Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 101
4.2. BIOPOLYMERS DISPLAY MULTI-EXPONEN-
TIAL OR HETEROGENEOUS DECAYS
At first glance the measurement of decay times seems
straightforward (Figure 4.3), so why do these measurements
receive so much attention? Interpretation of the data
in Figure 4.3 was relatively simple because the decays were
single exponentials. However, most samples display more
than one decay time. This situation is illustrated by a protein
with two tryptophan residues (Figure 4.4). Suppose that
both residues display lifetimes of 5 ns. Then the decay
would be a simple single exponential decay. The decay
would be simple to analyze, but one could not distinguish
between the two tryptophan residues. Now suppose a collisional
quencher is added and that only the residue on
the surface of the protein is accessible to quenching.
Assume that the added quencher reduces the lifetime of
the exposed residue to 1 ns. The intensity decay is now
a double exponential:
I(t) α 1e t/5.0 α 2e t/1.0
(4.7)
In this expression the α i values are called the pre-exponential
factors. For the same fluorophore in different environments,
which usually display the same radiative decay
rates, the values of α i represent the fractional amount of fluorophore
in each environment. Hence, for the protein
shown in Figure 4.4 one expects α 1 = α 2 = 0.5. The presence
of two decay times results in curvature in the plot of
log I(t) versus time (dashed). The goal of the intensity
decay measurements is to recover the decay times (τ i ) and
amplitudes (α i ) from the I(t) measurements.
The presence of two decay times can also be detected
using the frequency-domain method. In this case one examines
the frequency response of the sample, which consists
of a plot of phase and modulation on a logarithmic frequency
axis. The longer lifetime tryptophan (τ 1 = 5 ns, solid) and
the shorter lifetime tryptophan (τ 2 = 1 ns, dotted) each display
the curves characteristic of a single decay time. In the
presence of both decay times (τ 1 = 5 ns and τ 2 = 1 ns,
dashed), the frequency response displays a more complex
shape that is characteristic of the heterogeneous or multiexponential
intensity decay. The FD data are used to recover
the individual decay times (τ i ) and amplitudes (α i ) asso-
Figure 4.4. Simulated intensity decays of buried (W 1 ) and exposed (W 2 ) tryptophan residues in the absence and presence of a collisional quencher.