Principles of Fluorescence Spectroscopy

894 ANSWERS TO PROBLEMS
A1.4. A. The anisotropy of the DENS-labeled protein is
given by eq. 1.10. Using τ = θ, the steady-state
anisotropy is expected to be 0.15.
B. If the protein binds to the larger antibody, its
rotational correlation time will increase to 100
ns or longer. Hence the anisotropy will be
0.23 or higher. Such increases in anisotropy
upon antigen–antibody binding are the basis
of the fluorescence polarization immunoassays,
which are used to detect drugs, peptides,
and small proteins in clinical samples.
A1.5. The dependence of transfer efficiency on distance
(r) between a donor and acceptor can be calculated
using eq. 1.12 (Figure 1.41). At r = R 0 the efficiency
is 50%; at r = 0.5R 0 , E = 0.98; and at r = 2R 0 , E
= 0.02.
Figure 1.41. Effect of donor-to-acceptor distance on transfer
efficiency.
A1.6. The distance can be calculated for the relative
quantum yield of the donor in the presence or
absence of the acceptor. The data in Figure 1.37
reveal a relative tryptophan intensity of 0.37,
assuming the anthraniloyl group does not contribute
at 340 nm. A transfer efficiency of 63% corresponds
(see eq. 1.12) to a distance of r = 0.92R 0
= 27.7 Å.
In reality the actual calculation is more complex,
and the tryptophan intensity needs to be corrected
for anthraniloyl emission. 42 When this is done the
transfer efficiency is found to be about 63%, and
the distance near 31.9 Å.
A1.7. The changes in λ max , K, and r shown in Figure 1.38
are the result of the tryptophan residue being
exposed to or shielded from the water. Increases in
λ max and K indicate increased exposure to water,
and decreases in λ max and K indicate decreases in
exposure to water. Increases and decreases in r
indicate a less mobile and more mobile tryptophan
residue, respectively. The three parameter values
show a cyclical behavior with a period of about 3.5
amino acid residues per cycle. This suggests that
the MLCK peptide is in an α-helical state when
bound to calmodulin (Figure 1.42). The spectral
changes seen in Figure 1.38 are the result of the
tryptophan residue being alternately exposed to
water or shielded between the MLCK peptide and
calmodulin as its position is shifted along the peptide
chain.
Figure 1.42. Schematic of the interactions of the ?-helical MLCK
peptide with calmodulin. The position of the single tryptophan residue
is moved along the helix in 16 synthetic peptides. Reprinted with permission
from [40]. (O'Neil KT, Wolfe HR, Erickson-Vitanen S,
DeGrado WF. 1987. Fluorescence properties of calmodulin-binding
peptides reflect ?-helical periodicity. Science 236:1454–1456,
Copyright © 1987, American Association for the Advancement of
Science.)