Principles of Fluorescence Spectroscopy

810 FLUORESCENCE CORRELATION SPECTROSCOPY
Figure 24.16. Cleavage of rhodamine-labeled M13 DNA by four
restriction enzymes. The number of cleavage sites is shown under
each circle. Revised from [51].
eral τ D values in a mixed sample if the lengths were more
similar. The distributions were obtained from measurements
on a single species, with a single brightness, so that
resolution of multiple τ D values can be expected to be more
difficult for a mixture of species with different brightness.
In addition to monitoring the length of DNA oligomers,
FCS can be used to roughly estimate the number of
fragments formed during DNA cleavage. 51 Figure 24.16
shows the G(τ) curves for M13 DNA (7250 base pairs) after
cleavage by several restriction enzymes. From the known
sequence and enzyme specificity one can predict the number
of fragments formed by each enzyme. The G(0) values
from autocorrelation curves are largest for BspMI, which
generates only 3 fragments, and smallest for HaeIII, which
generates 15 fragments. Of course, the G(0) values give
only an apparent number of diffusing species since the fragments
are of unequal length and their contributions to G(τ)
are weighted according to eq. 24.18.
24.5. FCS IN TWO DIMENSIONS: MEMBRANES
FCS is not limited to three-dimensional samples, but can
also be used to study cell membranes. 52–61 FCS is especially
useful for studies of membranes because diffusion is limited
to two dimensions. Also, the typically viscous nature of
membranes result in a wide range of diffusion times for
membrane-localized fluorophores. The wide range of diffusion
times possible with cells or cell membranes is shown
in Figure 24.17. The correlation curves are for rhodamine
derivatives in solution (S), in the cytoplasm (C), and bound
to the membranes of a rat leukemia cell (M). Also shown is
the curve for Cy3-labeled IgE bound to the IgE receptor.
The diffusion times span four orders of magnitude. Hence
Figure 24.17. Autocorrelation curves for rhodamine derivatives in
solution (S), in the cytoplasm (C), and bound to the membranes (M)
of rat basophilic leukemia cells (RBL). A lipophilic rhodamine derivative
was used to bind to the membranes. Also shown is the curve for
Cy3-labeled IgE bound to the IgE receptor on the membrane (R). The
pinhole was 100 µm in diameter. Revised from [62].
we expect the autocorrelation curves to contain information
about diffusive transport in membranes. To obtain a similar
change in diffusion times for a three-dimensional solution
the molecular weight would need to change by a factor of
10 12 .
Recall that the correlation function eq. 24.12 was
derived assuming a three-dimensional Gaussian volume
(eq. 24.9). In a membrane the fluorophores are constrained
in a two-dimensional plane. In this case the observed volume
can be described by a planar two-dimensional Gaussian
distribution:
p(r) I 0 exp2(x 2 y 2 )/s 2
(24.28)
For this geometry the correlation function for a freely diffusing
species is
G(τ) G(0)(1 τ/τ D ) 1 G(0) ( 1 4Dτ
s 2 ) 1
(24.29)
where s is the radius of the disk and the diffusion time is
given by τ D = s 2 /4D (eq. 24.14). Intuitively this expression
is similar to eq. 24.12, except that the exit pathway out of
the plane is no longer available to the molecule, and the
square-root term is no longer present.
It is informative to examine the properties of the correlation
function in two and three dimensions: G 2D (τ) and