Principles of Fluorescence Spectroscopy

830 FLUORESCENCE CORRELATION SPECTROSCOPY
Figure 24.45. Measurement of photon antibunching and rotational
diffusion by FCS. CFD, constant fraction discriminator. TAC, time-toamplitude
converter. MCA, multichannel analyses. Revised from
[150].
both of these are shorter than the diffusion time. Also
assume that the absorption and emission dipoles are parallel,
and that the excitation is polarized in the z direction and
the emission is observed without polarizers, the observed
volume is long along the z-axis. The correlation function is
then given by
1
G(τ) G(0) [ 1 τ/τD 4
5
τ 9
exp ( )
θ 5
τ
exp ( )] τF (24.57)
The correlation time information is available without polarizers
because the probability of excitation depends on the
orientation of the fluorophore relative to the incident polarization.
This separation of correlation time from lifetime
can be seen in the middle term of eq. 24.57, where the exponential
relationship depends on the ratio of the experimental
correlation time τ to the rotational correlation time θ.
This is different from time-resolved anisotropy decays,
where the lifetime must be comparable to the rotational correlation
time to obtain useful information. The last term in
eq. 24.57 represents the photon antibunching, which
decreases exponentially with the ratio of the experimental
correlation time to the lifetime τ F .
Figure 24.46. Measurement of rotational diffusion of Texas Redlabeled
pancreatic lipase using FCS. Revised from [151].
It is interesting to notice that eq. 24.57 contains two
exponential terms plus the diffusion term. Recall that the
concentration autocorrelation function is also exponential
in τ (eq. 24.11). The averaging over a Gaussian volume
results in the dependence shown in eq. 24.57. The photon
antibunching term and the rotational diffusion terms still
show the exponential dependence because they do not
depend on the position of the fluorophore in the volume.
Figure 24.46 shows an AFCS experiment, in this case
for pancreatic lipase labeled with Texas Red. 151 The data
were collected using three parallel polarizers (Figure
24.45), so that eq. 24.57 is not appropriate for these data but
requires additional geometric factors. G(τ) is symmetrical
because of the random distribution of photons by the beamsplitter.
Notice that the timescale is ns rather than ms
because rotational diffusion occurs on this timescale. The
dip in the middle is due to photon antibunching and is several
ns wide, comparable to the lifetime τ F . The decays on
either side are due, at least in part, to rotational diffusion of
the protein.
24.15. FLOW MEASUREMENTS USING FCS
As a final application of FCS we will describe how it can be
used to detect the velocity in flowing samples. This is not a
trivial problem, especially in microfluidic structures where
the velocity will vary across the channel and will be different
in branches of a channel. The theory of FCS with flow
has been described, 156 and the interest in such measurements
appears to be growing rapidly. 157–162 A typical