Principles of Fluorescence Spectroscopy

430 ADVANCED ANISOTROPY CONCEPTS
Figure 12.26. χ R 2 surfaces for the three correlation times found for
perylene. From [65].
ly, for r 0 values near 0.1 one expects the out-of-plane rotation
to dominate the anisotropy decay. These slower
motions display a maximum value of ∆ ω of lower modulation
frequencies.
Global analysis of the frequency-domain data is performed
assuming the correlation times are independent of
excitation wavelength, and that the amplitudes are dependent
on wavelength. Under these assumptions the value of
χ R 2 is calculated using an expanded form of eq. 11.34,
where the sum extends over the excitation wavelengths. The
changes in shape of ∆ ω allow highly detailed resolution of
an anisotropy decay using global analysis. In fact, the data
allowed recovery of three rotational correlation times. The
fact that the three correlation times were needed to explain
the data was demonstrated for the χ R 2 surfaces (Figure
12.26). The presence of three correlation times for perylene
is somewhat surprising because the transitions of perylene
are along its long and short axes (Figure 12.35, below), and
it is shaped like an oblate ellipsoid. Hence, only two correlation
times are expected. The recovered correlation times
and amplitudes do not seem to fit any reasonable hydrodynamic
shape. 65 It appears that perylene displays partial slip
diffusion and thus an anisotropy decay different from that
predicted from the hydrodynamic model.
12.7.2. Global Anisotropy Decay Analysis with
Collisional Quenching
As shown in Chapter 10 (eq. 10.43), the steady-state
anisotropy is the average value of the anisotropy decay
averaged over the intensity decay of the sample. If the sample
displays several correlation times, eq. 10.49 indicates
that their contributions to the anisotropy would be different
if the lifetime was changed. This is possible using energy
transfer or collisional quenching. 66–68 Consider a sample
with a lifetime of 4 ns and a correlation time of 4.0 or 0.4
ns (Figure 12.27). The information about the anisotropy
decay is contained in the difference between the parallel (I || )
and perpendicular (I ⊥ ) components of the emission (Figure
12.27, left). For the 4-ns correlation time (dashed lines), the
Figure 12.27. Simulated anisotropy decays for unquenched and quenched decays. Left: Unquenched decay with τ = 4 ns and θ = 4 (dashed lines), or
0.4 ns (solid lines). Right: Quenched decay with τ = 0.4 ns and θ = 0.4 ns. r 0 is 0.4 for both decays. Reprinted with permission from [69]. Copyright
© 1987, Biophysical Society.