Theory of fluorescence depolarization in macromolecules and membranes

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Abstract
A comprehensive formalism is developed to describe the decay of the fluorescence emission anisotropy r(t) in macroscopically isotropic systems where both excited state and orientational dynamics contribute to the depolarization. It is shown how energy transfer, heterogeneity, and interconversion of excited states with different emission characteristics as well as both overall and internal reorientation can be treated in a unified way. Limits when the state and orientation dynamics are uncoupled and when the interconversion of the states is either much slower or much faster than the irreversible decay rates, are considered. A systematic treatment of the influence of internal motions is presented. First, the geometry of the transition dipoles is explicitly ‘‘factored out’’ and general expressions for r(t) are obtained for several cases including when the motion occurs about a fixed axis and an axis which in turn can ‘‘wobble’’ about a director. The initial and long‐time behavior of r(t) is examined and then, a variety of dynamical models (e.g., discrete jumps, free and restricted Langevin motion about an axis, diffusive motion of an axis in an orienting potential) are used to obtain the time dependence of the relevant correlation functions which appear in the above general expressions. In this way, one can obtain r(t) for a large class of models. Of particular interest is an approximate analytic expression for r(t), valid for any orientation of the transition dipoles and restricting potential, of a cylindrical probe in a membrane. The influence of collective (hydrodynamic) fluctuations of the membrane director are also considered.