Principles of Fluorescence Spectroscopy

818 FLUORESCENCE CORRELATION SPECTROSCOPY
Figure 24.28. Photon counting histogram for three fluorophores (top)
and for a fluorophore mixture. Also shown as a dashed line is the distribution
for fluorescein at a lower concentration. Revised from [91].
beads with radii of 0.05 and 0.115 µm. 87 Two populations
are already visible in the photon-count histogram.
Until recently the correlation functions were obtained
with dedicated circuit boards that calculate G(τ) in real
time. This was necessary because of the need to rapidly
sample the fluctuating signal on a timescale short enough to
characterize the process of interest. With modern electronics
and computers it is possible to record the intensities for
each time interval during the measurement. This allows the
data to be analyzed in a different way, which is called fluorescence
intensity distribution analysis (FIDA) or photoncounting
histograms (PCH) by different authors. 88–97
Unfortunately, actual use of this concept with fluorophores
rather than beads is not as clear as in Figures 24.26
and 24.27. This is because there are multiple Poisson distributions
that need to be considered. 91–92 The number of photons
observed during a given time interval shows a Poisson
distribution, as does the number of fluorophores in the volume.
Additionally, a given fluorophore will display a different
brightness in each region of the observed volume. As a
result the distribution of the number of photon counts is
broad even for a single fluorophore. These effects were less
important in Figure 24.27 because of the brightness of the
labeled beads and/or the mutual exclusion of the beads from
being in the laser beams at the same time. The theory of
FIDA/PCH is complex and not yet used in a standardized
way. Hence we will present just a few examples to illustrate
the nature of the data and the possible resolution.
Figure 24.28 (top) shows an example of FIDA data. 91
The top panel shows the photon-count histograms for three
individual fluorophores. The data represent the probability
a bin contained k photon counts. A different distribution
was observed for each fluorophore. While the histograms
appear distinct for each fluorophore this appearance is
somewhat misleading because the shapes of the distributions
depend on fluorophore concentration, as shown for a
lower concentration of fluorescein (dashed line). The lower
panel shows the use of these histograms to resolve a mixture
of fluorophores. Curves are shown for fluorescein, a
coumarin derivative, and a mixture of both fluorophores,
1.2 nM each. The PCH for the mixture was different from
each fluorophore alone, but the difference is due in part to
the overall higher photon counts when the two fluorophores
are present in the solution. The relative concentration and
brightness of each fluorophore to the PCH are determined
by fitting the data to simulated histograms. In this example
the difference in brightness was about twofold. It may be
difficult to use this approach if there is only a modest difference
in fluorophore brightness.
The resolution of FIDA increases as the fluorophores
display larger differences in brightness. Figure 24.29 shows
the photon-count histograms for TMR and R6G, and for a
mixture (top). 89 These data were used to recover two populations
of particles: one with a brightness of 36.6 kHz per
molecule (TMR) and the second about threefold brighter—
107 kHz per molecule (R6G). In this case the two populations
are well resolved. The dashed lines show the distributions
observed for the individual fluorophores, which are
already wide. This intrinsic width must be taken into
account when using the measured distributions to resolve
the underlying populations.