Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 799
Figure 24.2. Poisson distribution of a 1-nM fluorophore solution in a
1-fl volume, N = 0.6.
panel). In an FCS instrument a dedicated correlation board
is usually used to calculate the correlation between F(t) and
F(t + τ) for a range of delay times τ. This results in an autocorrelation
function G(τ) that contains information on the
diffusion coefficient and occupation number of the
observed volume. The dependence of the correlation function
on the rate of diffusion makes FCS valuable for measuring
a wide range of binding interactions, such as
protein–ligand binding and DNA hybridization. Note that
the correlation time τ in an FCS measurement is not related
to the lifetime of the fluorophore.
An important feature of FCS is a measurement of the
number of diffusing species in the observed volume. In
principle, this measurement does not rely on an external
calibration or the quantum yields of the fluorophores. In
practice, calibrations are performed using known solutions.
The important point is the amplitude of the autocorrelation
function at τ = 0 reveals the average number of molecules
being observed. Sometimes a proportionality constant is
used to adjust this number. FCS can thus be used to detect
changes in particle density due to association or cleavage
reactions. In contrast to single molecule detection, the
observed molecules are continually replaced by diffusion,
so that photobleaching is less of a problem. Additionally,
since only a few molecules are observed, FCS provides
high sensitivity. Intensity fluctuations can also occur due to
blinking of the fluorophores upon transition to the triplet
state, structural changes in biomolecules, and the rate of lateral
translation in flowing samples. There are also more
advanced types of FCS, such as dual-color cross-correlation
FCS, which selectively detects species that contain two fluorophores,
such as DNA oligomers labeled with two different
fluorophores.
Figure 24.3. Fluctuations in the number of fluorophores (N) in the
observed volume of 1 fl with c = 1 nM. The intensity axis is in units
of the intensity from a single fluorophore.
FCS can provide information about reaction kinetics
even when the reaction is in equilibrium. Consider a simple
reaction F + M ⇌ F*M, where F is a fluorophore that is
nonfluorescent in solution but fluorescent (F*) when bound
to a macromolecule (M). The reaction kinetics would usually
be studied by starting the reaction from a nonequilibrium
condition, such as mixing separate solutions of F and M
in a stopped-flow instrument. Upon mixing the intensity
would change as the reaction approached equilibrium.
When the reaction reaches equilibrium the fluorescence
intensity will remain constant and no additional information
is obtained by continuing to measure the intensity. In contrast,
FCS can measure the reaction kinetics under equilibrium
conditions. If a small number of molecules are
observed the intensity will fluctuate as the fluorophore
binds to and dissociates from the macromolecules. The rate
of intensity fluctuations contains information on the sum of
the forward and reverse reaction rates.
Because of the ability of FCS to determine the number
of observed particles, and to determine the rates of diffusion,
and other dynamic processes, there has been a rapid
expansion of FCS technology into a wide range of applications,
including high-throughput screening, DNA analysis,
and detection of small numbers of intracellular species. In
the following section we describe the theory and practice of
FCS with examples to illustrate the potential of this technology.