0.61 in contrast to 0.4 for the conventional one-photon induced fluorescence anisotropy r([1])(0). It is shown that only for some special cases the ratio of the two-photon r([2])(t) over the conventional one-photon r([1])(t) will be a constant at all times for fluorophores in macroscopically isotropic membrane systems. In oriented membrane systems, an additional order parameter can be determined by the use of angle-resolved fluorescence depolarization measurements resulted from two-photon excitation. The advantages of measuring time-resolved fluorescence anisotropy decays or angle-resolved fluorescence depolarization ratios by two-photon excitation for the study of orientational dynamics in isotropic or oriented membranes are discussed from the theoretical point of view.