Limiting anisotropy

P 0 is the apparent limiting anisotropy and P is the anisotropy (17). The slope is read as the straight line portion of the curves in Figures la-f and applied in equation 10 to obtain the equivalent-sphere molar volume. The difference between the extrapolated intercept of the linear portion of the line on they ordinate and the extrapolated intercept of the curved line is attributed to the internal rotation of the fluorophores in the molecule (5). 

Here r0 is the limiting anisotropy obtained in the absence of rotational motion. The dynamic range of anisotropy sensing is determined by the difference of this parameter observed for free sensor, which is commonly the rapidly rotating unit and the sensor-target complex that exhibits a strongly decreased rate of rotation. 

The difference between the theoretical value of the emission anisotropy in the absence of motions (fundamental anisotropy) and the experimental value (limiting anisotropy) deserves particular attention. The limiting anisotropy can be determined either by steady-state measurements in a rigid medium (in order to avoid the effects of Brownian motion), or time-resolved measurements by taking the value of the emission anisotropy at time zero, because the instantaneous anisotropy can be written in the following form ... 

It should first be noted that the measurement of emission anisotropy is difficult, and instrumental artefacts such as large cone angles of the incident and/or observation beams, imperfect or misaligned polarizers, re-absorption of fluorescence, optical rotation, birefringence, etc., might be partly responsible for the difference between the fundamental and limiting anisotropies. 

Fast librational motions of the fluorophore within the solvation shell should also be consideredd). The estimated characteristic time for perylene in paraffin is about 1 ps, which is not detectable by time-resolved anisotropy decay measurement. An apparent value of the emission anisotropy is thus measured, which is smaller than in the absence of libration. Such an explanation is consistent with the fact that fluorescein bound to a large molecule (e.g. polyacrylamide or monoglucoronide) exhibits a larger limiting anisotropy than free fluorescein in aqueous glycerolic solutions. However, the absorption and fluorescence spectra are different for free and bound fluorescein the question then arises as to whether r0 could be an intrinsic property of the fluorophore. 

The value of A in the absence of motion is referred to as the limiting anisotropy, A0. This value is related to the relative direction of the absorption and emission dipoles. For tryptophan, /40is negative, which indicates that the absorption and emission dipoles are approximately perpendicular to each other.(83)... 

If, however, the fluorophore exhibits free motion, the measured r is lower than that of the protein, and extrapolated anisotropy is lower than the limiting anisotropy. 

The data yield a rotational correlation time equal to 38 ps instead of 5.9 ns calculated theoretically for the cytochrome b2 core, with an extrapolated value A(o) of 0.208, lower than that (0.265) usually found for Trp residues at Xex = 300 nm at —45°C. The fact that the extrapolated anisotropy is lower than the limiting anisotropy means that the system is depolarized as a result of global and local motions within the protein. In this case, the value of the apparent rotational correlation time ( a) calculated from the Perrin plot is lower than the global rotational time of the protein ( bp). However, the fact that 4>a is 1000 times lower than 4>p indicates that a third process different than the global and local rotations is... 

Consider two limiting anisotropie particle shapes platelet-like and needle-like. The platelets, when packed in a flat sample holder, will tend to align parallel to one another and to the sample surface. Then, the amount of plates that are parallel or nearly parallel to the surface will be much greater than the amount of platelets that are perpendicular or nearly perpendicular to the surface. In this case, a specific direction that is perpendicular to the flat... 

The sum of the [1/ for m-C 1P3 and m-C 1P4 is substantially smaller than the limiting anisotropy. This strongly suggests that, at a time shorter than the resolution of single-photon timing, there is already a process leading to loss of fluorescence polarization in the meta-substituted dendritic systems. 

Energy transfer processes can be revealed by time-resolved anisotropy data. The large value for the limiting anisotropy (ro) of p-CIPi, p-C2P1 and m-CIPi... 

The QREA method allows determining the fraction fb and the limiting anisotropy of the non-accessible residues. Knowing the value of the anisotropy in absence of quencher, one can determine the intrinsic anisotropy of the accessible residues. 

The Weber method provides parameters characteristic of the environment of the rotating unit such as the limiting anisotropy and the thermal coefficient to resistance to a rotation. Also, the method permits to separate the motion of different classes of fluorophore. 

Case of motionless molecules with random orientation 137 Box 5.1 Fundamental and limiting anisotropies... 

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