Simultaneous Multicolor Fluorescence Cross-Correlation Spectroscopy
to Detect Higher Order Molecular Interactions Using Single Wavelength
Ling Chin Hwang,*yMichael Go ¨sch,yTheo Lasser,yand Thorsten Wohland*
*National University of Singapore, Department of Chemistry, Singapore 117543, Singapore; andyEcole Polytechnique Fe ´de ´rale de
Lausanne, Laboratoire d’Optique Biome ´dicale, CH-1015 Lausanne, Switzerland
dynamics in solution and even in living cells. Usually, in the optical setup, either two laser beams have to be superimposed in
their respective confocal volumes or two-photon excitation is used for a dual-color detection system. It has been shown recently
that fluorescence cross correlation can be achieved with spectrally similar fluorophores using single wavelength excitation
fluorescence cross-correlation spectroscopy (SW-FCCS). In this study, we show that SW-FCCS allows the simultaneous
excitation of up to three fluorophores in which the cross correlation of their fluctuation signals is detected separately in three
detection channels. The experimental and theoretical model to describe triple pairwise cross correlations incorporating cross
talk and possible changes in emission characteristics such as quenching upon binding are outlined. The effectiveness of
SW-FCCS to detect binding of three interacting partners is experimentally verified with a standard ligand-receptor model,
biotin-streptavidin, where differently labeled biotin ligands and their binding to a third-color labeled streptavidin are studied. The
cross-correlation amplitudes and their changes with stoichiometric binding are analyzed and the upper limits of dissociation
constants are determined. Performed with appropriate negative controls, SW-FCCS can determine interaction patterns between
ligands and receptors.
Fluorescence cross-correlation spectroscopy is a powerful method for the study of molecular interactions and
Fluorescence correlation spectroscopy (FCS) was introduced
three decades ago to measure intensity fluctuations of fluo-
rescent particles diffusing through a focused laser beam to
obtain information such as translational diffusion coeffi-
cients and chemical rate constants (1–3). The improvement
of this technique to single-molecule sensitivity was achieved
by using a confocal microscope system with a high numer-
ical aperture objective and single photon counting avalanche
photodiodes as detectors (4,5). Since then, it has become an
increasingly popular technique for the study of kinetics at
thermodynamic equilibrium. Besides being able to determine
the concentration and diffusion characteristics of the com-
ponent measured (6), it has also been used to measure
receptor-ligand interactions (7–9) and various processes such
as flow and chemical reactions (10,11).
The concept of FCS is based on the correlation analysis of
fluorescence fluctuations in a confined observation volume.
The sensitivity of the technique to detect binding of two or
more components depends on the relative change in mass
upon binding. For a multicomponent system consisting of
reactants and products labeled with the same fluorescent dye,
the only way of differentiating the product from the reactant
is when the product has a molecular mass that differs from
the reactants by a factor of at least 4–8 (12). This in turn
shifts the correlation curve to higher diffusion times by up to
a factor of 2 given by the Stokes-Einstein equation for
spherical diffusing particles (tD;M1=3). By separately
labeling the reactants with differently emitting fluorophores,
the labels can be simultaneously excited with two different
laser lines and detected in separate channels. The signals
from both detector channels can then be cross correlated and
the doubly labeled products easily distinguished from the
singly labeled reactants independent of their mass. Earlier
cross-correlation systems have made use of light scattering
or a combination with fluorescence to measure their cross-
correlation functions and determine rotational diffusion and
association-dissociation dynamics (13,14). In dual-beam
fluorescence cross-correlation spectroscopy, the setup con-
sisting of two spatially separated focal points has been
applied to characterize flow systems (15). Dual-color fluo-
rescence cross-correlation spectroscopy was first experimen-
tally realized by Schwille et al. to measure nucleic acid
hybridizations (16,17). The potential of this technique to
effectively measure biomolecular interactions has expanded
its applications to detecting PCR complexes (18), monitoring
enzyme kinetics (19,20), measuring protein-DNA interac-
tions (21), and the analysis of live cells (22,23). Cross
correlationhasalso beencombinedwithFCSandFo ¨rsterres-
onance energy transfer (FRET) for global data analysis (24).
Two-photon excitation laser sources have been used to
overcome the difficulty of aligning two laser beams to the
same confocal volume (25). Increased axial resolution from a
more confined focal spot reduces background fluorescence
and photobleaching making it suitable for in vivo studies
(26,27). Recently, two-photon excitation has achieved the
Submitted September 8, 2005, and accepted for publication April 5, 2006.
Address reprint requests to Dr. Thorsten Wohland, Tel.: 65-6516-1248;
Fax: 65-6779-1691; E-mail: firstname.lastname@example.org.
? 2006 by the Biophysical Society
Biophysical Journal Volume 91 July 2006715–727 715
excitation of up to three dyes simultaneously to perform
triple-color coincidence analysis (28). However, the high
cost of a high power femtosecond laser source and lower
emission rates limit its potential applications. A less ex-
pensive method is the excitation of two or more fluores-
cent dyes by one-photon excitation with single laser
wavelength by using dyes with similar excitation spectra
but spectrally different emission characteristics. With the
recent advent of long Stokes shift fluorophores such as
nanocrystal quantum dots (29,30) and tandem dyes (31,32)
or MegaStokes dyes (www.dyomics.com), multicolor imag-
ing using a single laser wavelength for excitation has been
achieved (33). Using single excitation wavelength in dual
color fluorescence cross-correlation spectroscopy (SW-
FCCS) was realized by Hwang and Wohland (34) to detect
ligand-receptor binding. The resolution of SW-FCCS was
explored by using dyes with similar emission characteristics
such as fluorescein and tetramethylrhodamine (35).
In this article, we present an extension of this technique to
multicolor SW-FCCS. Using a single laser wavelength to
excite up to three differently emitting dyes simultaneously,
we measured the binding of green ligand biotin-4-fluorescein
(BF) and yellow ligand R-phycoerythrin biotin (BPE) to
red receptor Alexa Fluor 647-R-phycoerythrin-streptavidin
(AXSA). We formulated a theory to explain the pairwise
cross correlations green 3 red (Ggr(t)), yellow 3 red (Gyr(t)),
and green 3 yellow (Ggy(t)) for this system. For ways to
extend the theory to take into account the sample impurities
and labeling ratios, refer to Weidemann (36) and Hwang
(35). It is shown that even with a higher amount of cross talk
between three differently emitting fluorescent labels all ex-
cited at the same wavelength, SW-FCCS is capable of dis-
criminating bound complexes from free reactants by more
than 6 SD difference in the cross-correlation amplitudes. The
capability of distinguishing trimers, dimers, and monomers
regardless of their molecular weight, when performed with
appropriate negative controls, opens up new possibilities of
studying higher order interactions in complex molecular
Cross correlation of triple species
Fluorescence correlation spectroscopy involves the statistical
analysis of fluorescence fluctuations coming from an illu-
minated observation volume. These fluctuations may arise
from fluorescently labeled molecules undergoing different
processes such as Brownian motion, fast transition between
singlet and triplet states, and receptor-ligand interactions.
Fluorescence signals Fi(t) and Fj(t) in detector channels i and j
are correlatedaccordingtothe normalizedcorrelationfunction
where i ¼ j for autocorrelation of a single detector channel
and i 6¼ j for cross correlation of two channels.
In the following we assume we have a system consisting
of R, a red fluorescent receptor with multiple binding sites for
one ligand, and Lgand Ly, the ligand that is either labeled
with a green or yellow emitting fluorophore. Considering a
solution of receptor and ligands, free ligands Lfwill bind
with free receptors Rfto form complex RLnat equilibrium
binding where n is the number of bound ligands on R. We
assume here that each complex formed consists of one
receptor with several ligands specifically bound, therefore
excluding oligomerization of this receptor.
disregard the multiplicity of the binding sites, the dissociation
concentration of reactants divided by the products,
¼RL 3 Lf
... ¼RLn?13 Lf
To take account of the multiple binding sites per receptor,
binomial coefficients are introduced to describe the possi-
bility of n ligands binding to ntbinding sites (37). The con-
centrations of free receptors and ligands are thus related to
the total concentrations of receptor Rtand ligand Ltminus the
sum of all bound receptors and ligands, respectively.
Rf¼ Rt? +
Lf¼ Lt? +
The concentrations of the complexes RLn, Lf, and Rfat
binding equilibrium can then be numerically determined by
simultaneously solving Eqs. 2–4.
The total concentration of ligand Ltconsists of the ligands
Lgand Ly. The probability of encountering either ligand Lgor
Lyto form a complex with a receptor is given by their mol
¼ 1 ? fLg:
Consider a receptor with ntbinding sites and n fluorescent
ligands bound, of which ngare Lgligands and nyare Ly
ligands (ng# n # nt). In this case we have to account for the
number of possibilities how to distribute firstly n ligands
over ntbinding sites and secondly ngligands Lgto the n
bound sites. The distribution of nyligands Lyto the ny(¼ n ?
716Hwang et al.
Biophysical Journal 91(2) 715–727
ng) remaining binding sites has then only one possibility.The
concentration of a complex with n bound ligands becomes
The first binomial coefficient describes the distribution of
n bound ligands over the total number of binding sites ntand
the second coefficient is the distribution of Lgover the total
number of bound ligands. Equations 3–7 will be used to
calculate the cross-correlation amplitude as shown below.
The time dependent total fluorescence signal Fi(t) in
detection channel i is the sum of all fluorescent species (s ¼
L, R, RL) contributing to the signal. It is determined by their
fluorescence yields Qi
s(often expressed as counts per
molecule per second), and the time dependent number of
particles NAVeffC(t) in the effective observation volume Veff.
NAis Avogadro’s number and C(t) represents the time-
dependent values of the averages Rf, Lf, or RL(n,ng) as defined
in Eqs. 3, 4, and 7, respectively. All possible species that
contribute with Qi
svia cross talk into the detection channels
are taken into account.
fluorophores. The second term represents the free receptor
and the third term denotes the complex itself with both types
of ligands bound to the receptor where the fluorescence yield
contribution of Lgand Lyare proportional to the number of
ligands bound; i.e., ng3 QLgand ny3 QLy. Changes in
fluorescence yields upon binding via processes such as
quenching or FRET are taken into account by the factors qLg,
qLywhere q ¼ 1.0 if there is no change in fluorescence yield.
Assuming that the emissionspectra do not undergo any shifts
in wavelength, qLg,qLyare the same in all channels.
in the cross-correlation amplitudes we calculate the cross-
correlation function at t ¼ 0. The fluorescence yield factor Qij
is obtained by the product of fluorescence yields in the cross-
uting from various species to the cross-correlation amplitude,
cross-correlation function in Eq. 1, and assuming a three-
dimensional (3D) Gaussian illumination intensity profile, the
cross-correlation amplitude then becomes
where the effective volume Veff is experimentally deter-
The cross-correlation function for the negative control
does not include binding of ligand to receptor therefore only
cross talk is contributing to the function
Equation 12 is based on the assumption that both Lgand
Lybind to R to form a trimer. But in the case where only one
type of ligand is bound to R and the other remains free, the
cross-correlation amplitude will resemble the positive con-
trol function for the bound ligand and receptor and the
negative control function for the free ligand. In this case we
have two possible cases.
Case1 : R1Lg1Ly/RLg1Ly:
In the case where all ligands binding to the red receptor R
are green ligands Lg(n ¼ ng) and the yellow ligands Ly
FiðtÞ ¼ Fi
¼ NAVeff Qi
¼ NAVeff ðQi
Biophysical Journal 91(2) 715–727
remain free, the probability of binding Lgbecomes 1. The
concentration of complex RLgfrom Eq. 7 becomes
All of the complexes formed consist of only RLg, therefore
there is no fraction of Lycontributing to the concentration of
free ligands Lfafter binding (fLy¼ 0) nor to the formation of
the complex RLg. Instead, all of Ly(¼ fLyLt) remains as
completely free ligands but still contribute to the cross-
correlation function between g 3 r via cross talk. These
conditions are substituted into the cross-correlation function
in Eq. 12 to obtain Gij(0) as a positive control for g 3 r
The first two terms in the numerator denote free Lgand
total nonbinding Ly, respectively. The third and fourth terms
represent the contribution from free R and complexes RLg,
respectively. The fluorescence yield factors Qij
(where s ¼ Lgor Lyor R) are described by
sfor species s
Because there are no bound complexes formed between Lg
and Lyor R and Ly, Ggy(0) and Gyr(0) represent the negative
controls and any contribution from the RLgligand-receptor
complexes comes via cross talk.
Case2 : R1Ly1Lg/RLy1Lg:
In the case where all ligands bound to red R are yellow Ly
(n ¼ ny) and green Lgremain free, the probability of binding
Lybecomes 1. Equation 14 then refers to the concentration of
complex RLy formed and the cross correlations can be
derived from Eqs. 15–17 by exchanging indices g and y.
Application of theory to biotin-streptavidin
The biochemical system we present here consists of the red
AXSA receptor R with up to four specific binding sites (nt¼
4) for biotin ligand that is differently labeled with fluorescein
(Lg) and R-phycoerythrin (Ly). In this case, we vary the
number of ngand nyligands bound to R from 0 to 4, such that
the complex is always at full binding with all streptavidin
binding sites occupied with biotin (see Materials and
Methods). The cross-correlation functions for the positive
and negative controls Gijcan be any permutations of detec-
tion channels in the green, yellow, and red, corresponding
to the colors at the emission maximum of the binding
MATERIALS AND METHODS
The SW-FCCS optical setup (Fig. 1) consisted of a CW Argon ion laser
(Lasos Lasertechnik GmbH, Jena, Germany) with two laser lines 488 and
514 nm. An excitation filter z488/103 (Chroma Technology, Rockingham,
VT) is used to transmit only the 488-nm excitation line. The collimated laser
beam is expanded by two biconvex lenses f ¼ 10 mm and f ¼ 150 mm and
illuminates the back aperture of a 403/1.15 NA water immersion objective
(Olympus, Hamburg, Germany) mounted on an Olympus microscope IX70.
The beam is focused to a diffraction-limited spot in a sample solution
containing fluorescent dyes. The emitted fluorescence is collected by the
same objective and is transmitted by a dichroic mirror 505DRLP (Omega
Optical, Brattleboro, VT), which separates the fluorescence from the
scattering and excitation light. Two more dichroic mirrors 560DRLP and
630DRLP(Omega)split the emission pathwayinto three detectionchannels:
green, yellow, and red. The intermediate focus by the tube lens is imaged
(magnification M ¼ 1) via three Achromat lenses f ¼ 30 mm (green), 40 mm
consists of a typical FCS setup with three detection pathways. A single laser
beam is expanded and collimated by lenses L1 and L2. The microscope
objective focuses the beam into the sample. The fluorescence light emitted is
focused by the tube lens L3 and split three ways into different wavelength
regions via dichroics D2 and D3. Lenses L4–L6 focus the emission beams
onto fibers O1–O3. F1, excitation filter; F2–F4, bandpass filters; L1–L6,
lenses; D1–D3, dichroic mirrors; O1–O3, optical fibers.
The three-color cross-correlation fluorescence spectrometer
718Hwang et al.
Biophysical Journal 91(2) 715–727
(yellow), and 50 mm (red) (Thorlabs, Newton, MA) onto the proximal end
of a 50-mm fiber (Thorlabs). Bandpass filters 520DF40 (Omega), HQ585/
40m and HQ700/90m (Chroma) are placed in front of the fiber ends to
further restrict the wavelength interval for an enhanced wavelength filtering.
Photons are detected with three avalanche photodiodes (Perkin-Elmer
SPCM-AQR-13 in the green and yellow channel and SPCM-AQR-14 in the
red channel). The signals are split between three hardware correlator cards
Flex02-12D, Flex99 (Correlator.com, Bridgewater, NJ), and three pairwise
cross correlations between green and red, yellow and red, and green and
yellow channels are performed at the same time on three separate personal
Ligands biotin-4-fluorescein, R-phycoerythrin biotin-XX conjugate and
receptor Alexa Fluor 647-R-phycoerythrin-streptavidin were purchased
from Invitrogen (Basel, Switzerland). Streptavidin is a homotetrameric
protein with four biotin-binding sites. To maintain AXSA always at full
binding with varying BF and BPE concentrations, 9 aliquots of AXSA was
fixed at constant concentration 5 nM whereas BF was added in increasing
concentrations from 0 to 20 nM to give BF/AXSA concentration ratios ¼ 0,
0.5, 1...4. This was incubated before adding decreasing concentrations of
BPE into the same aliquots from 20 to 0 nM at BPE/AXSA concentration
ratios ¼ 4, 3.5, 3...0 to fully occupy the remaining free binding sites of
AXSA. Three types of negative controls with all three reactants at the same
concentrations as the positive control were prepared in 9 aliquots to inhibit
(1) all binding sites, (2) BPE binding, and (3) BF binding. Negative control
(1) was prepared by first incubating AXSA with excess unlabeled D-biotin
(Invitrogen, 1 mM) to saturate completely all binding sites then adding BF
and incubating it before adding in BPE. In negative control (2), BPE binding
was inhibited by first incubating BF with AXSA and then saturating all
available binding sites with excess D-biotin (1 mM) before mixing BPE.
Likewise, negative control (3) was prepared by first incubating BPE to
AXSA and the remaining binding sites saturated with excess D-biotin
(1 mM) before adding the inhibited BF ligand. All incubation times were
;30 min and all samples were prepared in PBS buffer pH 7.4 (Sigma-
Aldrich Chemie GmbH, Buchs, Switzerland).
RESULTS AND DISCUSSION
Characterization of fluorophores for SW-FCCS
The fluorophores used for SW-FCCS have to be selected
based on several criteria. First, they have to have largely
different Stoke’s shifts for minimal emission spectral cross
talk in the detection channels. Second, the fluorophores have
to have similar excitation characteristics where they can be
optimally excited at the same laser wavelength and power
with negligible photobleaching. A suitable set of dichroics
and emission filters has to be chosen to match the maximum
emission wavelengths of the fluorophores while reducing
In this work, fluorescein, R-phycoerythrin, a 240-kDa
phycobiliprotein, and Alexa Fluor 647-R-phycoerythrin, a
tandem dye, were selected for SW-FCCS due to their over-
lapping excitation spectra and minimal cross talk. Tandem
dyes are shorter wavelength emitting dyes such as phyco-
biliproteins linked to a red emitting dye, e.g., Alexa Fluor
647 or Cy5. They are excited at 488 nm and due to strong
fluorescence energy transfer between the proteins and the red
emitting dyes; emission is mainly detected in the red. Their
molar extinction coefficients at 488 nm are shown in Table 1.
The series of installed dichroic mirrors and bandpass filters
effectively separates the emission wavelengths yet provide
high count rates. Their absorbance and emission spectra are
shown in Fig. 2, A and B. The fluorescence yields Q in each
channel were calculated from the photon counts per second
divided by the number of molecules determined from the
amplitude of the autocorrelationfunction. The Q-values were
corrected for background from Raman scattering of water in
the yellow and Rayleigh scattering of the laser line (Table 1).
The quenching of BF and BPE upon binding was
measured independently by adding excess unlabeled strep-
tavidin (Sigma-Aldrich) and by monitoring the changes in
their fluorescence intensities. The average fluorescence in-
tensity for BPE remains the same (q ¼ 1.0) upon binding
streptavidin but BF is quenched 83% (q ¼ 0.17) correspond-
ing to literature values (38). Note that the shorter biotin-4-
fluorescein ligand is quenched more than fluorescein-biotin
(;75%) due to stronger, faster, and noncooperative binding
between the less hindered biotin-4-fluorescein and strepta-
vidin (38). The fluorescence yields Q and the quenching
factors q in all three channels contributed by the fluorophores
are tabulated in Table 1. These values are used to calculate
the fits from Eq. 12 for the positive control curves. Average
photon count rates detected for all three channels were mea-
sured and compared between the positive and negative con-
trols for all binding ratios (data not shown). There were no
relative changes observed in fluorescence intensities upon
binding to form BPE-AXSA and BF-BPE complexes; there-
fore, FRET was excluded from the equations.
Other fluorophore combinations have also been consid-
ered for SW-FCCS. Organic dye pairs and quantum dots
have been measured previously with this technique (34,35).
In particular, quantum dots have become a convenient choice
for multicolor detection due to high quantum yield and
continuously tunable emission spectra that can all be excited
with one laser line. In these experiments, organic dyes were
selected instead of quantum dots due to the relative ease of
control of binding ratios of biotin to streptavidin. Commer-
cially available quantum dots are developed mainly for
imaging purposes and usually have high protein to label
conjugation (10–15 streptavidin molecules to 1 quantum
dot), making the binding concentrations difficult to manip-
ulate between three binding partners. In addition, aggrega-
tion problem with quantum dots has been previously
fluorescence yields (Q) in Hz/molecule and residual
fluorescence factor (q) after binding of the receptor
and ligands measured at a laser power of 50 mW
Molar extinction coefficients e at 488 nm,
Biophysical Journal 91(2) 715–727
reported (34). Thus although quantum dots are better in
terms of photostability and brightness, their aggregation in
solution makes it difficult to unambiguously determine
interactions. Alternatively, tandem dyes have been widely
used in flow cytometric applications for simultaneous de-
tection of multiple fluorophores excited with a single laser.
We use these bright dyes for the same advantages for the
application to SW-FCCS.
The large sizes of phycobiliproteins may pose problems as
labels for smaller-sized target biomolecules. Therefore, a
range of other possible dyes that could be used for in vitro
and in vivo SW-FCCS, including fluorescent proteins and
Megastokes dyes, have been measured. Their fluorescence
yields in the different channels are listed with their filter sets
in the Supplementary Material.
Calibration measurements were performed with Fluorescein
(Invitrogen, 1 nM) in the green and yellow channels and
AXSA in the red channel. Autocorrelation functions of BF,
BPE, and AXSA were measured with increasing laser power
from 50 to 500 mW to investigate the change of photon count
rates per particle and triplet state population against excita-
tion intensity. The diffusion times of the different molecules
showed deviations at higher excitation intensities; however,
this change depended on the molecular species and was
minimal in our setup below 100 mW for all three species. The
laser power of 50 mW was selected for minimal optical
saturation and photobleaching of the dyes, as well as optimal
count rates and low triplet fraction obtained between all three
fluorescent dyes. Ten correlation functions measured for 10s
were taken for all auto and cross-correlation functions. All
correlation curves were fitted with the Levenberg-Marquadt
fitting algorithm in Igor Pro (v4.0 Wavemetrics, Portland,
OR). A fitting model for one-component diffusion model
with triplet state (39) was used for the autocorrelation curves
of BF and AXSA. The BPE autocorrelation curves were
fitted with the one-component diffusion model with two
triplet states where the first decay corresponds to the singlet-
triplet lifetime in the microsecond timescale (40). The second
decay in the tens of microseconds timescale could be due to
other photodynamic process involved with R-phycoerythrin.
The normalized autocorrelation functions and their fits are
shown in Fig. 2 C. Fluorescein with a relative molecular
weight of 376.3 Da and a reported diffusion coefficient D of
3.0 3 10?6cm2/s (6) was used as a standard dye to
characterize the excitation volume. The beam waist radius wo
of 0.29 mm is calculated from the equation w2
where the average diffusion time tdof 70.6 ms of fluorescein
was determined from the fits of the autocorrelation functions.
The diffusion coefficients of BF, BPE, and AXSA at 2.6 3
10?6cm2/s, 2.2 3 10?6cm2/s, and 1.7 3 10?7cm2/s,
respectively, are calculated from the beam waist and the
respective diffusion times that are obtained from the fits in
Fig. 2 C. The relative molecular weights of the molecules are
then determined from the Stokes’-Einstein equation, which
assumes spherical molecules, to be 547.6 Da, 964 kDa, and
2,100 kDa, respectively. The experimentally determined
and AXSA. The excitation probabilities at the laser excitation line 488 nm
are 93%, 56%, and 50%, respectively. (B) Fluorescence emission spectra of
the three dyes. The detection windows of the molecules are specified by the
dichroics and bandpass filters selected. All spectral curves are normalized.
(C) Autocorrelation functions (gray curves) and their fits (black curves) all
normalized to their total number of molecules in the green, yellow, and red
detection channels for BF, BPE, and AXSA, respectively. The inset box
shows the average diffusion times obtained from the fitting of the functions.
(A) Absorbance spectra of the fluorophores labels of BF, BPE,
720 Hwang et al.
Biophysical Journal 91(2) 715–727
relative molecular weight of BF is similar to the literature
value of 644.7 Da. However, the molecular weights of BPE
and AXSA are much higher than the reported values of 240
and 294 kDa. This is most likely due to the nonspherical
shapes of the molecules (41) that the equation does not take
into account. A deviation from the spherical shape will lead
to a decrease in the diffusion coefficient (9).
The blinking times of the triplet states for different labels
are uncorrelated to each other despite being bound to the
same complex. Thus, the triplet fractions that are detected in
the autocorrelation functions are not detectable in the cross-
correlation functions. The triplet state will reduce the count
rate of the dye but the total number of molecules in the auto/
cross-correlation functions remains constant. All the cross-
correlation functions could be fitted sufficiently well with the
one-component diffusion model and the structure parameter
K (6) was obtained as 1.02 6 0.02 for Ggr(t), 1.06 6 0.18 for
Gyr(t), and 3.45 6 1.45 for Ggy(t). The average K parameter
was then fixed at 2 for all future cross-correlation fits.
Experimental results of biotin-streptavidin binding
In the following discussion, we will refer to AXSA as R,
BPE as Ly, and BF as Lg. In general the cross-correlation
functions exhibit the following trends. Under otherwise
equal conditions the positive controls will have higher cross-
correlation amplitudes due to complexes with multiple co-
lors than the negative controls. The negative controls show
phores into different channels. But both negative and pos-
itive controlswillshow decreasing amplitudes with increasing
numbers of complexes or ligands and receptors.
Correlations of triple-color complexes
At any one time, three different components were mixed
together in one sample aliquot and Ggr(t), Gyr(t), Ggy(t)
were measured simultaneously. The cross-correlation func-
tions and their fits for a ligand/receptor concentration ratio
Lg/Ly/R ¼ 2:2:1 are shown in Fig. 3, A–C. The negative
control amplitudes are due to cross talk between the re-
spective channels but the positive control amplitudes are
clearly higher due to the bound species. The amplitudes for
each ligand/receptor ratio for positive and negative controls
are plotted in Fig. 4, A–C. Fig. 4 A shows Ggr(0) decreasing
with 0–4 Lgand 4–0 Lymolecules bound to R due to the
formation of complexes containing R and Lg(Eq. 12). In the
case of the negative control (Eq. 13) where there is an
absence of receptor-ligand complexes, the curve decreases
sharply. The contribution to the amplitude is from cross talk,
which is analogous to the autocorrelation curves. Likewise
for Fig. 4 B, Gyr(0) decrease toward increasing concentration
of complexes containing R and Ly. Although there is no
direct binding between Lgand Ly, the binding through an
intermediate receptor R gives rise to Ggr(t) as shown in Fig.
4 C. In this case, the positive control amplitude drops to a
minimum toward the center of the curve where a maximum
of complexes containing Lgand Lyis reached due to the
presence of equal concentrations of Lgand Ly. As predicted,
the correlation amplitudes are smaller for negative controls
compared with positive controls in all cases.
Fitting analysis of triple-color complexes
It is well known that biotin-(strept)avidin has one of the
strongest interactions known at present between a receptor
and its ligand (Kd¼ 10?15M). To determine how accurate
the fitting parameters are to model the experimental curves,
we vary the parameters Kd and Veff and determine the
maximum values it can vary by changing the goodness-of-fit
x2-value no more than 50% from the minimum best fit value.
The negative control curves as shown by the shaded regions
in Fig. 4, A–C, are fitted (Eq. 12) to give Veff 1.1–2.1
femtoliters (Table 2). The fitted Veffvalues generally increase
with the emission wavelengths detected from the fluorescent
dyes; i.e., Veff (Ggy(0)) # Veff (Ggr(0)) # Veff (Gyr(0)).
Positive controls are modeled with Eq. 12 to give the range
of Veffand Kdvalues (Table 2) as shown by the shaded
regions in Fig. 4.
The obtained Kdvalues are well above the predicted 10?15
M. One reason for this is that the experiments were per-
formed with sample concentrations in the nanomolar range
(sensitivity limit of FCS), which makes it difficult to
determine Kdvalues at six orders below this concentration
limit. The Kdvalues determined from these fits, however, are
close to FCS measurements done on the same binding
system at similar concentration levels (42). Another reason
could be due to ligand and/or receptor impurities that cause
the binding curve to alter its slope. Labeling ratios between
protein and label is another possible factor affecting the slope
of the binding curve. Having more than one label increases
the brightness of the product and this contributes to the au-
tocorrelation amplitude with the square of its fluorescence
yield and the cross-correlation function with the product of
the fluorescence yields. Here we assume that all labeling
ratios for ligands and receptor are 1:1 as stated by the sup-
plier, and we use the average photon counts per particle per
second to model the curves.
Nevertheless, it is the magnitude of difference in ampli-
tudes between the positive and negative control curves that
resolves the binding of two components. To determine
complex formation, we demand that the difference between
the positive (1) and negative (?) control should be at least
6 SD; i.e., G1ð0Þ ? G?ð0Þ$3 ? ðSD11SD?Þ. Factors that
affect this difference include fluorescence yields, cross talk,
and impurities (35). Although Gyr(0) has a smaller difference
because of larger cross talk between Lyand R from yellow
emitting R-phycoerythrin molecules in R conjugates, the
differences between all positive and negative control curves
are more than 6 SD. Hence by measuring multiple cross-
Biophysical Journal 91(2) 715–727
correlation curves with a single sample at one Lg/Ly/R
concentration ratio, it is possible to determine binding
between the different biomolecules.
The most significant difference between positive and
negative controls are found when working at stoichiometric
concentrations (see Supplementary Material). When mea-
suring biotin/streptavidin ratios above 4:1 increasing free
Lg molecules contribute larger background to the cross-
correlation function, decreasing the amplitudes sharply to-
ward the negative control, thus making binding irresolvable
Correlations of complexes with alternate
The difference in amplitudes between the positive and neg-
ative controls of Fig. 4, A and B, show that binding occurs
between both Lgand Lyligands with receptors. However,
this does not prove the existence of complexes formed
between Lg, Ly, and R simultaneously. Only Ggy(t) confirms
the existence of complexes containing Lg, Ly, and R.
However, this conclusion is based on the assumption that
the components are known beforehand and the nature of
binding is identified. In this case, itis knownthat biotin binds
specifically to streptavidin and does not dimerize with itself.
In fact, Ggy(t) may even be sufficient to determine
complexation between Lg, Ly, and R here (43). In cases
where the nature of binding is not known, additional
negative controls will have to be performed to confirm that
complexes RLgLyare formed. We have further performed
these negative controls where only one ligand at a time is
bound to the receptor and the binding of the second ligand is
inhibited. The cross-correlation curves for a ligand/receptor
concentration ratio of Lg/Ly/R ¼ 2:2:1 are shown in Fig. 3,
D–F. The binding and nonbinding cases are clearly distin-
guishable for Ggr(t) and Gyr(t) (Fig. 3, D and E) where the
interacting species possess the higher cross-correlation
amplitudes. The similar cross-correlation curves for Ggy(t)
green 3 red, yellow 3 red, and green 3 yel-
low at concentration ratios Lg/R ¼ Ly/R ¼ 2
and R ¼ 5 nM. (A–C) Positive control
(black curves) and negative control (gray
curves) of Lgand Lybinding to R. (D–F)
Binding and inhibition curves of alternate
ligand, Lgbinding to R and Lyinhibited
(black curves) or Lybinding to R and Lg
inhibited (gray curves). Dotted curves
showcross-correlation dataandbold curves
show their fits. Excitation wavelength,
488 nm; laser power, 50 mW.
Cross-correlation functions of
722 Hwang et al.
Biophysical Journal 91(2) 715–727
(Fig. 3 F) demonstrate that the ligands are not complexed ei-
ther directly or indirectly via streptavidin. The cross-correlation
amplitudes over the whole range of ligand/receptor ratios are
plotted in Fig. 5, A–C.
Case 1: When Lgis added to R with Lyinhibited, Ggr(0)
(Fig. 5 A, open circles) decreases gradually comparable to
the positive control (Fig. 4 A), whereas the Gyr(0) and Ggy(0)
curves (Fig. 5, B and C, open circles) are similar to the neg-
ative controls of Fig. 4, B and C.
Case 2: Binding between Lyand R with Lginhibited shows
the Gyr(0) values (Fig. 5 B, solid circles) eventually
decreasing at higher Lyconcentrations, as expected. Con-
versely, the Ggr(0) and Ggy(0) negative controls curves
(Fig. 5, A and C, solid circles) decrease rapidly to lower
amplitudes similar to the negative control curves in
Fig. 4, A and C.
In Fig. 5 A the cross correlations Ggr(0) have the same
amplitudes when no ligand Lgis present. The same effect can
be observed in Fig. 5 B, where the cross-correlation am-
plitudes are similar when no ligand Lyis present. For all
other cases the cross correlations representing the interacting
molecules are always higher in amplitude than the cross
correlation representing the noninteracting molecules. In Fig.
5 C, the Ggy(0) values are similar, no matter whether Lyor Lg
is inhibited from binding. The curves are comparable to the
negative control of Fig. 4 C because no complexes con-
taining Lgand Lysimultaneously exist. In addition, it should
be noted that if all three species are present, the amplitudes of
the cross-correlation functions are always highest for the
case of interacting molecules. For instance, when inhibiting
Lyfrom binding (open circles) the highest amplitudes are
found in Fig. 5 A, the Ggr(0) channel. Conversely, when
inhibiting Lg from binding (solid circles) the highest
amplitudes are found in the Gyr(0) channel (Fig. 5 B). The
triple pairwise cross correlations directly show which mol-
ecules are interacting, thus substantiate the initial results
from Fig. 4, A–C, that trimers are indeed formed between
both ligands and the receptor.
Fitting analysis of complexes with alternate
Additional negative control curves with Lyor Lgbinding
inhibited are also modeled with Eq. 15 to give the best fit
range of Veffand Kdwithin 50% of the lowest x2(shaded
regions, Fig. 5, A–C). The exception is the Ggr(0) curve
representing Lybinding and Lginhibition (Fig. 5 A, solid
circles), which could not be fitted to give Kdvalues within
the limits of 10?15–10?6M. This is due to the fact that Ly
does have negligible cross talk into the green channel (see
Table 1) and thus the RLycomplexes do not contribute to the
cross-correlation function and a determination of a Kdvalue
is not possible. Therefore, the data points are fitted instead
with Eq. 13 where cross talk from free Lyand RLycomplexes
into the green channel could be taken to be negligible. The
fitting analysis yield Kdvalues of biotin-streptavidin binding
from 10?11to 10?8M (Table 2). The difference between
Ggr(0) positive and negative control curve is more than 6 SD
(Fig. 5 A). This excludes the first point that does not have any
Lg present and consists of only background from RLy
complexes. Gyr(0) on the other hand fulfills the condition for
binding only at higher concentrations of Ly/R (Fig. 5 B). This
show the change of the cross-correlation amplitudes with increasing ligand/
receptor concentration ratios. The top schematic drawing depicts R with four
binding sites binding to 0–4 of Lgmolecules and 4–0 of Lymolecules
keeping the number of biotin ligands constant; and the bottom drawing
depicts the negative control where all binding sites are inhibited with
D-biotin. Experimental data points for positive control (solid circles) and
negative control (open circles) show the binding between Lgand R (A); Ly
and R (B), and Lgand Ly(C). The error bar at each data point is calculated
from the standard deviation of 10 measurements. The black curve shows the
best fitting model to the data points and the shaded regions show the Kdand
Vefflimits where models are fitted within 50% of the minimum best fit
parameter x2(Table 2). The curves show a clear distinction between the
positive and negative controls in their cross-correlation amplitudes. Ex-
citation wavelength, 488 nm; laser power, 50 mW.
Simultaneous binding experiments of Lgand Lyligands to R
Biophysical Journal 91(2) 715–727
is because at low Ly/R concentrations, free Lgmolecules
contribute to the cross correlation as background via cross
talk, making binding indistinguishable. Both the negative
controls with Lyor Lginhibited have no contribution to
Ggy(t) from simultaneous binding of Lyand Lgto R (Fig. 5
C). Therefore both curves at low amplitudes show little
difference from each other and the contribution to the cross-
correlation amplitudes come mainly from cross talk of the
Limitations of SW-FCCS
Influence of Kdon cross correlations
The effect of Kdon cross-correlation amplitudes were cal-
culated from the models as a function of ligand/receptor con-
centration ratios. Kdvalues were varied from 10?15to 10?7
M at full binding conditions (Fig. 6, A–C). The changes in
cross-correlation amplitudes of the negative control curves
are due to cross talk in both channels. The positive control
curves decrease toward higher ligand concentrations for
Fig. 6, A and B, but remain relatively constant for Fig. 6 C.
At higher Kdvalues (10?7M) where more free reactants
contribute to the cross-correlation functions and fewer com-
plexes are formed, the separations of amplitudes between the
positive and negative control curves diminish. Thus the limit
of measurable Kdis reached when the positive and negative
control have a difference that is smaller than 6 SD. This in
turn is dependent on the count rates of the different reactants
and their cross talk into the different channels.
Influence of impurities on cross correlations
Various types of impurities influence cross-correlation
measurements. Inactive or unlabeled receptors or ligands
contribute to the reduction in the difference between the
positive and negative controls and decreases the sensitivity
of the method. Multiple labeling sites on a reactant may as
well affect the cross-correlation amplitudes. Some of these
problems can be circumvented in cellular measurements
when fluorescent proteins are used and labeling ratios are
fixed. These parameters and its effects on dual-color SW-
FCCS have been analyzed in detail (35).
The determination of stoichiometry with SW-FCCS has been
demonstrated previously for direct binding with dual-color
biomolecules (34,35). In this case for triple-color cross
correlations, the ligands bind indirectly over a common in-
teraction partner. With higher background due to an ad-
ditional third color, the stoichiometry can still be determined
in a similar way depending on the Kdvalues of the ligands.
By varying each ligand Lgand Lyacross a range of con-
centrations while maintaining the receptor concentration
constant, a plot of G1
gyð0Þ with Lgand Lywill reveal the
stoichiometry of the binding system. Various simulations of
different stoichiometric ratios and further explanations are
presented in the Supplementary Material.
Applications of multicolor SW-FCCS
The extension of FCCS to three colors diminishes the signal/
noise ratio of the measurements because a narrower wave-
length range is available for each channel and cross talk be-
biological variability between cells is often so high that any
only be detected when all relevant molecules are observed
simultaneously in a cell. Secondly, complex biochemical re-
actions in cellular systems involve higher order molecular in-
teractions. These interactions consist of temporal association
constants (Kd), determined from the various binding curves
Lower to upper limits and best fit values obtained for effective observation volumes (Veff) and equilibrium dissociation
SamplesLower to upper Best fitLower to upper Best fit
1 3 10?8
7 3 10?10
4 3 10?8
1 3 10?8
5 3 10?11
5 3 10?11
9 3 10?11
6 3 10?9
Bound (1); free (?).
724Hwang et al.
Biophysical Journal 91(2) 715–727
and dissociation reactions that multicolor SW-FCCS has the
potential to detect and monitor. For instance, the detection
of binding of the various proteins involved in signaling
complexes in a cellular environment over time can only be
followed when the different interaction partners are labeled.
To be able to detect these intermediate complexes, the
lifetimes ofthese complexes havetobelonger thanthetimeit
takes for the complexed molecule to diffuse through the ob-
servation volume and the characteristic times of the inter-
actions have to be of the same order or longer than our
measurement time, which is limited by ;1 s for FC(C)S. If
that is the case, SW-FCCS measurements with three colors
can differentiate between trimers, dimers, and monomers and
can elucidate temporal sequence of biological interactions.
In this study, we have performed fluorescence multicolor
cross correlations using single laser wavelength for the exci-
tation and simultaneous detection of three spectrally distin-
guishable fluorophores. The independent binding of two
differently labeled ligands to a receptor tagged with a third
color was verified with the standard biotin-streptavidin sys-
tem. Modeling the positive control curves with the described
FCCS theory enabled the determination of dissociation
constants. Although several factors such as cross talk, im-
purities, and potential multiple labeling ratios limit the
accurate determination of Kdfrom the positive control curves
with D-biotin are shown in the top and bottom schematic drawings,
respectively. The cross-correlation amplitudes versus ligand/receptor con-
centration ratios are depicted. Lgbound and Lyfree (open circles) give
higher amplitudes for Ggr(0) indicating RLgcomplexes formed (A), but no
binding shown for Gyr(0) (B) and Ggy(0) (C). The cross correlations with Ly
bound and Lgfree (solid circles) give higher amplitudes for Gyr(0) indicating
RLycomplexes formed (B), but no binding shown for Ggr(0) (A) and Ggy(0)
(C). Black curves show the best fit curve with the lowest x2and the shaded
regions give the limits of Kdvalues and Veffvalues fit to within 50% of the
lowest x2(Table 2). Excitation wavelength, 488 nm; laser power, 50 mW.
Controls withalternateligandLgor Lyinhibitedindependently
bindingof LgandLyto RusingfluorescenceyieldsfromTable1 at Veff¼ 1.0
fl and 4:1 stoichiometry. Cross-correlation amplitudes are plotted versus
ligand/receptor concentration ratios for (A) Ggr(0); (B) Gyr(0), and (C)
Ggy(0). The positive control curves with lower binding affinity converge
toward the negative control.
Effect of Kdon cross-correlation amplitudes calculated for the
Biophysical Journal 91(2) 715–727
compared with the literature value, we have shown that the
method succeeds in resolving the different possible com-
plexes of three interacting molecules.
Multicolor SW-FCCS provides a fast and convenient
method to offer yes or no answers to interacting biochemical
systems, determine an upper Kdlimit, and determine the
stoichiometry of binding. Existing FCS optical setups can
be easily modified to perform SW-FCCS by including
three detectors at the detection pathway while keeping the
excitation path unchanged with one CW laser. Multiple laser
excitation setups, in contrast, involve the complicated
alignment of several laser beams in 3D to the same excitation
volume and suffer from artifacts of nonideal overlap of ex-
citation volumes that arise because of chromatic aberrations.
Compared to multiphoton FCCS, SW-FCCS utilizes one-
photon excitation that not only uses less expensive lasers but
also offers higher count rates per particle and a better signal/
noise ratio (44). In addition, recent advances in the setup of
the detection pathways by using dispersive elements further
simplify the setup and offer a simpler way of choosing wave-
length ranges for detection and thus minimization of spectral
cross talk (45,46).
SW-FCCS uses fluorophores that require similar excita-
tion spectra but spectrally different emission characteristics
with minimal cross talk. It has been shown to work with
tandem dyes, quantum dots, and even with spectrally similar
organic dyes. In Supplementary Material we give as well ex-
perimental count rates per particle for fluorescent proteins
and small organic dyes with large Stokes shifts, both of
which are potential fluorophores for this technique. The high
sensitivity of FCS and its ability to probe spatial and tem-
poral reactions coupled with the capability to detect multi-
color labels simultaneously using single laser excitation,
provides the opportunity to study higher order complex for-
ing membrane receptors, intracellular signaling proteins, and
DNA transcription factors in signaling networks.
An online supplement to this article can be found by visiting
BJ Online at http://www.biophysj.org.
We thank Horst Vogel and Ruud Hovius for discussions and assistance.
This work was supported by the Academic Research Fund of the National
University of Singapore and funding from Ecole Polytechnique Fe ´de ´rale de
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