Theory Of Fluorescence Depolarization Research Articles

Solvent-Dependent Changes in Molecular Reorientation Dynamics: The Role of Solvent−Solvent Interactions

We report on the rotational diffusion dynamics of two different chromophores, resorufin and 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)hexanoic acid (NBDHA) in water and N-octyl-2-pyrrolidone (NOP) solvents. We measure the induced orientational anisotropy function, R(t), using time-correlated single photon counting. Our data show that both chromophores exhibit single exponential anisotropy decays in aqueous solution and two-component exponential anisotropy decays in NOP. The change of the anisotropy decay functionality indicates that the effective rotor shape swept out by solute rotational motion is different in the two solvents. We interpret these findings in the context of Chuang and Eisenthal's theory of fluorescence depolarization by rotational diffusion. The similarity in the behavior of the two different chromophores in these solvent systems points to solvent-solvent interactions and local organization as the dominant factors in mediating motional dynamics.

Theory of fluorescence depolarization in macromolecules and membranes

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.

A theory of fluorescence depolarization in membranes

A theory of time dependent fluorescence depolarization for a probe in a membrane vesicle or in a poly-liquid-crystalline system is presented. General, model independent expressions for the polarization ratio r(t) as a function of time are obtained in terms of orientational correlation functions ϕmn(t). It is shown that only certain combinations of ϕmn(t) corresponding to relative orientations correlation functions contribute to r(t). Short time, r(0) and long time, r(∞) values are worked out in detail for biaxial and cylindrically symmetric probes in a locally uniaxial mesophase. The dynamical information available in the experiment is discussed in detail for uniaxial probes using the diffusional and strong collision reorientation model. It is shown that the two models predict different initial slopes r(0). Steady state expressions are obtained and the differences with previous theories discussed. Finally the effect of overall vesicle reorientation is briefly examined with a view to the application of the...

Effect of librational motion on fluorescence depolarization and nuclear magnetic resonance relaxation in macromolecules and membranes

The theory of fluorescent emission anisotropy [r(t)] of a cylindrical probe in a membrane suspension is developed. It is shown, independent of any model, that the limiting anisotropy [r(infinity)] is proportional to the square to the order parameter of the probe. The order parameter determines the first nontrivial term in the expansion of the equilibrium orientational distribution function of the probe in a series of Legendre polynomials. Following Kinosita, Kawato, and Ikegami, the motion of the probe is described as diffusion ("wobbling") within a cone of semiangle theta 0. Within the framework of this model, an accurate single-exponential approximation for r(t) is considered. An analytic expression relating the effective relaxation time, which appears in the above approximation, to theta 0 and the diffusion coefficient for wobbling is derived. The model is generalized to the situation where the probe is attached to a macromolecule whose motion cannot be neglected on the time scale of the fluorescence experiment. Finally, by exploiting the formal similarity between the theory of fluorescence depolarization and 13C-NMR dipolar relaxation, expressions for T1, T2, and the nuclear Overhauser enhancement are derived for a protonated carbon which is nonrigidly attached to a macromolecule and undergoes librational motion described as diffusion on a spherical "cap" of semiangle theta 0.

Theory of Fluorescence Depolarization by Anisotropic Brownian Rotations. Discontinuous Distribution Approach

In this paper, we generalize to molecules devoid of symmetry the phenomenological treatment of depolarization of the fluorescence by the Brownian rotations of a spherical molecule due to Spencer and Weber. There are six ways in which a system of orthogonal coordinates rigidly bound to the molecule may be made to coincide with the laboratory coordinates. The transitions between these permissible orientations gives rise to a system of six differential equations of transport, the solution of which entails that of a differential equation of sixth order. However, because of the equivalence of some of the rotations as regards the depolarizing effects, on account of the symmetry conditions, the solution of a differential equation of third order is only necessary. Consequently, after an instantaneous light pulse, a polarized component of the fluorescence will show a maximum of three exponential decays and the difference of parallel and perpendicular components a maximum of only two decays. The steady-state fluorescence polarization from a completely assymetric molecule is given by a simple expression containing as only parameters a mean rotational rate, the variance of three orthogonal rates of rotation, and an average of these rates weighted according to their angles with the emission oscillator. A qualitative comparison of this treatment with previous theories of depolarization that make use of classical rotary diffusion theory shows that the former is better suited to an intuitive understanding of the phenomena and to experimental usage.