Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 415
Figure 12.3. Intensity and anisotropy decays corresponding to the
individual species shown in Figure 12.1.
For the non-associated decay there is a single intensity
decay I(t) and a single anisotropy decay, even though both
decays can be multi-exponential. A non-associated decay
describes the motions of a single type of fluorophore in a
single environment.
For an associated system each fluorophore population
displays its own intensity and anisotropy decay. The polarized
intensity decays are given by
(12.6)
(12.7)
where the subscript m represents each fluorophore population,
and not a component of a multi-exponential decay.
Each fluorophore population is described by a different
intensity decay I m (t) and a different anisotropy decay r m (t).
The nature of an associated anisotropy decay can be
understood by considering eqs. 12.6 and 12.7 for a twocomponent
mixture. Assume each species displays a single
lifetime (τ m ) and a single correlation time (θ m ). The amplitudes
at t = 0 can be represented by α m , which is the amplitude
of the mth population at t = 0. The anisotropy decay for
this mixture is then given by
r(t)
I ||(t) 1
3 ∑ m
I (t) 1
3 ∑ m
∑ m
α m exp(t/τ m) r 0m exp(t/θ m)
∑ m
I m(t) 1 2 r m(t)
I m(t) 1 r m(t)
α m exp(t/τ m)
(12.8)
The fractional intensity of the mth component at any time t
is given by
fm(t) αm exp(t/τm) ∑ αm exp(t/τm) m
and the time-dependent anisotropy is given by
r(t) ∑ m
f m(t) r m(t)
(12.9)
(12.10)
This equation states that the anisotropy at time t is given by
the intensity-weighted average of the anisotropies of each
species at the same time. Equation 12.10 is the additivity
law for anisotropies at each time in the total decay. More
detailed descriptions of the theory for associated anisotropy
decays can be found elsewhere. 1–8
12.1.2. Time-Domain Measurements of
Associated Anisotropy Decays
Experimental studies of associated anisotropy decays started
with early reports on cis- and trans-parinaric acid. 9–11
The anisotropy was observed to increase at long times (Figure
12.4). In this case the probe cis-parinaric acid was covalently
linked to the second position on a phosphatidylcholine
molecule (cis-parinaroyl-PC). 12–13 The increase in
anisotropy at times longer than 10 ns was explained as the
result of a population of fluorophores with a longer life-
Figure 12.4. Intensity and anisotropy decay of cis-parinaroyl-PC in
rat skeletal sarcolemmal membranes. From [12].