Biophysical Journal Volume 101 December 2011 2855–2870
2855
Fluorescence Correlation Spectroscopy: Past, Present, Future
Elliot L. Elson*
Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, Washington University in St. Louis,
St. Louis, Missouri
ABSTRACT In recent years fluorescence correlation spectroscopy (FCS) has become a routine method for determining
diffusion coefficients, chemical rate constants, molecular concentrations, fluorescence brightness, triplet state lifetimes, and
other molecular parameters. FCS measures the spatial and temporal correlation of individual molecules with themselves and
so provides a bridge between classical ensemble and contemporary single-molecule measurements. It also provides information on concentration and molecular number fluctuations for nonlinear reaction systems that complement single-molecule
measurements. Typically implemented on a fluorescence microscope, FCS samples femtoliter volumes and so is especially
useful for characterizing small dynamic systems such as biological cells. In addition to its practical utility, however, FCS provides
a window on mesoscopic systems in which fluctuations from steady states not only provide the basis for the measurement
but also can have important consequences for the behavior and evolution of the system. For example, a new and potentially
interesting field for FCS studies could be the study of nonequilibrium steady states, especially in living cells.
INTRODUCTION AND HISTORICAL BACKGROUND
During the almost 40 years since its introduction (1), fluorescence correlation spectroscopy (FCS) has evolved from
an esoteric and difficult measurement to a technique
routinely used in research and technology (2,3). Yet, the
value of FCS for the physical and biological sciences
consists not only in the measurements it makes possible
but also in the concepts that it illustrates and that form its
basis. FCS provides a window on the mesoscopic world
and is one progenitor of the field of single-molecule
measurements (2). Two groups, one at Cornell University
(Ithaca, NY) and the other at the Karolinska Institute (Stockholm, Sweden) simultaneously developed the FCS approach. The Ithaca group focused on lateral diffusion and
chemical reaction kinetics (1,4–6) and the Stockholm group,
on rotational diffusion (7,8). This minireview describes
some of the motivations for the development of FCS, current
applications, and suggests some new directions for the
future.
One of the original motivations for FCS in Ithaca was to
study the mechanism of DNA untwisting (9). An elegant
model had been proposed to account for the untwisting of
the DNA strands after a perturbation of state sufficiently
large to release all basepair interactions (10). Still open
was the question of how the strands untwisted when only
a fraction of the basepairs was melted. Because of the differences in AT and GC basepair stability, regions of the DNA
molecule rich in AT melt at lower temperatures than those
rich in GC, forming interior loops. To test a kinetic model
that accounts for this conformational heterogeneity, it was
desirable to measure the kinetics of melting in steps that
Submitted September 7, 2011, and accepted for publication November 10,
2011.
*Correspondence: [email protected]
included the least number of interior loops. Thus a small
perturbation, e.g., temperature jump, is essential, but the
smallest perturbation is no perturbation at all. The initial
plan, therefore, was to measure the kinetics of fluctuations
of helicity of DNA molecules maintained in equilibrium
within the helix-random coil transition region. The hypochromic effect on ultraviolet absorbance that results from
the unstacking of the nucleotide basepairs was to be the
indicator of fluctuations of helicity (11). Fortunately, studies
then being carried out by Bresloff and Crothers (12) suggested that a useful tune-up experiment would be to measure
fluorescence fluctuations caused by binding and unbinding
of ethidium bromide (EB) to DNA. Eventually this preliminary experiment led to the development of FCS, and it was
clear that the original idea of measuring helix fluctuations
by hypochromicity was utterly impractical.
The aim of the EB-DNA studies was to demonstrate that
the kinetics of chemical reactions could be measured via
spontaneous fluctuations of reaction progress in a system
resting in equilibrium, and this was accomplished (1,4,5).
The origins of this idea are rooted in chemical relaxation
kinetics (13) and in dynamic light scattering (14–17) on
the experimental side and on Onsager’s regression hypothesis on the theoretical side. Although elegant theoretical
treatments of measurements of chemical reaction kinetics
in equilibrium systems by dynamic light scattering had
been developed (18,19), experimental measurements were
unsuccessful. Dynamic light scattering is an excellent
approach for measuring molecular transport in highly purified, relatively concentrated systems. It is less useful for
measuring chemical reaction progress; the polarizability
that determines the magnitude of scattering typically
changes very little because of chemical transformation.
This realization led to the idea of using more chemically
sensitive optical parameters such as fluorescence, optical
Editor: Edward H. Egelman.
Ó 2011 by the Biophysical Society
0006-3495/11/12/2855/16 $2.00
doi: 10.1016/j.bpj.2011.11.012
2856
absorbance, or optical rotation as indicators of reaction
progress. Of these, fluorescence has some important advantages. Not only can it provide a sensitive indicator of
reaction progress in favorable systems, fluorescence
measurements are 1), simple and rapid; 2), have a low background due to the Stokes shift of the fluorescence emission
away from the excitation wavelength; 3), can be measured
with high sensitivity down to the nanomolar and even
single-molecule range; and 4), have a selectivity that allows
for the measurement of specific fluorescent molecules in
systems that contain high concentrations of molecules that
are not fluorescent in the same spectral range. Furthermore,
fluorescence microscopy enables the facile application of
FCS to small systems, especially biological cells.
The original FCS experiment was set up on an optical
bench with the EB-DNA sample contained in a flat thinwalled cell with 150- or 25-mm path-length. A long-focallength lens focused the laser beam through the sample so
that the beam was effectively uniform (5.7-mm radius)
through the sample. This lack of variation along the optical
(z) axis provided an effectively two-dimensional system (5).
Immediately after the first successful demonstration of
FCS with the EB-DNA system, the experiment was performed on a confocal microscope (20) for the study of the
mobility of molecules on cell surfaces. At that stage of its
development, however, FCS was no longer suitable. To
obtain a statistically adequate fluctuation record required
excessively long times for measurements on labile systems
like live cells. It became clear that fluorescence photobleaching, which had previously been introduced by Peters
et al. (21) and Edidin et al. (22), would be more useful. Our
group developed a general fluorescence photobleaching
recovery method (20,23), and applied it to study the
mobility of membrane proteins (24–28) along with many
other laboratories (29). The advantage of fluorescence photobleaching recovery over FCS for these studies arose from
the fact that, being a measurement of a macroscopic fluorescence recovery, the signal is larger, and a single recovery
transient is sufficient to characterize the diffusion rather
than a record of many fluctuations that each required a comparable time. Although FCS and photobleaching recovery
seem rather different, their implementation on a confocal
microscope (20) and their theoretical interpretation are
fundamentally quite similar (30).
CONCEPTUAL BASIS OF FCS
Fluorescence fluctuation autocorrelation
function
FCS provides information about both kinetic and thermodynamic properties of fluorescent molecules in solution. The
temporal relaxation of the measured fluorescence fluctuations provide the former; the amplitudes of the fluctuations,
the latter. Conventional methods for measuring diffusion
Biophysical Journal 101(12) 2855–2870
Elson
coefficients and chemical reaction rate constants rely on
establishing an initial state displaced from equilibrium and
then measuring the rate of the system’s relaxation back to
equilibrium. For example, diffusion coefficients can be
measured by observing the dissipation of an initial concentration gradient (31) and chemical rate constants by
observing the rate of return of system to equilibrium after
a temperature jump (13). FCS determines these coefficients
in systems that remain in a steady state, either equilibrium
or nonequilibrium.
Although the average concentrations in these systems
remain constant in space and time for long (in principle
infinite) time-periods, they spontaneously fluctuate locally
within the system due to Brownian motion in space and as
a Poisson process for chemical reaction. Thus, molecules
constantly diffuse into and out of a local subvolume of the
system, causing fluctuations of their local concentrations
and therefore, if the molecules are fluorescent, fluctuations
in the fluorescence measured from the subvolume. Similarly,
the concentrations of the reactants in a chemical reaction
system fluctuate about their equilibrium values, which, if
the reaction causes a change in fluorescence, also produce
fluorescence fluctuations. These fluctuations are stochastic
and differ one from another over time and position. Therefore, it is not possible to determine accurately a transport
coefficient, e.g., for diffusion or electrophoretic mobility,
or a chemical rate constant by measuring a single fluctuation.
Nevertheless, the rates at which the fluctuations dissipate are
determined on average by the same phenomenological transport coefficients and rate constants that govern macroscopic
dynamic processes (32).
To extract these commonly used coefficients it is necessary to carry out a statistical analysis of the fluctuation
data. A fluorescence fluctuation autocorrelation function,
G(t), accomplishes this for systems in which fluorescent
molecules participate in dynamic processes. G(t) ¼ hdF(t)
dF(t þ t)i ¼ hdF(0)dF(t)i. The symbols h.i imply averaging over a long (in principle, infinite) time-period. The
second equality emphasizes that the system is stationary
and can be understood as an average over many randomly
selected intervals t or as an ensemble average. The fluorescence fluctuation is dF(t) ¼ F(t) hFi, where hFi is the
average value of F(t). That G(t) is independent of t arises
from the fact that the system is in a steady state. Except
for nonequilibrium systems, e.g., oscillating systems, the
average product of a fluctuation amplitude at some time,
0, and a later time, t, hdF(0)dF(t)i is a decreasing function
of t as the fluctuation regresses to the steady state.
The fluctuations of fluorescence report on fluctuations of
concentration in the measurement subvolume. The fluorescence photons emitted by molecules of a single fluorescent
component, say the ith component, from a subvolume dV
at position r and time t is dFi(r,t) ¼ giI(r)ci(r,t)dV, where
I(r) is the intensity of the excitation laser beam and ci(r,t)
and gi are, respectively, the concentration and a factor that
Biophysical Reviews
2857
accounts for absorbance and quantum yield of the ith component. The number of photons detected by the photodetector
(typically, a photomultiplier or avalanche photodiode) is
dF(r,t)cef(r), where cef(r) is the collection efficiency function that specifies the fraction of the emitted fluorescence
intensity that is registered (33). Thus, concentration and
th
fluorescence fluctuations are
R Nrelated for the i fluorescent
component as dFi ðtÞ ¼ gi N IðrÞcef ðrÞdci ðr; tÞdV, with
the integral taken over the volume of the entire system.
For simplicity in the following, we will suppose that
cef(r) ¼ 1. Finally, for a system that has M fluorescent
components,
FðtÞ ¼
M
X
Fi ðtÞ; dFðtÞ ¼
i¼1
M
X
Fi ðtÞ hFi i;
i¼1
and so
M P
M P
dFi ð0ÞdFj ðtÞ
GðtÞ ¼
i¼1 j¼1
M P
M
P
¼
i¼1 j¼1
M
P
2
hFi ðtÞi
i¼1
gi gi
RN
N
IðrÞIðr 0 Þ dci ðr; 0Þdcj ðr 0 ; tÞ dVdV 0
p
M
P
i¼1
2
;
gi hci i
(1)
RN
where the laser excitation power is P ¼ N IðrÞdV:
Experimental measurements are a sequence of numbers
of photons counted during time intervals or bins of duration
specified to suit the experimental system. The duration of
the time bin should be short compared to the shortest characteristic time of interest, but, to minimize the shot or
detector noise, no shorter. For the ith time bin of duration
b
dt, the experimentally measured photon count is FðidtÞ.
b
(The accented F indicates an experimental measurement
of F(t).) Then, the experimentally measured correlation
function is defined operationally as
N
1 P b
b
limN/N
d FðidtÞd Fðidt
þ tÞ
N
i¼1
b
;
GðtÞ ¼
b 2
h Fi
N
1 Pb
b
b
b
b
FðidtÞ and d FðidtÞ
¼ FðidtÞh
Fi:
h Fi ¼ limN/N
N i¼1
(2)
Dynamics
The phenomenological rate parameters, diffusion coefficients, chemical kinetic rate constants, etc., are derived
from the experiment by comparison with analytical models
of the dynamic processes in the system. For example,
a system containing M chemical components in which diffusion, convection, and chemical reaction are all taking place
would be described with equations of the form
M
vdci ðr; tÞ
vci ðr; tÞ X
Tij dcj ðr; tÞ:
¼ Di V2 dci ðr; tÞ Vi
þ
vt
vx
j¼1
(3)
The first two terms on the right-hand side of Eq. 3 refer,
respectively, to diffusion with diffusion coefficient Di and
convection along the x axis at constant velocity Vi, of the
ith component. The third term represents chemical reaction
kinetics with Tij being the rate coefficient for the transformation of component j to component i. Note that Tij contains
chemical kinetic rate constants and, for nonlinear reaction
steps, also steady-state reactant concentrations. Each kind
of process yields a different characteristic relaxation rate.
For simplicity, consider a two-dimensional system, e.g.,
a cell membrane, interrogated by a Gaussian laser excitation
intensity profile: cef(r)I(r) ¼ I0 exp(2r2/w2), where r2 ¼
x2 þ y2 with x and y being coordinates in the plane of focus
of the microscope. Table 1 shows the correlation functions
for common dynamic molecular processes. The characteristic times each have a different dependence on the beam
radius w. The correlation functions for these different
processes are readily distinguishable in theory, but data of
high quality are required to accomplish this in practice.
Examination of the initial slope of the correlation function
can provide useful information about the mechanism of fluctuation relaxation.
For simple diffusion and diffusion plus convection, the
initial slope is limt/0 dGðtÞ=dt ¼ t 1
D . Because tD ¼
w2/4D, the initial slopes for these processes vary as w2,
which can tested by changing the objective lens or by using
a variable beam expander to vary w (34). For simple convection, the initial slope vanishes. The correlation times for
chemical reactions are independent of w and vary with reactant concentrations for reactions of order higher than first.
For coupled diffusion and reaction, the dependence of the
initial slope on w and concentrations is more complicated,
as can be seen from the analysis of the simple isomerization
reaction (4). Sometimes it is important to use different
methods to verify transport mechanisms that have been
deduced from FCS measurements (119).
In general, the solution of systems of equations in the
form of Eq. 3 is complicated. Significant simplification is
possible, however, if all the reaction components have the
same diffusion coefficients (or convection rates). Then the
autocorrelation function can be expressed as a simpler
product of a function that depends only on the transport
coefficients and a function that depends only on the chemical kinetic rate constants and equilibrium reactant concentrations (35).
Biophysical Journal 101(12) 2855–2870
2858
TABLE 1
Elson
Some of the processes that can be measured by FCS
Process
vdci
vt
2
Diffusion
Di V dci
Convection
Vi Vdci
Diffusion þ convection
Chemical reaction
Di V2 dci Vi Vdci
M
P
Tij dcj
j¼1
GðtÞ
Gð0Þ
t 1
1þ
t Di
h t 2 i
Exp t
" tVi2 #
tVi
Exp
t
1þ
t Di
t
1þ
t Di
h ti
N
P
As Exp ts
s¼1
Parameter
Reference
2
w
4Di
(5)
w
Vi
(6)
As above
(6)
Tij, As, and ts are functions of the rate constants
and equilibrium concentrations
(5)
t Di ¼
t Vi ¼
For simplicity, we suppose a two-dimensional system. There are M chemical components with concentration ci and N chemical reactions. For the ith component, the diffusion coefficient and convection velocity are Di and Vi, respectively. For coupled diffusion and reaction typical for an FCS measurement in an
open chemical reaction system (Eq. 3), the relaxation modes are often complicated functions mixing diffusion (and convection) and chemical reactions (5).
Amplitudes
Although the time dependence of G(t) yields a system’s
dynamic characteristics such as transport and chemical
kinetic coefficients, the correlation function amplitude,
G(0), is a thermodynamic property that provides information about the concentrations and brightnesses of the fluorescent molecules in the system. For a simple illustration,
suppose that n(t) is the number of molecules at time t in
an observation area or volume exposed to uniform excitation
intensity and that the fluorescence is proportional to n:
F(t) ¼ qn(t) and dF(t) ¼ q(n(t) hni), where q is the brightness of the molecules, i.e., the number of photon counts
emitted per second by a molecule observation region. The
normalized amplitude of the correlation function is
G(0) ¼ h[dF(0)]2i/hFi2 ¼ q2h(dn)2i/(qhni)2. FCS is almost
universally carried out on systems in which the concentrations of fluorescent molecules are very low, in the nanomolar range. Hence, the fluorescent molecules interact
negligibly with each other and so, as an ideal system, the
number of molecules in the observation volume can be
described by a Poisson distribution for which h(dn)2i ¼
hni (36). Then, G(0) ¼ hni1. Hence, we have the remarkable result that G(0) yields the absolute number of the molecules of the fluorophore in the observation region, and,
knowing the volume of the observation region, their concentration in solution. The mean fluorescence, hFi, then provides the brightness, q, of the fluorophore: q ¼ hFi/n ¼
G(0)hFi. These results can be derived directly from Eq. 1,
noting that as a consequence of ideality and the Poisson
distribution,
(4)
dci ðr; 0Þdcj ðr; 0Þ ¼ cj dðr r 0 Þdi;j
(4,37), where di,j is the Krönecker delta and d(rr0 ) is the
Dirac delta function. For a system with N species of fluorescent molecules, the result is more complex,
Biophysical Journal 101(12) 2855–2870
N
P
hci iq2i
1
i¼1
Gð0Þ ¼
N
2 ;
pw2 P
hci iqi
i¼1
as can readily be demonstrated using Eqs. 1 and 4. Adapting
this concept to laser scanning microscopy provides the basis
of the useful number-and-brightness (N&B) method for
characterizing fluorophores on cell surfaces (38).
One way to obtain information about the distribution of
the concentrations and brightnesses of a mixture of fluophores {ci,qi} is to evaluate the higher moments of the fluorescence fluctuations (39,40). In a system containing M
distinct components, with the concentration and brightness
of the kth component being ck and qk, respectively, the cumulants of the measured fluorescence
fluctuations are related to
P
n
c
moments of the brightness, M
K¼1 k qK ; n ¼ 1,2,.. (A probability distribution can be reconstructed from its moments
(41). Cumulants are related to moments. Just as moments
can be derived from a Taylor’s expansion of a momentgenerating function, cumulants can be derived from a cumulant-generating function that is the logarithm of the
moment-generating function. Compared to moments, photocount cumulants have the advantage that they properly
account for detector (shot) noise.) For example, the brightnesses and concentrations in a two-component system can
be determined from the first three cumulants of the fluorescence fluctuations. An alternative is to evaluate the zerotime amplitudes of high-order correlation functions, e.g.,
hdFm ð0ÞdFn ðtÞi hdFm ihdFn i
mþn
hFi
(42,43). This approach has recently been simplified and extended (44). The practical applicability of this latter intriguing
method remains to be demonstrated in practical applications.
Biophysical Reviews
A
0.1
0.01
PCH
1E-3
1E-4
1E-5
1E-6
1E-7
0
5
10
15
20
25
30
Photons
B
1.10
G(τ)
More effort has been devoted to developing and applying
methods based on the photon count histogram (PCH) to
provide information about the distribution of molecule concentrations and brightnesses (45,46). As indicated above,
the data record for an FCS measurement is a sequence of
time bins each of which contains some number, n, of
photons including the possibility that n ¼ 0. The PCH is
the probability, P(n), that a time bin contains n photons.
To determine the values of the {ni,qi} of the fluorescent
particles from an experimental measurement it is necessary
to postulate an analytical model that has a given number
of particle species with specified values of ni and qi. A
good fit, e.g., using a nonlinear least-squares method, of
the measured PCH to one derived from the model corroborates the adequacy of the model and provides values of
{ni,qi}. The model is either based on prior knowledge of
the composition of the system or else is a minimal model
just sufficient to account for the measurements.
To construct the model PCH one accounts for the probabilities that m molecules are in the observation volume and
that these m molecules
produce n photons. For a single comP
ponent, PðnÞ ¼ N
m¼0 Pm ðmÞPn ðnjmÞ, where Pm(m) is the
probability that m molecules are in the laser-illuminated
observation volume and Pn(njm) is the conditional probability that n photons are emitted from the m molecules
(45). Both Pm and Pn are Poisson probability distributions.
The PCH for a multicomponent system can be expressed
as convolutions of the PCHs of the various system components (47) or as a product
of the generating functions,
P
n
H(x) (where HðxÞ ¼ N
n¼1 PðnÞx ) for the PCHs of each
component (45).
Fig. 1 A illustrates experimentally measured PCH curves
for a preparation of allophycocyanine. The PCH is most
simply interpreted in terms of a two-component system
with one component at low concentration that is 15-fold
brighter than the component at higher concentration.
Fig. 1 B shows the fluctuation autocorrelation function measured for the same solution. For spherical particles, the ratio
of diffusion coefficients should vary inversely as the cube
root of the molecular weight. Hence, if the aggregate were
approximately spherical, the diffusion coefficients of the
two components should be in the ratio of (15/1)1/3 ¼ 2.5.
The FCS data are well fitted by fixing the correlation times
in the ratio of 2.5 although the best fit to the correlation
function yields a ratio of 4.5. These graphs are meant to
illustrate the relationship between the PCH and the diffusion
correlation function for an aggregation system. Because a
range of parameters will fit both PCH and FCS curves,
however, these data alone are insufficient to define the
brightness and numbers of the components of the system.
A proper PCH/FCS analysis of this system requires more
measurements.
In principle, this approach can supply the values of {ni,qi}
for an arbitrary multicomponent system. In practice, however, to identify the values even of only a few components
2859
1.05
1.00
1E-5
1E-4
1E-3
0.01
0.1
1
τ (sec)
FIGURE 1 Illustration of the application of PCH and FCS to an aggregating system. (A) Experimental PCH measurements fit to a two-component
model system. These data are from a preparation of allophycocyanin
trimers from the thermophilic cyanobacterium Thermosynechococcus
vulcanus (sample from Liron David and Robert Blankenship). Data were
binned at 200 ms. (Solid curve) Best fit of the data to a two-component
system that yields the number and brightness of each of the components:
N1 ¼ 23.4 5 0.3, q1 ¼ 4100 5 60 s1; N2 ¼ 0.06 5 0.003, q2 ¼ 65000 5
1400 s1. (Dashed and dotted curves) One-component PCH curves calculated for the dimmer and brighter components, respectively. (B) Fluorescence fluctuation autocorrelation function for the sample shown in panel
A. The data are compared to two theoretical curves that are virtually indistinguishable. One is a two-component, unconstrained fit (first line in table
inset), and the second curve has fixed diffusion times in a ratio of 2.5:1.0,
which is the cube root of the brightness ratio in the PCH. The errors
are provided by the ConfoCor software (Carl Zeiss Microimaging, Jena,
Germany); these are presumably the asymptotic standard errors. N is the
number of fluorescent particles in the sample volume; t1 and t2 are the
diffusion correlation times for the two components; and F1 is the fraction
of the correlation function amplitude assigned to component 1. (Both
curves have triplet components with approximately the same correlation
time and amplitude fraction; not shown.)
Biophysical Journal 101(12) 2855–2870
2860
Elson
requires an extensive fluctuation data record. One source of
ambiguity is the fact that a dim particle near the center of the
Gaussian laser excitation profile appears similar to a bright
particle farther from the beam center. The ability of the PCH
approach to distinguish between models has been explored
(46) and the approach has been extended to the time domain
and the use of several fluorescence colors (e.g., (48–52)).
Digman and Gratton (64).) Earlier implementation of the
pair correlation concept involved cross correlation of fluorescence from two laser foci separated by a fixed distance
(e.g., (65–67)). An advantage of the approach described
above is that position pairs are sampled over the entire
scan range rather than only at the two foci of the split laser
beam (64).
Single-molecule aspects of FCS
FCS measurement error
Although our formulation of FCS theory uses conventional
continuum chemical concentrations c(r,t), FCS is essentially
a single-molecule measurement. Due to the ideality of
systems investigated by FCS, fluorescent molecules do not
significantly interact with one another, and so the motion
of each fluorescent molecule is correlated only with itself
and is uncorrelated with that of all the others. FCS measures
the behavior of many individual molecules without dwelling
on any of them. In this sense, it differs from current
approaches that identify individual single-molecules and
characterize their behavior one at a time (e.g., (53–55)).
Nevertheless, FCS can be regarded as a precursor of these
kinds of measurements and is capable of single-molecule
sensitivity (56,57).
The improvement of sensitivity to the single-molecule
level, which was crucial in transforming FCS from an
esoteric and difficult to a routinely applied measurement
(3), resulted from a variety of technological advances
including improvements in lasers, correlators, and microscopes. The reduction of the laser-illuminated sample region
to a diffraction-limited volume reduced background fluorescence and was an essential step in enabling single-molecule
sensitivity (56). Moreover, the reduction of the sample
volume and therefore also the diffusion fluctuation correlation time accelerated the acquisition of statistically significant correlation functions. Nevertheless, the use of
diffraction-limited confocal optics can raise problems in
precisely defining the shape of the laser-defined observation
volume. Diffraction effects can distort the shape of the
sample volume enough to have a substantial effect on FCS
autocorrelation functions (58). Using two-photon excitation
(59–61) diminishes the magnitude of these effects (58).
Finally, an interesting application of the principle that
a molecule’s motion correlates only with itself is the pair
correlation function approach, recently demonstrated for
tracking populations of single fluorescent molecules, typically on cell surfaces (62). Because of the exclusive selfcorrelation of a molecule with itself, cross correlation
from two regions of an object will reveal the extent to which
a molecule can move from the first to the second region.
This approach is useful for mapping barriers to diffusion
on cell surfaces that define regions of the surface that are
inaccessible to the diffusing molecule and has been applied
to study transport through nuclear pores (63). (For an
instructive explanation of the pair correlation method, see
To understand the level of significance of FCS measurements, it is important to understand and evaluate the contributions of various error sources including both systematic
errors and random noise. Systematic errors are consistent
from measurement to measurement and can result, for
example, from misalignment of the optical system resulting
in distortions of the measurement volume and therefore in
errors in diffusion measurements. Random errors can result
both from photon (shot) noise and from finite character of
the fluctuation record. Shortly after the introduction of
FCS, Koppel (68) provided a pioneering analysis of the variance and signal/noise ratio of FCS measurements. This was
then extended by several authors (69–71). These articles
provide analytical calculations of the theoretical variance
of FCS measurements that can be used to optimize experimental measurements and to assess their validity.
Biophysical Journal 101(12) 2855–2870
FCS measurements below the optical resolution
limit
To measure diffusion by FCS, the diffusing fluorescent particles must be able to move between regions of high and low
excitation intensity. Hence, the volume of the laser-excited
observation region, the detection volume, must be smaller
than the volume in which the particles are confined. The
minimum detection area in the focal plane, set by the optical
diffraction limit, can be gauged by the full width at halfmaximum (FWHM) of the point spread function (PSF) of
the microscope objective: dxy ¼ PSFFWHM z 0.61l0/NA,
where l0 is the excitation wavelength and NA is the numerical
aperture of the objective (72). Also, dz z nl0/NA2, where n ¼
refractive index of medium (72). For currently available high
NA objectives, PSFFWHM values are in the range 200–250 nm
in the focal plane and 500–700 nm along the optical axis. It
could be useful to measure diffusion in compartments
smaller than this size range (for example, in endocytic vesicles or to test small-scale heterogeneity on cell membranes).
Furthermore, because the amplitude of the correlation function varies inversely as the number of fluorescent molecules
in the observation volume, smaller observation volumes
would allow FCS measurements at higher concentrations.
Recently, several approaches to shrink the observation
volume have emerged (72) that are applicable to FCS (73).
Among these is stimulated emission depletion microscopy, a method developed for superresolution fluorescence
Biophysical Reviews
microscopy that shrinks the excitation laser diameter by
using a second, ring-shaped laser intensity profile to deplete
the fluorescence excited by the peripheral regions of the
excitation beam (74). For example, stimulated emission
depletion FCS measurements have shown that cholesterolrich nanodomains <20 nm in diameter transiently trap glycophosphatidylinositol-anchored cell membrane proteins
(75). Methods based on evanescent radiation fields provide
another way to reduce observation volume. Of these, the
best known is total internal reflection fluorescence microscopy (TIRFM) in which the evanescent field illuminates
a thin layer of the object above its interface with a glass
substratum. Applications of TIRFM to FCS and to photobleaching recovery date back 30 years (76) and continue
to be actively pursued (e.g., Lieto et al. (77), Ohsugi et al.
(78), and Vobornik et al. (79)). Although TIRFM strongly
reduces the illuminated dimension, special measures are
needed to obtain a small spot in the x,y plane.
Using a parabolic mirror objective yields a detection
volume <5 attoliters (<5 1018 liter), well below a typical
value for conventional confocal microscopy (~100 attoliters) (80). By using this approach, it was possible to perform
FCS measurements at concentrations as high as 0.2 mM
(80). Zero-mode waveguides or nanometric apertures allow
FCS to be performed with even smaller detection volumes in
the zeptoliter range (1021 liter) so that samples are in the
single-molecule regime even at concentrations as high as
200 mM (81). FCS with zero mode waveguides has been
used to measure single-molecule motion on cell membranes
(82). Before this approach can quantitatively determine
diffusion coefficients, however, the shape of the effective
detection volume must be better defined. Near-field optical
microscopy provides another way to reduce observation
volume (83) that can be applied to study membrane transport (79). A study using near-field scanning optical microscopy FCS of transport through nuclear pores provides an
interesting illustration of this approach (84).
SELECTED APPLICATIONS
FCS has become a practical measurement method with
applications ranging from photophysics, e.g., triplet state
dynamics (85,86) and photon antibunching (87,88), to polymer physics (89–93) and to biology and medicine including
studies of living cells (2,3,64,94–96). An extensive survey
over this wide range is beyond the scope of this minireview.
Studies in two areas—molecular interactions and chemical
kinetics, respectively—illustrate how FCS concepts have
been extended in many directions.
Interactions, aggregation, polymerization
In biology and chemistry, it is often desirable to learn
whether molecular species can form heterologous complexes or polymerize (or aggregate). Archetypal examples
2861
include clustering of cell membrane proteins and amyloid
polymerization. The former phenomenon is central for the
activation of growth factor receptors, e.g., Yarden and
Schlessinger (97), and the latter, for the formation of pathogenic amyloid fibers (98). FCS enables study of these
phenomena at high dilution and in small systems like biological cells or in nonbiological nanostructures.
Fluorescence cross-correlation spectroscopy (FCCS)
detects interactions between molecules that have fluorophores with different fluorescence emission wavelengths,
e.g., la and lb (99,100). The fluorescence intensities of the
two colors, Fa(t) and Fb(t), detected in the same observation
volume, are separately registered by two different detectors.
If the a-colored and b-colored molecules move independently, their fluctuations are uncorrelated, and so the
cross-correlation function, Gab(t) ¼ hdFa(0)dFb(t)i ¼ 0.
If, however, the a-colored and b-colored molecules are
linked so that they diffuse into and out of the fluorescence
detection volume together, then Gab(t) s 0, and its initial
amplitude, Gab(0), depends on the fraction of the molecules
that are linked (101). Measurement of FCCS, using standard
one-photon excitation, requires precise alignment of the two
excitation lasers that excite the two fluorescence colors
to maximize their coincidence, with calibration to assess
cross talk between the detection channels and supply an
accounting of photobleaching (102). Using two-photon
excitation circumvents the alignment difficulties. Because
different selection rules pertain to one-photon and twophoton excitation, it is possible to simultaneously excite
spectrally distinct fluorophores with a single two-photon
excitation wavelength, eliminating the need for coincident
alignment of two separate one-photon excitation lasers
tuned to different wavelengths (103). It is also possible
with a favorable choice of fluorophores to carry out FCCS
measurements with a single one-photon excitation laser
(104). Pulsed interleaved excitation or alternating laser excitation provides a way to reduce cross talk between two fluorophores (105–107). The lasers that excite the two different
fluorophores are alternatively pulsed at intervals that allow
complete decay of the fluorescence intensity of one color
before the excitation of the other. This allows uncontaminated detection of the photons emitted from the two fluorophores. Several applications of FCCS have been described
in a recent review (99).
Aggregation and interaction can also be detected through
their effects on molecular frictional coefficients and on
brightness. An early approach was to measure the decrease
in the diffusion coefficients of the reactant molecules due to
their formation of larger and therefore more slowly diffusing
structures (3). Although this approach was applied successfully, it is relatively insensitive because diffusion depends
weakly on the size of a compact diffusing particle. The
diffusion coefficient of a sphere varies inversely as its radius
and therefore as the cube root of its molecular weight, i.e., as
the cube root of the number of subunits in an approximately
Biophysical Journal 101(12) 2855–2870
2862
Elson
spherical aggregate. In contrast, fluorescence brightness can
be much more sensitive to aggregation. Suppose that each
monomer or subunit in an aggregate or polymer has a fluorescent label and that the fluorophores in the aggregate do
not interact electronically, i.e., they do not quench or
enhance each other. Then, the brightness of the aggregate
will be directly proportional to the number of subunits (6).
As we have seen, the average molecular brightness is readily
available in a FCS measurement from G(0)hFi.
The accuracy of brightness measurements increases with
the number of observed fluorescence fluctuations. For
methods such as standard FCS or PCH fluorescence intensity distribution analysis (FIDA), the rate at which fluctuations are observed depends on the diffusion rate of the
fluorescent molecules or particles. If the lifetime of the
fluctuations, tD, is large, an excessively long time may be
required to collect enough fluctuations. For solution
samples, one could accelerate the accumulation of fluctuation data by flowing the sample past the laser beam. This
acceleration will occur if tV < tD, where tV and tD are the
characteristic times of flow and diffusion (Table 1) (6). A
simpler approach, called scanning FCS (sFCS), avoids the
need to account for velocity gradients in the flow pattern
by scanning the laser beam over the sample. sFCS is most
readily applicable to measurements on stable structures
and in particular to cell surface measurements of membrane
protein aggregation (108). One obtains a record of the fluctuations of fluorescence intensity at positions along the scan
line to yield a correlation function of the form
GðxÞ ¼
hdFðxÞdFðx þ xÞi
;
2
hFðxÞi
or, operationally, if the fluorescence is measured at points
k ¼ 1.N along the scan,
Nk
P
b
b þ kÞÞ
d FðjÞd
Fððj
1 j¼1
b
GðkÞ
¼
!2
N
Nk
1 X
b
FðjÞ
N j¼1
;
where Nk ¼ Nk. Both FCS and sFCS detect series of independent samples of particle brightness, the former as particles diffuse into and out of the sample volume, the latter as
the laser beam is scanned across the object. Hence, for sFCS
as well as for FCS, G(0) ¼ 1/hNi, and so both methods can
yield average particle brightness and therefore aggregation.
This approach, based on spatial rather than temporal autocorrelation, can be further generalized to an analysis of
fluorescence fluctuations in images acquired by confocal
scanning laser microscopy, an approach called image correlation spectroscopy (ICS) (109). ICS is the progenitor of
a series of image correlation methods summarized below
and in Table 2 that have been admirably reviewed (110).
These methods are used mainly to obtain information about
Biophysical Journal 101(12) 2855–2870
TABLE 2 Image correlation spectroscopy and its
descendents
Name
STICCS
ICS
TICS
Correlation function
Reference
hdFa ðx; y; tÞdFb ðx þ x; y þ h; t þ tÞi
Gab ðx; h; tÞ ¼
hFa ðx; y; tÞihFb ðx; y; t þ tÞi
(110)
Gðx; h; 0Þ ¼
hdFðx; y; tÞdFðx þ x; y þ h; tÞi
hFðx; y; tÞi2
hdFðx; y; tÞdFðx; y; t þ tÞi
hFðx; y; tÞihFðx; y; t þ tÞi
(138)
hdFa ðx; yÞdFb ðx þ x; y þ hÞi
hFa ðx; yÞihFb ðx; yÞi
(138)
hdFa ðx; y; tÞdFb ðx; y; t þ tÞi
hFa ðx; y; tÞihFb ðx; y; t þ tÞi
(110)
hdFðx; y; tÞdFðx þ x; y þ h; t þ tÞi
hFðx; y; tÞihFðx; y; t þ tÞi
(113)
Gð0; 0; tÞ ¼
ICCS
Gab ðx; hÞ ¼
TICCS
Gab ð0; 0; tÞ ¼
STICS
Gðx; h; tÞ ¼
(109)
The most general space-time correlation approach is STICCS. The other
methods correlate subsets of spatial and temporal correlations (110). Abbreviations: ICS, image correlation spectroscopy; STICCS, spatiotemporal
image cross-correlation spectroscopy; TICS, temporal image correlation
spectroscopy; ICCS, image cross-correlation spectroscopy; TICCS,
temporal image cross-correlation spectroscopy; STICS, spatiotemporal
image correlation spectroscopy.
aggregation of or interactions among cell surface proteins.
They have two important advantages: 1), large quantity of
fluorescence fluctuation data is simultaneously and rapidly
acquired in individual images, and 2), the morphological
information in the image can be correlated with the
measurements of aggregation.
ICS extends the sFCS approach to planar objects, e.g.,
cell surfaces, in the form of a two-dimensional spatial correlation function,
GICS ðx; hÞ ¼
hdFðx; yÞdFðx þ x; y þ hÞi
;
2
ðhFðx; yÞiÞ
and
N P
M
P
b kÞd Fðj
b þ x; k þ hÞ
d Fðj;
1
k¼1 j¼1
b hÞ ¼
Gðx;
:
#2
"
NM
N P
M
P
b kÞ
Fðj;
k¼1 j¼1
Using a confocal or two-photon laser scanning microscope,
the excitation laser intensity profile, determined by the point
spread function of the microscope objective lens, integrates
the emission intensity detected from the object area (pixels)
that it spans at each scan location. Given the usual Gaussian
intensity profile, I(x,y) ¼ I0 exp[2(x2þy2)/w2],
2
x þ h2
GICS ðx; hÞ ¼ GICS ð0; 0Þexp
w2
(110). Fitting this Gaussian function then yields GICS(0,0).
(This fitting process evades a shot noise artifact at x ¼ 0,
Biophysical Reviews
2863
h ¼ 0 (109).) The interpretation of ICS data is based on the
presumption of a random distribution of fluorescent particles (molecules) that is described by the Poisson distribution. Therefore, as with data acquired by time correlation
or by scanning, GICS(0,0) ¼ 1/hNi, where hNi is the average
number of fluorescent particles in the beam area (¼ pw2) in
the fluorescence image. As before, one can determine the
mean brightness of the fluorescent particles as hqi ¼
GICS(0,0) hFi and the mean aggregate size from GICS(0,0)
hFi/qm, where hFi and qm are the mean fluorescence over
the measured surface and the monomer brightness, respectively. In practice, it is essential to take into account background fluorescence from the cell surface (110). Because
FCS measures fluctuations from particles that diffuse into
and out of the sample volume, aggregates are detected as
dynamically linked. This is not so for ICS and sFCS for
which the sampling process is independent of the dynamics
of the particles in the system. ICS can also be implemented
using a high-sensitivity charge-coupled device camera to
view a full-field microscope image. For example, TIRFM
has been used with ICS to study IgE clustering on cell
surfaces (111).
For temporal image correlation spectroscopy (TICS),
fluctuations of fluorescence among area elements in the
measured surface are correlated over a time sequence of
images (Table 2) (112). Fluorescent particles can enter or
leave a particular area element on the cell membrane,
dxdy, by a number of dynamic mechanisms including diffusion, convective flow, or chemical reaction. For example, as
we have seen, diffusion into and out of dxdy yields a characteristic correlation function ~(1 þ t/tD)1. If diffusion is
homogeneous across the surface, then
GTICS ¼
Gð0; 0Þ
t þ GN ;
1þ
tD
where GN is a long-time offset and, as before, tD ¼ w2/4D.
Image cross-correlation spectroscopy (ICCS) is the
straightforward extension of FCCS to an imaging mode
(Table 2) and, as with FCCS, ICCS can detect the association of molecules that have been labeled with fluorophores
of different fluorescence colors. Note that for FCCS the
cross-correlation signal requires the associated molecules
to move together into and out of the observation area. In
contrast, ICCS provides a measure of colocalization within
areas defined by the PSF of the microscope but does not
indicate a dynamic linkage. Temporal image cross-correlation spectroscopy (TICCS), the cross-correlation analog of
TICS, dispenses with spatial cross correlation but does
provide this dynamic link (Table 2); Gab(0,0,t) s 0 only
if a-colored and b-colored particles move together.
Spatiotemporal image correlation spectroscopy (STICS)
includes both spatial and temporal correlation of image
fluorescence and reveals the direction and velocity of systematic motion, e.g., convective flow, of fluorescent parti-
cles (Table 2). The spatial autocorrelation provides a
Gaussian peak that moves away from its initial center
(t ¼ 0) as the time-lag increases. Tracking this peak yields
direction and speed of the systematic motion (113).
Transformation of the STICS correlation function by a
two-dimensional spatial Fourier transform allows an easy
extraction of the desired dynamic contributions to the autocorrelation function from interfering dynamic processes
such as photobleaching and fluorophore blinking. This is
the aim of k-space image correlation spectroscopy (kICS)
(114). Space-dependent dynamic processes such as diffusion and flow depend on the Fourier variable, k. The correlation functions for diffusion and flow vary as k2 and k,
respectively. Photobleaching and blinking do not depend
on spatial variables and so are independent of k. Hence,
plots of the logarithm of the correlation function versus k
or k2 extract diffusion and flow rates from blinking and photobleaching. Of course, the situation becomes more difficult
if space-independent processes such as chemical reaction
kinetics are to be measured and the time constants of the
interfering and the desired processes are similar. A further
advantage of kICS is that it can be used without requiring
a calibration of the PSF of the optical system (114)
A scanning microscope sequentially scans the object field
line-by-line to form a rectangular grid of pixels that compose the image. This raster scanning occurs on three distinct
timescales: First, pixels along a line are rapidly scanned
with a dwell-time on the order of a few microseconds per
pixel. Second, scanning the entire line of pixels requires
a time on the order of a few milliseconds. Finally, the full
quota of lines required to produce the entire image requires
a time on the order of a second. Hence, correlating fluorescence fluctuations along a single line, across a range of
lines, and from image to image yields information about
dynamics, e.g., diffusion, that occurs on the microsecond,
millisecond, and second timescales. This is the basis of
raster ICS (115). Advantages of this approach include the
wide time-range over which dynamics can be measured,
the ability to relate the dynamic information to the structural
information in the image, and that readily available
commercial scanning confocal microscopes suffice for the
measurements. (Note, however, that using line or circular
orbit scanning may have some advantages over raster scanning: the former have millisecond temporal and submicron
spatial resolution, whereas the latter has microsecond
time-resolution but spatial resolution in the range of
micrometers (115).) A recent review presents a brief survey
of applications of ICS and related methods (110).
Measuring the clustering on cell membranes of growth
factor receptors has become a test case for fluorescence fluctuation and other methods. For example, ICS was initially
applied to demonstrate clustering of platelet-derived growth
factor receptors on human fibroblasts (109,116). A recent
article provides a survey of the application to this subject
of various fluorescent methods and also an analysis of
Biophysical Journal 101(12) 2855–2870
2864
clustering of ErbB receptors using the number-and-brightness (N&B) method (117). The ErbB proteins are a family
of tyrosine kinases of which ErbB1, the EGF receptor, is
the prototype. The N&B approach is based on the statistics
of fluorescence fluctuations in individual pixels of
a sequence of microscope images, taking into account not
only the fluctuations due to fluorescent molecules entering
and leaving the pixel but also the detector noise (38). The
basic principles of the N&B approach follow directly from
our earlier discussion of fluctuation amplitudes. The variance of the fluorescence, sn2, due to fluctuations in the
number of particles in the illuminated sample volume is
equivalent to the nonnormalized correlation function
defined as above as g(0) ¼ h[dF(0)]2i ¼ q2h(dn)2i ¼
q2hni ¼ sn2, where q is the particle brightness.
The total photocount variance, s2, also includes a shot
(detector) noise contribution: sd2 ¼ qhni. (The shot noise
is described by a Poisson distribution, and so its variance
is proportional to its mean.) Hence, the total variance is
s2 ¼ sn2 þ sd2 ¼ hniq(q þ 1). Similarly, the mean photon
count is hki ¼ qhni. An apparent brightness is defined as
B ¼ s2/hki ¼ q þ 1 and an apparent particle number as
N ¼ hki2/s2 ¼ qn/(q þ 1). If the fluorescent molecules are
entirely immobile, sn ¼ 0, and B ¼ 1. A useful feature of
the N&B method is that N and B values can be mapped
onto the object, e.g., a cell. The B parameter is therefore
useful to distinguish regions of a cell surface in which, for
example, fluorescent membrane proteins are entirely immobile (B ¼ 1) from those in which they are mobile (B > 1).
Note also that the mobile contribution to B increases as
the laser excitation power increases while the immobile
contributions remains at B ¼ 1, independent of laser power.
Finally, it is straightforward to see that q ¼ (s2 hki)/hki
and hni ¼ hki2/(s2 hki). In most applications, especially
to biological objects like cells, it is also necessary to correct
for a constant background fluorescence and also slow photobleaching. This is accomplished in a straightforward manner
as described in Digman et al. (38).
Using N&B, Nagy et al. showed that members of the
ErbB family differed in their tendency to cluster and that
this tendency also depended on the concentration of the
receptor on the cell surface (117). Their results agreed
with earlier work using FIDA (118). Although FIDA holds
the promise of yielding the size distribution of receptor clusters, this method requires exceptionally high-quality data
that may be difficult to obtain on living cells. N&B supplies
only the mean values of the brightness and occupation
number, but it obtains a large volume of data from the
many pixels in an image. Different N&B values can be mapped to different regions of the cell surface.
Chemical reaction kinetics
To determine the rate of a chemical reaction, the reaction
must cause some change in a measurable property of the
Biophysical Journal 101(12) 2855–2870
Elson
reaction system. For FCS, this would typically be a change
in fluorescence intensity, i.e., the reaction quenches or
enhances the fluorescence of the reactants. Cross-correlation measurements could also detect changes in fluorescence color. FCS can be used to measure kinetics of
chemical reactions that are slow compared to the time
required to collect a sufficient fluctuation data set (minutes
to tens of minutes) by taking serial FCS measurements to
determine the relative concentrations of the reactants and
products over time. In this instance not only changes in fluorescence but also changes in transport rates, e.g., diffusion
or convection, could be used to measure reaction progress.
In most cases, however, transport coefficients are relatively
insensitive indicators of reaction progress. For reactions that
are fast compared to transport (diffusion or convection), the
reaction kinetics are uncoupled from transport rates and so
can be measured directly via fluorescence change as early
relaxation components in the fluctuation autocorrelation
function.
When transport and reaction rates are comparable, the
extraction of the kinetic parameters is more complex. In
general, the solutions to Eq. 3 take the form of eigenmodes
in which chemical reaction and transport are coupled in a
complicated fashion (4). Independent measurements of the
diffusion coefficients of the reactants and, for reactions of
order two or higher, the dependence of the correlation decay
rates on reactant concentrations are essential (e.g., Magde
et al. (5)). For systems in which the diffusion coefficients
and/or convection rates are the same for all components,
expression of the correlation function as a product of correlation functions that separately describe reaction kinetics and
transport is an important simplification that allows the extraction of the correlation function for reaction kinetics using
independent measurements of transport (35). Any study of
chemical kinetics requires a reaction model that is the
simplest possible to describe the experimental data. Finally,
it is always helpful to test the model by obtaining kinetic
data by several different experimental approaches (119).
Although the original motivation for FCS was to develop
a method that could measure the kinetics of chemical reaction
systems in equilibrium, there have been far fewer applications to this kind of problem than to measurements of transport rates and brightness. Conformational fluctuations of
proteins and other polymers is one kind of reaction kinetics
that has been studied by FCS (e.g., (54,120–122)). FCS has
also been used to measure the kinetics of DNA hairpin
helices, a subject that has recently received an excellent
review (123). Studies of hairpin helix formation date back
to work from the 1960s and 1970s on oligomers of the alternating poly(deoxyadenylate thymodylate) copolymer (dAT)
(124–126). Because of their alternating self-complementary
structure, dAT oligomers display numerous intermediate
helical conformations that complicate the interpretation of
experimental measurements. Nonalternating oligonucleotides provide simpler systems with which to study hairpin
Biophysical Reviews
2865
helix formation. The first application of FCS to this subject
used oligonucleotides with a fluorophore and a quencher
attached to the 50 and 30 ends, respectively (127).
The nucleotide sequences at the two ends were 50 CCCAA and 30 -TTGGG. Intervening were the loop nucleotides composed of varying lengths of T or A. In the hairpin
helix conformation, the fluorescence was quenched. When
the stem helix melted, the fluorophore and quencher were
no longer held in apposition and the fluorescence increased.
At temperatures near the helix opening transition, FCS
measurements reflected both diffusion (tD ~150 ms) and
the relaxation time for the opening and closing of the hairpin
helix (tR ¼ 5 ms – 1 ms). Assuming that the diffusion coefficient of the oligonucleotide was sufficiently insensitive
to its conformation, the correlation function could be
expressed as G(t) ¼ GD(t)GR(t), and GD(t) could be
measured with control oligonucleotides that did not produce
fluorescence fluctuations from the conformational process.
Then GR(t) ¼ G(t)/GD(t) provides tR. An important
assumption is that the transition between open (O) and
kþ
closed (C) conformations is a single-step process: O % C,
k
with rate constants kþ and k and the equilibrium constant
K ¼ k/kþ. Then,
GR ðtÞ ¼ 1 þ
1p
expðt=t R Þ;
p
where p is the fraction of the oligonucleotides in the open
conformation and 1=t R ¼ kþ þ k. By measuring the
open-closed (melting) equilibrium (using simple fluorometry) at various temperatures one can determine K(T)
1=t R
and k ¼ kþK.
independently, and then kþ ¼
ð1 þ KÞ
Thus, the rate constants are obtained from the FCS results
and the activation energies for opening and closing can be
determined from the dependence of kþ and k on temperature (127).
Despite its elegant demonstration of how FCS can be used
to dissect a chemical reaction system, an important flaw in
this analysis appears to be its assumption of a one-step
opening-closing transition. Additional studies using both
FCS and laser temperature-jump for kinetics and PCH to
determine the relative concentrations of open and closed
states revealed that the one-step model was insufficient to
describe the data. A three-state mechanism was proposed
in which the unfolded oligonucleotide forms an intermediate
with closed loop and quenched fluorescence but incomplete
helical stem (123). The FCS measurements describe this
process that occurs in the time-range of tens of microseconds.
Formation of the complete hairpin helix is a slower process
requiring milliseconds or longer. Further studies that define
the energy landscape for hairpin helix formation and characterize kinetic traps that slow the formation of the native
hairpin are summarized by Van Orden and Jung (123).
An essential requirement for direct measurements of
kinetics of chemical reactions (or conformational changes)
by FCS is that the chemical relaxation rate be fast or, at least
comparable, to the correlation times for diffusion. If diffusion is fast compared to reaction then the reaction components diffuse into or out of the detection volume before
the effects of the reaction can be detected. It is also essential
that the reaction cause a substantial change in fluorescence.
Both criteria are satisfied in the hairpin measurements
described above. It may also be useful to note that transport
depends on the radius of the detection volume, w, but chemical kinetics do not. Therefore, varying this radius can help
to disentangle contributions from transport and reaction
kinetics.
Possible future application to nonequilibrium
steady states
In biological cells, some types of molecules (e.g., genes,
mRNA molecules, and regulatory proteins) may be present
in concentrations so low that spontaneous fluctuations can
influence physiological behavior. These fluctuations can
cause functional epigenetic differences among isogenic
cells (128,129) and could contribute to evolutionary adaptation and disease (130). Single-molecule approaches have
proved very useful to analyze stochastic effects in gene
expression (131,132). It seems likely that measurements
of the dynamics and concentrations of sparse molecules in
cells (e.g., some transcription factors and regulatory
kinases) by FCS could also help us to investigate mechanisms of cellular stochastic variation. The field of nonequilibrium steady states (NESSs) is both central to cell
behavior and relatively untouched by FCS. The possibility
of using FCS to study stochastic effects on NESSs in living
cells is worth considering (133).
A major virtue of FCS is that it provides measurements of
dynamic parameters for systems that remain unperturbed in
equilibrium; however, FCS is also suitable for measurements in systems in NESSs. In both NESS and equilibrium,
the concentrations of the reaction participants are statistically stationary in time, but, in contrast to equilibrium
steady states, energy must be dissipated to maintain a
NESS. Consider the following simple first-order system:
k1
k2
k3
k1
k2
k3
A % B % C % D:
(5)
If this system is in equilibrium, then the net flux for each
reaction must vanish, e.g., k2 CB ¼ k2 CC , where Cx is the
equilibrium concentration of x and for the system overall,
CD
k1 k2 k3
¼
:
k1 k2 k3
CA
In a NESS, however, there can be a net flux either to the left
or right. For example, if k2CBss > k_2CCss and Cxss is the
Biophysical Journal 101(12) 2855–2870
2866
Elson
NESS concentration of x, there is a net flux to the right, and
A is continuously transformed into D. To maintain the
steady state, the concentrations of A and D must be held
constant (guaranteeing that B and C are constant), and so
A must be continually supplied to, and D continually withdrawn from, the system—processes that expend energy.
(In a test-tube experiment, this can be achieved by a regenerating system.)
In cells, networks of metabolic and signaling reactions
drive physiological functions. When a cell is in a stable
functional quiescent state, e.g., as an interphase fibroblast
or endothelial cell, its underlying biochemical networks
are in stable NESSs. An important goal for systems biology
is to characterize these NESSs in molecular terms, i.e., to
determine the concentrations and reaction fluxes that
support the NESSs. If appropriate fluorescent reaction
components can be found, FCS can contribute substantially
to achieving this goal. As we have seen, concentrations can
be obtained directly from G(0), e.g., GBB(0) ¼ hNBssi1.
Because reaction constituents in a NESS have constant
concentrations, conventional chemical kinetic methods that
rely on measuring rates of macroscopic concentration change
are not useful in small systems (although perturbationrelaxation kinetics methods can be used for macroscopic
NESS systems). FCS, however, can measure reaction fluxes
in steady states without perturbing the system (133,134).
Consider the four-component system, Eq. 5. When the
system is in equilibrium, the two-color cross-correlation
functions GBC(t) ¼ GCB(t), as guaranteed by the principle
of detailed balance (4). In a NESS, however, GBC(t) s
GCB(t). Moreover, as can be seen from an analysis of the
simple one-step isomerization reaction (4), the flux from B
to C and the flux from C to B can be obtained with appropriate
normalization by taking the limit as t/0 of the appropriate
cross-correlation function divided by the time,
GBC ðtÞ
fluxB/C ¼ limt/0
t
and
fluxC/B ¼ lim
t/0
GCB ðtÞ
;
t
respectively (133). For this approach to work, B and C must
have sufficiently different fluorescent colors and sufficiently
high fluorescence intensities to supply a substantial twocolor cross-correlation signal.
One possible approach is Förster resonance energy transfer (FRET) (135). When energy is transferred from a donor
to an acceptor, the fluorescence of the donor is quenched,
and the fluorescence of the acceptor is enhanced. Because
the donor emits at a lower and the acceptor at a higher wavelength, it would be possible to obtain a two-color crosscorrelation function by cross correlating at the donor and
acceptor emission wavelengths. The measurement would
Biophysical Journal 101(12) 2855–2870
require that the chemical reaction change the energy transfer
efficiency, perhaps due to a large conformation change or
a redox reaction. To carry out this type of measurement
would require finding an appropriate system in which the
chemical relaxation rate was fast compared to diffusion
and the donor and acceptor fluorophores were both bright
and experienced a large change in FRET efficiency due to
the chemical reaction. Note, however, that unless the
FRET efficiency, E, of the donor acceptor pair changes
from nearly E ¼ 0 in one state to nearly E ¼ 1 in the other,
the extraction of the needed cross-correlation function is
complicated by the fact that for both B and C, both donor
and acceptor fluorescence is detected. The application of
FRET to conformational change and reaction kinetics has
been perceptively discussed (136,137).
CONCLUSIONS
Over the past four decades, FCS has evolved from an
esoteric and difficult experiment to a routine measurement
used in chemistry, biology, biophysics, and biotechnology.
Not only is it a useful measurement method, its conceptual
basis also provides an introduction to the behavior and characterization of mesoscopic systems. It is a bridge between
measurements on macroscopic systems and on single molecules. FCS is itself a type of single-molecule method, in that
the signal results from self-correlation of individual molecules although many molecules (rather than only one)
provide the signal. This information is extremely important
for fluctuating nonlinear chemical reaction systems and is
not available in data on state transitions within an individual
molecule. When the method was first introduced, it would
have been difficult to predict the variations and extensions
of FCS that have been developed in fluctuation amplitude
analysis, imaging, and diverse types of optical approaches
such as two-color cross correlation and multiphoton excitation. Similarly, we may also presume that the future will
bring further unexpected developments. Some of these
may be in the areas of nonequilibrium steady states and
stochastic behavior of individual cells, each of which is
a biochemical reaction system.
The development and application of FCS at Cornell and beyond resulted
from the work of many people. I can list only a few whose contributions
seem to me notably conspicuous. All of the work at Cornell benefitted
greatly from the wisdom, enthusiasm, and experimental expertise of Watt
Webb. The initial demonstration of FCS could not have happened without
the persistence and technical know-how of Douglas Magde. Dennis Koppel
and Daniel Axelrod established the microscope-based versions of FCS and
developed our version of fluorescence photobleaching recovery. Joseph
Schlessinger was the prime mover in the early applications of these
methods to cells. In later work, Hong Qian provided a number of important
contributions including, among others, analyses of the FCS optical system,
measurement noise, and the high moment approach to measuring molecule
number and brightness. Saveez Saffarian extended the analysis of measurement noise and carried out studies of the aggregation of EGF receptors and
of a matrix metalloproteinase Brownian ratchet. I am also grateful to Rudolf
Biophysical Reviews
Rigler for the work that he and his colleagues have done that led to the
establishment of FCS as a widely accessible measurement method as
well as for the many interesting and wide-ranging applications that they
have provided. Thanks also to K. M. Pryse for supplying Fig. 1 and to
Hong Qian for suggestions about the text.
I thank the National Institutes of Health (R01-GM084200) and the National
Science Foundation (CMMI 0826518) for their financial support.
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