Principles of Fluorescence Spectroscopy

916 ANSWERS TO PROBLEMS
Figure 17.49. Arrhenius plot for the rotational correlation times of
RNase T 1 . Data from [54].
total anisotropy. The fractional contribution of the
long correlation time (t L ) is given by
f L r 01
r 01 r 02
(17.7)
This fraction can be related to the displacement of the
transition dipole according to the definition of
anisotropy:
cos 2 β 2f L 1
3
(17.8)
Alternatively, this fraction can be related to the angle
(θ c ) through which the tryptophan rotates before striking
an energy barrier:
f L [ 1
2 cos θ c (1 cos θ c) ] 2
(17.9)
Application of these expressions to the data in Table
17.4 yields the following results in Table 17.9.
A17.3. The time-zero anisotropy, r(0), for RNase T 1 in Table
17.7 is derived from the time-domain data and is lower
than from other reports. One possible origin of the difference
is the shorter excitation wavelength (295 nm)
for the time-domain data and the possibility of a small
error in the reported excitation wavelength. Another
difference is that r(0) was a variable parameter in the
analysis of the time-domain data. It is possible that a
short component in the anisotropy decay was missed
by limited time resolution, as suggested by molecular
dynamics simulations or RNase T 1. 149
A17.4. A. The intensity decays more slowly at longer
emission wavelengths. This indicates that the
mean decay time is increasing. In this case the
effect is due to an increasing fractional contribution
of the long-lived component (9.8 ns).
B. The decay-associated spectra are calculated
using the data in Table 17.8 and eq. 17.3, resulting
in the DAS shown in Figure 17.50. In order
to interpret the DAS one has to assume that each
decay time (3.8 or 9.8 ns) is associated with one
of the tryptophan residues. Using this assumption
the 3.8 ns decay time is associated with a
blue-shifted emission and a lower quantum yield
than the red-shifted 9.8 ns residue.
C. The most rigorous way to confirm assignment of
the DAS is to create the single tryptophan
mutants. Each mutant should display one of the
calculated DAS. One could also use quenching
by iodide or acrylamide with the two tryptophan
Table 17.9. Angular Freedom of NATA and Tryptophan Residues in Single-Tryptophan
Peptides and Proteins at 20°C
Proteins r 0 = r 01 + r 02 f L β (deg) θ c (deg)
RNase T 1 , 20°C 0.310 1.00 0.0 0.0
Staph. nuclease 0.321 0.944 11.1 11.2
Monellin 0.315 0.768 23.2 23.8
ACTH 0.308 0.386 39.8 43.8
Gly-trp-gly 0.325 0.323 42.2 47.3
NATA 0.323 1.00 0.00 0.00
Melittin monomer 0.323 0.421 38.4 41.9
Melittin tetramer 0.326 0.638 29.4 30.8