Principles of Fluorescence Spectroscopy

822 FLUORESCENCE CORRELATION SPECTROSCOPY
Figure 24.34. FCS with TIR. Top: Simulated correlation functions
near a planar surface, without (G D (τ)) and with (G R (τ)) binding sites
for the diffusing species. Bottom: Experimental data for labeled IgG
near a lipid surface, without and with receptors for the Fc region.
Revised from [111].
the interface is slow due to the large diameter of the spot. If
the fluorophores are bound to the surface then they can only
leave the volume by lateral diffusion along the surface or
dissociation from the surface. Because of the difference in
geometry and diffusion paths the correlation functions have
a different functional form. This theory has been developed
109–111 and TIR-FCS has been used to study diffusion
and binding near glass or membrane interfaces. The equations
are rather complex and can be found elsewhere. 112–115
However, we will present an experimental example.
The correlation function for diffusion with TIR geometry
has a characteristic shape (Figure 24.34). The shape
depends strongly on whether the labeled molecules simply
diffuses near the surface G D (τ) or, if there are receptor sites
on the surface, G R (τ). The presence of binding sites results
in a long time component in the correlation function that
can be used to detect binding to the surface. The lower
panel in Figure 24.34 shows experimental data for Alexa
Fluor 488-labeled IgG. The correlation function was meas-
ured near a lipid-coated surface, or near a lipid-coated surface
that contained a receptor for the Fc region. The presence
of binding sites results in a dramatic shift in G(τ). One
can imagine such measurements being used to measure
binding to cells to screen for drug–receptor interactions.
24.12. FCS WITH TWO-PHOTON EXCITATION
Two-photon (TPE) or multiphoton excitation (MPE) is very
useful in FCS. When using MPE the excited volume is
small because of the quadratic dependence on light intensity.
Importantly, the z-axis resolution is improved because
the excited volume is less elongated. Sensitivity is also
improved because the emission can be observed without a
confocal aperture. The theory for FCS using MPE is very
similar to that for one-photon excitation. The molecules can
still enter and exit the observed volume from three directions.
However, the shape of the volume is changed due to
the quadratic dependence on intensity. For two-photon excitation
diffusion time is related to the volume diameter:
τ D s2
8D
(24.48)
where s is the distance at which the intensity is 1/e 2 of its
maximum value. Equation 24.48 for two-photon excitation
is different than eq. 24.14 because the intensity profile is
squared to provide the two-photon excitation profile. 62 That
is, the dimensions of the excited volume are described in
terms of the original long-wavelength intensity profile
rather than the square of the intensity profile. For two-photon
excitation the correlation function for diffusion
becomes 116–117
G D(τ) G(0) ( 1 8Dτ
s 2 ) 1
( 1 8Dτ
u 2 ) 1/2
(24.49)
For the same diameter beam the diffusion times are smaller
with TPE even if the diffusion coefficient is not changed
because of the quadratic dependence on intensity and the
smaller excited volume. Some authors assume the excitation
intensity is Gaussian in the focal plane and Lorentzian
along the z-axis. This assumption results in an expression
for G D (τ) that is different from eq. 24.49 and more complex,
but the visual shape of G D (τ) is similar. A significant fraction
of the publications on FCS 118–121 use two-photon excitation
because of its experimental advantages. When using