Depolarization fluorophore rotation

One can employ linearly polarized light to excite selectively those fluorophores that are in a particular orientation. The difference between excitation and emitted light polarization changes whenever fluorophores rotate during the period of time between excitation and emission. The magnitude of depolarization can be measured, and one can therefore deduce the fluorophore s rotational relaxation kinetics. Extrinsic fluorescence probes are especially useful here, because the proper choice of their fluorescence lifetime will greatly improve the measurement of rotational relaxation rates. One can also determine the freedom of motion of the probe relative to the rotational diffusion properties of the macromolecule to which it is attached. When held rigidly by the macromolecule, the depolarization of a probe s fluorescence is dominated by the the motion of the macromolecule. 

Fluorescence polarization cannot attain the +1 theoretical limits for maximum beam polarization owing to the nature of the absorption and emission processes, which usually correspond to electric dipole transitions. Although the excitation with linearly polarized radiation favours certain transition dipole orientations (hence certain fluorophore orientations, and the so-called photoselection process occurs), a fairly broad angular distribution is still obtained, the same happening afterwards with the angular distribution of the radiation of an electric dipole. The result being that, in the absence of fluorophore rotation and other depolarization processes, the polarization obeys the Lev shin-Perrin equation,... 

The two most important depolarization mechanisms that give rise to a time-dependent anisotropy are fluorophore rotation and energy transfer. Energy transfer leads to depolarization as the hopping of excitation from one fluorophore to another, when not parallel, is equivalent to an angular displacement. 

In these multichromophoric cyclodextrins the fluorophores are randomly oriented. Excitation of one of the naphthoate fluorophores is followed by efficient dipole-dipole excitation energy transfer between the seven fluorophores, with a Forster radius of 14 A. This process is not detectable by fluorescence intensity measurements, as neither the intensity nor the decay law are affected by energy transfer between identical fluorophores (also called homotransfer. The dynamics of energy hopping are on the other hand reflected in the fluorescence anisotropy. To avoid depolarization by rotational motion of the fluorophores, experiments were conducted in a low temperature and optically clear rigid glass (9 1 ethanol-methanol at 110 K). 

Several phenomena can render the measured anisotropy to values lower than the maximum achievable theoretical values. The most common cause is diffusion of a macromolecule to which the fluorophore is attached. Such rotational diffusion occurs during the lifetime of the excited state and displaces the emission dipole of the fluorophore. Measurement of this parameter provides information regarding the relative angular displacement of the fluorophore between the times of absorption and emission. In fluid solution, most fluorophores rotate extensively in 50-100ps. Hence, the molecules can rotate many times during the typical 1-10 ns excited-state fluorescence lifetime, and the orientation of the polarized emission easily becomes randomized or depolarized. For... 

If the only significant process for depolarization is rotational relaxation, then the fluorescence anisotropy, for a single molecule or fluorophore, may be given by a form of the Perrin equation ... 

By the use of fluorescence lifetime instrumentation, one can further determine the evolution of the fluorescence anisotropy with time during and beyond the lifetime of the excited state. In the simplest case of a fluorophore in solution, with a single fluorescence lifetime and depolarization through rotational relaxation alone, the fluorescence anisotropy will decay according to... 

Molecular Rotational Diffusion. Rotational diffusion is the dominant intrinsic cause of depolarization under conditions of low solution viscosity and low fluorophore concentration. Polarization measurements are accurate indicators of molecular size. Two types of measurements are used steady-state depolarization and time-dependent (dynamic) depolarization. 

Steady-State Fluorescence Depolarization Spectroscopy. For steady state depolarization measurements, the sample is excited with linearly polarized lig t of constant intensity. Observed values of P depend on the angle between the absorption and emission dipole moment vectors. In equation 2 (9), Po is the limiting value of polarization for a dilute solution of fluorophores randomly oriented in a rigid medium that permits no rotation and no energy transfer to other fluorophores ... 

Time Resolved Fluorescence Depolarization. In Equation 3, it is assumed that the polarization decays to zero as a single exponential function, which is equivalent to assuming that the molecular shape is spherical with isotropic rotational motion. Multiexponential decays arise from anisotropic rotational motion, which might indicate a nonspherical molecule, a molecule rotating in a nonuniform environment, a fluorophore bound to tbe molecule in a manner that binders its motion, or a mixture of fluorophores with different rotational rates. 

Analysis of rotational mobility of fluorophores by observation of fluorescence depolarization with nanosecond time resolution(28) or by variation of the lifetime (by the action of quenchers ).(9,29 30)... 

Figure 2.4. Schematic representation of processes which lead to fluorescence depolarization in proteins rotation of the protein molecule as a whole with correlation time rotation of the fluorophore with correlation time d, and excitation energy transfer, represented by the wavy arrow.

Values of +0.4 and +0.5 are theoretically expected for r0 and pm respectively, if the absorption and emission transition moments are in the same direction, as is often the case with excitation at the longest-wavelength absorption maximum. However, due to rapid internal rotation of the emission transition moments immediately after excitation, the experimentally determined values of rQ and p0 are always lower than the maximal values. Thus, the highest value ever observed for rQ is+ 0.35. In the common case where the fluorophore undergoes rotational motion during the excited-state lifetime, values of r or p closer to zero are observed depending on the extent of depolarization, and in the case of complete depolarization these parameters assume values of zero. The dependence of the anisotropy on rotational motion is described by eq 9[55]... 

We have not measured fluorescence depolarization with fluorophors and our polymers, but such measurements have been made by others, particularly with proteins and, as you indicate, it is possible to determine rotational relaxation times for the macromolecule and thus to obtain some insight into its behavior in solution. 

For chromophores that are part of small molecules, or that are located flexibly on large molecules, the depolarization is complete—i.e., P = 0. A protein of Mr = 25 kDa, however, has a rotational diffusion coefficient such that only limited rotation occurs before emission of fluorescence and only partial depolarization occurs, measured as 1 > P > 0. The depolarization can therefore provide access to the rotational diffusion coefficient and hence the asymmetry and/or degree of expansion of the protein molecule, its state of association, and its major conformational changes. This holds provided that the chromo-phore is firmly bound within the protein and not able to rotate independently. Chromophores can be either intrinsic—e.g., tryptophan—or extrinsic covalently bound fluorophores—e.g., the dansyl (5-dimethylamino-1-naphthalenesulfonyl) group. More detailed information can be obtained from time-resolved measurements of depolarization, in which the kinetics of rotation, rather than the average degree of rotation, are measured. For further details, see Lakowicz (1983) and Campbell and Dwek (1984). 

Whether fluorophores are intrinsic or extrinsic to the macromolecule (protein, peptide, or DNA), depolarization is the result of two motions, fluorophore local motions and macromolecule global rotation. 

Where Aq, dp, dp and dx are the intrinsic anisotropy, the depolarization factor due to the global rotation of the protein, the depolarization factor due to the local motions of the fluorophore and the depolarization factor due to the energy transfer and Brownian motion, respectively. 

Steady-state fluorescence anisotropy In low-viscosity solvents the rotational depolarization of low molecular weight compounds occurs on the picosecond timescale [124]. Since in this case the rotation is much faster than the fluorescence, the steady-state emission is unpolarised. If the rotational motion of the fluorophore is on the same timescale as the fluorescence, a steady state polarisation is observed. In the simplest case for a spherical rotor and a single-exponential fluorescence intensity decay (r), the measured anisotropy is given by... 

The effects of rotational difhision and energy transfer ate easily sqiarated fey juifidous choice of the experimental conditions. For example, Brownian rotations cause negligible depolarization when the rotational rate is much slower than the rate of fluorescence emisaon. In contrast, RET occurs only in concentrated solution where the average distance between the fluorophore molecules is comparable to a characteristic distance Rg, which is typically near 40 A. One may readily calculate that millimolar concentrations are required to obtain this average distance (Chapter 13). Hence, since the usual concentradons requited for fluotesoence measurements ate about l0r U, RET is easily avdded by the use of dilute solutions. 

Rotational diffusion of fluorophores is a dominant cause of fluorescence depolarization. This mode of depolarization is described in the simplest case for spherical rotors... 

In the case of a molecule that is free to explore a wide range of orientations rapidly, compared with the lifetime of the excited state, the emission will be essentially depolarized and r = 0 since fy = However, if the molecule experiences some degree of hindered rotation or alignment, r will be non-zero. For completely polarized light, for example scattered polarized laser light, r = 1. Note that the absorption and emission dipoles for typical fluorophores are never perfectly parallel and so some degree of depolarization is intrinsic even for a rota-tionally frozen molecule (hence the use of scattered light in this example). 

Steady state anisotropy measurements described in Section 2.7.5 can sometimes be misleading if a number of sources of depolarization are present. For example, as discussed, it can be difficult to differentiate global molecular rotation from local rotational freedom of the fluorophore when it is attached to a larger molecule [ 1,127]. In these cases time resolved single molecule fluorescence anisotropy measurements can be of use since the contributions to the depolarization may well act on different timescales. For example, for a labelled protein segmental motion of the protein backbone near the label and motion in the linker by which... 

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