Principles of Fluorescence Spectroscopy

786 SINGLE-MOLECULE DETECTION
face shows that even under good conditions S/N is unlikely
to exceed 100. Also, S/N is adequate over a limited range of
incident intensities and sample sizes. S/N initially increases
with incident power, but decreases at higher power due to
increased contributions from the background. The useful
range of conditions is even more limited if photobleaching
is considered (lower panel) because the fluorophore disappears
after emitting some average number of photons. The
surfaces in Figure 23.51 shows that SMD is possible
because of several favorable conditions, including high
photon detection efficiency, high photostability, and low
dark counts. An unfavorable change in any of these parameters
can make it impossible to detect the emission from a
single fluorophore.
23.11.2. Polarization of Single Immobilized
Fluorophores
In Figures 23.33 and 23.34 we described the polarization of
single molecules when excited with polarized light. These
concepts are clarified by a mathematical description of this
system. Consider a fluorophore on a glass slide, with colinear
absorption and emission dipoles (Figure 23.52). The
Figure 23.52. Polarized intensities for a single immobilized fluorophore.
transition moment is oriented at an angle θ from the x-axis
and an angle φ from the optical z-axis. The polarized components
of the emission are separated with a polarizing
beamsplitter. The intensity of each polarized component is
given by the square of the electric field projected onto the
axis. Hence,
I s I x k sin 2 φ cos 2 θ
I p I y k sin 2 φ sin 2 θ
(23.7)
(23.8)
where k is an instrument constant assumed to be the same
for both channels. Notice that it was not necessary to consider
the polarization of the incident light. The intensity a
fluorophore emits along the x- and y-axes depends only on
the orientation of the emission dipole, regardless of how the
molecule was excited. The polarization of the emission is
given by
P Ip Is 1 2 cos
Ip Is 2θ (23.9)
Perhaps surprisingly, the polarization does not depend on
the angle φ because the intensity is proportional to the same
factor sin 2 φ in both channels.
23.11.3. Polarization Measurements and Mobility
of Surface-Bound Fluorophores
The ability to measure the polarization of single molecules
makes it possible to measure their mobility. Because only a
limited number of photons per fluorophore can be detected
it may be difficult to determine the correlation time from
the polarized intensity decays. An alternative approach to
mobility measurements is to measure the polarized emission
interaction when the excitation polarization is rotated.
96 Figure 23.53 shows such measurements of Texas Red
using an electrooptic device to repetitively rotate the excitation
polarization. The intensity of this single Texas Red
molecule changes from nearly zero to a maximum value
with rotation of the polarization. The insert shows the averaged
intensities at various angles of incident polarization.
There is an angle near 60E where the intensity is near zero.
Recall that excitation of a single molecule is proportional to
cos 2 θ, so that the intensity minimum occurs where the
absorption transition is perpendicular to the excitation
polarization. Such a high contrast ratio is not seen for