Principles of Fluorescence Spectroscopy

912 ANSWERS TO PROBLEMS
B. A covalently linked acceptor is somewhat equivalent
to one acceptor per sphere of 30 Å, or 8.84
x 10 18 acceptors/cm 3 . This is equivalent to an
acceptor concentration of 15 mM. Covalent
attachment of an acceptor results in a high effective
acceptor concentration.
CHAPTER 15
A.15.1. Using the data provided in Figure 15.28 one can calculate
the following values:
Mole% Rh-PE Rh-PE/Å 2 Rh-PE/R 0 2 F DA /F D
0.0 0.0 0.0 1.0
0.2 2.8 x 10 -5 0.071 0.62
0.4 5.7 x 10 -5 0.143 0.40
0.8 11.4 x 10 -5 0.286 0.21
1.2 17.1 x 10 -5 0.429 0.15
The distance of closest approach can be estimated by
plotting the last two columns of this table on the simulations
shown in Figure 15.17. The observed energy
transfer quenching is greater than predicted for no
excluded area, r C = 0, or much less than R 0. This suggests
that the donors and acceptors are fully accessible
and probably clustered in the PE vesicles. The R 0
value was not reported in [64].
A15.2. The decay times can be used with eq. 15.20 to obtain
the transfer rate k T = 1.81 x 10 3 s –1 . Dividing by the
EB concentration (2.77 µM) yields k T b = 6.5 x 10 8
M –1 s –1 .
Using eq. 15.25 and the values of R 0 and r C , the
maximum bimolecular rate constant is 1.1 x 10 6 M –1
s –1 . The measured values could be larger than the theoretical
values for two reasons. The positively charged
donors may localize around the negatively charged
DNA. This results in a larger apparent concentration
of EB. Given the small value of r C we cannot exclude
the possibility of an exchange contribution to k T b.
A15.3. To a first approximation the donor intensity is about
50% quenched when C/C 0 = 0.5. This value of C/C 0
can be used to calculate the acceptor concentration in
any desired units, as listed in Table 15.3.
Acceptor concentrations near 2 mM are needed in
homogeneous solution. This is generally not practical
for proteins because the absorbance due the acceptor
would not allow excitation of the protein. Also, such
high concentrations of acceptors are likely to perturb
the protein structure.
Table 15.3. Approximate Concentrations for 50%
Quenching in One, Two, and Three Dimensions
Concentrations for
Equation 50% energy transfer
C 0 = (4/3πR 0 3) –1 9.55 x 10 17 acceptors/cm 3 = 1.59 mM
C 0 = (πR 0 2) –1 6.4 x 10 11 acceptors/cm 2 = 4.5 x 10 –3 acceptors/lipid
C 0 = (2R 0 ) –1 5 x 10 5 acceptors/cm = 1.7 x 10 –2 acceptors/base pair
The situation is much better in proteins and nucleic
acids. In this case the acceptors need only to be about
one per 222 lipids or one per 59 base pairs. This favorable
situation is the result of a locally high concentration
of acceptors due to their localization in the lipid
or nucleic acid. The bulk concentration of acceptors
can be low and is determined by the bulk concentration
of membrane or nucleic acid.
A15.4. The simulations in Figure 15.31 determine the R0 value because the two-dimensional concentration of
acceptors is known from the area/lipid and the fractional
acceptor concentrations. Any point on these
curves can be used to calculate R0 . For an acceptor
density of 0.05 and t = τD the value of IDA (t)/I 0
D is
about 0.003. The value of β can be found from eq.
15.9, yielding β = 2.41. For A/PL = 0.05 the area per
acceptor molecule is C0 = 1400 Å/acceptor. Using eq.
15.10 and 15.11 yields R0 = 39.8 Å, which agrees with
the value of 40 Å given in [50].
CHAPTER 16
A16.1. A. Without experimentation, it is not possible to
predict how the fluorescence properties of the
protein will vary when it is unfolded. In general,
one can expect the extent of tyrosine fluorescence
to increase when the protein is unfolded.
This could be detected by excitation at 280 nm.
The tyrosine emission would appear near 308
nm. It is also probable that the fluorescent intensity
or the emission maxima of the single-tryptophan
residue would change as the protein is
unfolded. Once the spectral characteristics of the
native and unfolded states are determined, the
data can be used to quantify the unfolding
process. It is important to remember that
anisotropy or lifetime measurements may not