Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 437
Figure 12.39. Simulated lifetime Perrin plots for a protein with an overall correlation time θ P = 20 ns, and a fast segmental motion with θ F = 1.0 or
0.1 ns. Revised and reprinted with permission from [94]. Copyright © 1983, American Chemical Society.
where d i represents the extent to which anisotropy is
decreased by each depolarization factor. This relationship
can be clarified by a specific example. Suppose a fluorophore
has an anisotropy less than 0.4 due to a displacement
of the transition moment by an angle β and due to
rotational diffusion. The steady-state anisotropy can be
written as
r d 1d 2d 3 2
5 ( 3< cos 2β> 1
) ( 2
3< cos 2ω> 1
) 2
(12.50)
In this expression the first depolarization factor (d 1 ) is
0.4, which accounts for excitation photoselection
(eq. 10.20). The second term (d 2 ) accounts for the
angle between the transition moments (eq.
10.22). The third term (d 3 ) is the average angular (ω) displacement
of the fluorophore during the excited state lifetime
. This factor is also given by d 3 = (1 + τ/θ) –1
(eq. 10.44). It is sometimes useful to be aware of Soleillet's
rule when attempting to account for the overall loss of
anisotropy.
12.12. ANISOTROPIES CAN DEPEND ON
EMISSION WAVELENGTH
The anisotropy is generally independent of the emission
wavelength. However, the presence of time-dependent
spectral relaxation (Chapter 7) can result in a substantial
decrease in anisotropy across the emission spectrum. 105–108
A biochemical example is shown in Figure 12.40 for egg
PC vesicles labeled with 12-AS. Because of time-dependent
reorientation of the local environment around the excited
state of 12-AS, the emission spectra display a timedependent
shift to longer wavelengths. 109 Such relaxation is
often analyzed in terms of the time-resolved emission spectra,
but one can also determine the mean lifetime at various
emission wavelengths (Figure 12.40, bottom). The mean
lifetime increases with wavelength because the lifetime at
short wavelengths is decreased by relaxation, and longwavelength
observation selects for the relaxed species.
Recall that the steady-state anisotropy is determined by
r(t) averaged over I(t) (eq. 10.43), resulting in Perrin eq.
10.44. Because of the longer average lifetime at long wavelengths,
the anisotropy decreases with increasing wave