Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 369
Figure 10.14. Perrin plots for determination of protein volume. The
curves are drawn for a protein molecular weight of 25,000 daltons in
water, h = 0.4 and τ = 4 ns. The value of r 0 = 0.4 represents a rigidly
bound probe and r 0 = 0.3 represents a probe with some segmented
mobility. The upward curving dashed lines indicate the protein is
denaturing at high temperature.
For example, assume the segmental motion of the fluorophore
is much more rapid than the rotational diffusion of
the protein. Then, the value of r 0 is effectively reduced to
r app
0 r0 ( 1
2
(10.48)
where α is the angle through which the probe undergoes
this segmental motion. The term (1/r 0 app) cancels in the calculation
of the molecular volume, and the apparent volume
represents overall rotation diffusion of the protein. It is
important to note that, if the short correlation time for segmental
motion (θ S ) is not much faster than the overall correlation
time (θ L ), then the apparent volume can be substantially
decreased due to contributions from the more rapid
motions (Section 10.9). Some information is available by
comparison of the extrapolated and frozen solution values
of r 0 . If r 0 app is much smaller than r 0 one may infer the existence
of segmental motions of the probe on the macromol-
)
ecule, independent motions of domains of the protein, or
possibly RET in multiply labeled proteins. Another behavior
seen in Perrin plots is a rapid increase in 1/r at high temperatures.
Such an increase is usually the result of denaturation
of the macromolecule, resulting in an increase in
independent motion of the probe and a decrease in the
anisotropy.
A different version of the Perrin equation is often
found in the older literature:
( 1
P
1 1
) ( 3 P0 1 τRT
) ( 1
3 ηV )
( 1
P0 1
3 ) ( 1 3τ
ρ )
(10.49)
This equation is equivalent to eq. 10.47, except for the use
of polarization in place of anisotropy. When using the equation,
a plot (1/P – 1/3) versus T/η is used to obtain the
molecular volume. The intercept yields the apparent value
of (1/P 0 app – 1/3), which can be larger than the true value
(1/P 0 – 1/3) if there is segmental motion of the probe. The
term ρ is the rotational relaxation time (ρ = 3θ). At present
the use of anisotropy, the rotational correlation time, and eq.
10.44 is preferred.
10.5.2. Examples of a Perrin Plot
It is instructive to examine a representative Perrin plot (Figure
10.15). 16 These data are for 9-anthroyloxy stearic acid
in a viscous paraffin oil, Primol 342. The anisotropies were
measured at various excitation wavelengths, corresponding
to different r 0 values (Figure 10.8). The y-axis intercepts are
different because of the different r 0 values. Also, the slopes
are larger for shorter excitation wavelengths because the
value of r 0 appears in the denominator of eq. 10.47. In spite
of the very different values of 1/r for different excitation
wavelengths, the data are all consistent with a correlation
time near 15 ns at 25EC (Table 10.5). For a spherical molecule,
the correlation time is independent of r 0 . In Chapter 12
we will see that the correlation times can depend on the
value of r 0 for non-spherical molecules. This effect may be
the cause of the somewhat different correlation times found
for different excitation wavelengths.
The y-axis intercepts yield the apparent values of r 0
extrapolated to high viscosity, which can be compared with
measured values in a glassy solvent (Table 10.5). The