Principles of Fluorescence Spectroscopy

436 ADVANCED ANISOTROPY CONCEPTS
Figure 12.38. Lifetime-resolved anisotropies of human luteinizing
hormone (hLH) and its β subunit. The lifetimes were varied by oxygen
quenching, and calculated from the dynamic portion of the
observed quenching. Revised and reprinted with permission from
[101]. Copyright © 1987, American Chemical Society.
ured and calculated values are reasonably close, but the yintercepts
yield apparent r 0 values smaller than the expected
value of 0.27. This result is typical of other reports that
suggest segmental freedom of tryptophan residue in many
proteins. 93–96
12.10.1. Effect of Segmental Motion on the
Perrin Plots
The effect of segmental motion on the Perrin plots can be
seen by deriving the Perrin equation for the anisotropy
decay expected in the presence of segmental motions.
While the results are the same whether one measures
anisotropy versus T/η, or versus lifetime, these effects are
somewhat easier to understand in terms of the lifetimeresolved
measurements. In addition, the experiments are
easier to interpret because the temperature and solution
conditions are not changed, so that changes in protein
dynamics and conformation do not complicate the analysis.
Suppose a fraction α of the total anisotropy is lost by
the segmental motion, with a fast correlation time θ F , and
the remainder of the anisotropy decays by overall rotational
diffusion of the protein (θ P ). For independent segmental
motions and rotational diffusion the anisotropy is given as
the product of the depolarization factors, so that
r(t) r 0α exp(t/θ F ) (1 α) exp(t/θ P )
(12.46)
where f F + f P = 1.0. Use of eq. 10.43 with eq. 12.46 yields
r(τ)
αr 0
1 ( 1
θF 1 ) τ
θP (12.47)
In this expression we used the notation r(τ) as a reminder
that the steady-state anisotropy depends on the lifetime τ. In
many cases the internal motions are more rapid than overall
rotation (θ F