SW-FCCS, Hwang and Wohland
1
Single wavelength excitation fluorescence cross-correlation spectroscopy
with spectrally similar fluorophores: Resolution for binding studies
Ling Chin Hwang, Thorsten Wohland*
Department of Chemistry, National University of Singapore, 3 Science Drive 3,
Singapore 117543
*
author to whom correspondence should be addressed; e-mail: chmwt@nus.edu.sg
Abstract
It was shown recently that fluorescence cross correlation spectroscopy (FCCS) can be
performed using a single laser wavelength for excitation (SW-FCCS, ChemPhysChem,
2004 (5), 549-551). This method simplifies the FCCS setup since it does not require the
simultaneous alignment of two lasers to the same focal spot. But up to now the method
was shown to work only with dyes possessing large Stokes’ shifts, and thus was limited
to the use of quantum dots and tandem dyes. In this work we show that standard organic
dyes
with
overlapping
emission
spectra,
for
instance
fluorescein
and
tetramethylrhodamine, can be used as fluorescent pairs in SW-FCCS. As a biological
model system for ligand-receptor interactions we studied the binding of biotin to
streptavidin. To investigate the applicability of SW-FCCS for binding studies we adapt
the existing FCCS theory for SW-FCCS and calculate limits for the measurement of
dissociation constants in dependence on sample concentration, sample purity, and
spectral cross talk between the different detection channels.
Keywords
SW-FCCS, fluorescence, correlation, ligand-receptor interactions, streptavidin, biotin
SW-FCCS, Hwang and Wohland
2
Introduction
Fluorescence Correlation Spectroscopy (FCS) was developed more than 30 years ago
as a method to study kinetic properties of chemical reaction systems in thermodynamic
equilibrium by observing the spontaneous intensity fluctuations from a small observation
volume 1. Although, in the majority of cases the signal stems from fluorescence labels on
the particles of interest, Raman and scattering signals have also been used
2,3
. Since then
FCS has found many applications especially in the life sciences where it is by now a
routine tool for the study of biomolecular interactions
4,5
. For a recent comprehensive
review see Krichevsky and Bonnet 6. However, FCS has limitations in its ability to
distinguish between different particles and can do so only if their diffusion coefficient
differs by about a factor 2. Since the diffusion coefficient is proportional to the cubic root
of the mass, particles with a mass difference of a factor less than 8 cannot be
distinguished
conducted
3
7
. Therefore, early on the first cross correlation experiments were
using in fact a single laser beam in a confocal setup for excitation and
detecting scattered light and fluorescence light from polystyrene particles to calculate the
cross correlation function (CCF). First dual-color fluorescence cross-correlation
experiments on a single molecule level where performed by Schwille et al.
8
and the
theory including ligand-receptor binding interactions has been described 9,10. However, to
reach that sensitivity two lasers at different wavelength had to be used. Although this
approach improved the detection of interacting particles compared to FCS 9, the
requirement of aligning two laser beams to the same spot made it experimentally
challenging
11,12
. Therefore, multi-photon FCCS for the simultaneous excitation of two
distinct fluorophores has been proposed 11 and has recently found several applications
13-
SW-FCCS, Hwang and Wohland
15
3
. To further simplify the setup it has been suggested that fluorophores with large
Stokes’ shifts could be employed to perform FCCS
11,12
and first measurements for the
study of biomolecular interactions with single laser wavelength excitation FCCS (SWFCCS) have been performed recently 16.
In this work it is demonstrated that SW-FCCS can be conducted with fluorophores
with similar excitation and emission spectra. By adapting FCCS theory 3,9,10 we derive the
equations for the cross-correlation amplitudes and determine the limitations of SW-FCCS
in dependence of cross-talk, quenching, and sample impurities. Of special interest here
are interactions of 1:1 stoichiometry where neither the mass nor the molecular brightness
change is enough to allow the detection of binding by FCS. The use of organic dyes with
similar emission spectra will inevitably result in a lower sensitivity of SW-FCCS
compared to FCCS using two excitation lasers due to the higher spectral cross-talk.
However, it is shown that even for measurements at a single concentration ratio between
receptor and ligand, differences of more than 6 standard deviations in the amplitude can
be reached. In this work binding between fluorescein labeled biotin (BF) and
tetramethylrhodamine labeled streptavidin (TMRSA) is shown and the dissociation
constant and stoichiometry of binding is determined. Although this system exhibits very
strong binding (Kd  10-15 M) and has a stoichiometry of binding of 4:1, it demonstrate
the feasibility of this approach.
Thus SW-FCCS is an extension of FCS that allows the measurement of the
interaction of biomolecules irrespective of their mass and/or diffusion coefficients. This
makes SW-FCCS an interesting tool for the measurement of dimerization of molecules in
vitro and in vivo as well as for high throughput screening.
SW-FCCS, Hwang and Wohland
4
Theory
Receptor-ligand complexes
The samples used in SW-FCCS binding studies are ligands and receptors, which are
both fluorescently labeled, with total concentrations Lt and Rt, respectively. Both ligands
and receptors can be active or inactive. We denote this by a “+” or “-“ sign in the
superscript ( Lt , Lt , Rt , Rt ). In addition, ligands and receptors can have varying
numbers of fluorophores attached which will depend on the specific labeling procedure
adapted. A ligand can have between 0 and N fluorophores attached, where N is the
number of labeling sites. The probability to have a specific number n between 0 and N
fluorophores attached will be denoted by pL(N,n). Similarly, a receptor can have between
0 and M fluorophores attached, where M is the number of labeling sites. The probability
to have a specific number m between 0 and M fluorophores attached will be denoted by
pR(M,m). The ligand and receptor concentrations can thus be described as
Lt  Lt  Lt 
N
N
n 0
n 0
 p L N , n Lt   p L N , n Lt
(1)
and
Rt  Rt  Rt 
M
M
m 0
m 0
 p R M , mRt   p R M , mRt
(2).
The signal in SW-FCCS will be determined by the fluorescent particles, but binding
will be determined by the active particles. In the rest of this section we derive the
concentrations of the different possible complexes that are formed by the interaction of
ligands and receptors.
SW-FCCS, Hwang and Wohland
5
For the active particles, the probability of encountering a labeled (*) or unlabeled (0)
active ligand/receptor is given by their mole fractions:
N
*
pL 
 p L N , n Lt
n 1
N
 p L N , n 
Lt
n 0
0
pL 
N
(3)
  p L N , n 
Lt
n 0
p L N ,0 Lt
N
 p L N , n 
Lt
n 0
N
(4)
  p L N , n 
n 0
Lt
M
*
pR 
 p R M , m Rt
m 1
M
 p R M , m 
Rt
m 0
0
pR 

M
(5)
 p R M , m 
m 0
Rt
p R M ,0 Rt
M
 p R M , m
Rt
m0

M
(6)
 p R M ,m
m0
Rt
Assuming nt ligand binding sites per receptor, we calculated numerically the number
of complexes with different ligands bound (Mathematica 5.0, Wolfram Research,
Champaign, IL) by simultaneously solving the following equations for equilibrium
binding.
Kd 
Lf R f
RL
; Kd 
Lf RL
RL 2
; … ; Kd 
Lf RL nt 1
RL nt
;
(7)
and
nt n
 
Rt  R f    t  RL nb
n 1  nb 
(8)
nt
n 
Lt  Lf   nb  t  RL nb
n 1
 nb 
(9).
SW-FCCS, Hwang and Wohland
6
Concentrations of total and free active ligands or receptors are denoted by Lt , Lf ,
Rt , and R f , respectively. The binomial coefficient was introduced to account for the
different possibilities how n ligands can bind to a receptor with nt binding sites. RLn are
the concentrations of complexes containing n ligands. We assumed here that all binding
sites on the receptor have the same Kd. The extension of the equations to different Kds can
be achieved by using different Kds in Eqs. 7-9. Furthermore, we demand that every
ligand-receptor complex contains only one receptor but can possess several bound
ligands. We thus exclude aggregation and oligomerization in this theory.
Assuming a receptor with nt possible binding sites and nb (0  nb  nt) occupied
binding sites, each of these sites can have either a fluorescent or a non-fluorescent active
ligand as given by the probabilities of Eqs. 3 and 4. Each ligand-receptor complex can
contain either a fluorescent or a non-fluorescent active receptor as given by the
probabilities in Eqs. 5 and 6. The concentration of all active fluorescent receptors
containing nb ligands of which n* are fluorescent (and n = nb - n* are non-fluorescent)
can thus be expressed by 10
*
 n  n 
RLnb ,n*    t  b  0 p Lnb n* * p Ln* * p R  RL nb
 nb  n* 
(10)
The first binomial coefficient represents the number of possibilities to distribute nb
ligands over nt binding sites. The second binomial coefficient is the number of
possibilities to distribute n* fluorescent ligands over the nb occupied binding sites.
Although every ligand receptor complex contains only one receptor, it can contain
several ligands with different amounts of fluorophores attached. Thus we have to
calculate the probability pC(n*,n) that a complex with n* fluorescent ligands contains n
SW-FCCS, Hwang and Wohland
7
fluorophores. If we denote the number of ligands by k and the number of fluorophores
each ligand carries by nk, we have:
 n*

pC n* , n    p L N , nk 
k 1
 Sum over all
(11)
n*
perm utations with  nk  n
k 1
We can calculate now the concentration cn,m of particles that contain n ligand
fluorophores and m receptor fluorophores. Since bound and free particles can have
different fluorescent yields we calculate the concentration of all bound and free particles
containing n or m fluorophores respectively, and the concentration of receptor ligand
complexes containing m receptor and n ligand fluorophores.
Free fluorescent ligands with n fluorophores:
nt nb


c n ,0  p L  N , n  Lt    n* * RL nb ,n*  
nb 1 n* 1


(12)
The sum in brackets denotes the total ligand concentration minus the bound ligands.
Free fluorescent receptors with m fluorophores:
nt nb


c0 ,m  p R M , m  Rt    * RL nb ,n*  
nb 1 n* 1


(13)
The sum in brackets denotes the total receptor concentration minus the bound
receptors.
Fluorescent ligands bound to non-fluorescent receptors:
c~n ,0  pC n* , n  p R M ,0 * RL nb ,n* 
(14)
Fluorescent receptors bound to non-fluorescent ligands:
c~0 ,m  p R M , m * RL nb ,0 
(15)
The concentrations of particles containing both fluorophores are given by:
SW-FCCS, Hwang and Wohland
8
n
t
c~n ,m  p R M , m   pC n* , n * RL( nb ,n* )
(16)
nb 1
These concentrations of particles with defined numbers of fluorophores can be used
to calculate the CCF as shown in the next section.
The Cross-correlation function
In this section we first derive a general expression for the CCF for the case that both
interaction partners are labeled. The normalized CCF is given by
G (  ) 
F1 ( t )F2 ( t   )
F1 ( t ) F2 ( t )

F1 ( t )F2 ( t   )
F1 ( t ) F2 ( t )
1
(17).
Fi(t) denotes the fluorescence intensity detected in either of the two detection channels at
a time t,  is the correlation time, and the angular brackets denote the time average. For
the case of differently labeled ligands and receptors, which are detected in two different
channels, the fluorescence in the different channels i is given by:
Fi t  
N
M
N
M
n 1
m 1
n 1
m 1
N
M
 n ,0 ,i cn ,0  0 ,m ,i c0 ,m  ~n ,0 ,i c~n ,0  ~0 ,m ,i c~0 ,m   ~n ,m ,i c~n ,m
(18).
n 0 m 0
Every particle containing different numbers of ligand fluorophores n and receptor
fluorophores m will have their own fluorescence yield (counts per particle and second) in
channel i. The fluorescence yields for free particles are given by  n ,m ,i , the fluorescence
yields for bound particles are given by ~n ,m ,i . These different fluorescence yields have to
be included to account for the fluorescence of single and multiply labeled complexes,
quenching effects (upon labeling or upon binding) and possible fluorescence resonance
energy transfer (FRET) in the different ligand-receptor complexes.
SW-FCCS, Hwang and Wohland
9
For a solution of the whole CCF a characteristic time dependent process (diffusion,
flow etc.) has to be assumed. In this work we concentrate only on the amplitudes of the
CCF but the extension to the full CCF is straightforward and the solutions have been
previously published 10.
Putting equation 18 into equation 17, accounting for 2 detection channels, and
assuming a focal intensity profile that is Gaussian in all three axes
17
the CCF can be
calculated 18.
N
G x 0  
M
N
M
N
M
  n ,0 ,1 n ,0 ,2 c n ,0    0 ,m ,1 0 ,m ,2 c0 ,m   ~n ,0 ,1~n ,0 ,2 c~n ,0   ~0 ,m ,1~0 ,m ,2 c~0 ,m    ~n ,m ,1~n ,m ,2 c~n ,m
n 1
m 1
n 1
m 1
n 0 m 0

~ ~
~
~
~
~  
   n ,0 ,1 c n ,0    0 ,m ,1 c0 ,m    n ,0 ,1 c n ,0    0 ,m ,1 c0 ,m     n ,m ,1 c n ,m  
m 1
n 1
m 1
n 0 m 0
 
Veff N A  n N1
M
N
M
N M

~ ~
~
~
~
~ 
    n ,0 ,2 c n ,0    0 ,m ,2 c 0 ,m    n ,0 ,2 c n ,0    0 ,m ,2 c0 ,m     n ,m ,2 c n ,m  
m 1
n 1
m 1
n 0 m 0

  n 1
N
M
N
M
N
M
For the negative control, i.e. no binding, the fluorescence in the channels i is given by
Fi t  
N
M
n 1
m 1
 n ,0 ,i cn ,0   0 ,m ,i c0 ,m
(20)
and the CCF simplifies to
G x 0  
N
M
n 1
m 1
  n ,0 ,1 n ,0 ,2 c n ,0   0 ,m ,1 0 ,m ,2 c0 ,m
M
M
 N
 N

Veff N A    n ,0 ,1 c n ,0    0 ,m ,1 c0 ,m    n ,0 ,2 c n ,0    0 ,m ,2 c0 ,m 
m 1
m 1
 n 1
 n 1

(21).
We assume that the fluorescence yields of the different species do not change in the
presence of the competitor for the negative control. Equations 19 and 21 are the general
solutions for the CCF for binding interactions when both interaction partners are labeled.
(19)
SW-FCCS, Hwang and Wohland
10
Detection threshold for binding in SW-FCCS
In the case that SW-FCCS is used to detect simple binding, e.g. in a screening assay,
the positive and negative control must differ by at least 6 standard deviation at least at
one of the measured ligand and receptor concentrations. For the data collected in this
work the standard deviation of the amplitude of the CCFs is on the order of Δ = 10% or
lower. To detect binding we demand that the difference between positive and negative
control differs by at least 6 standard deviations, i.e.


G x 0  G x 0  3  G x 0  G x 0 
(22).
This demand can be expressed in an inequality
R
G x 0  1  3
1
G x 0  1  3
(23),
where we define the detection threshold R as the left hand side of Eq. 23. A
measurement at a specific concentration can thus only succeed when inequality 23 is
fulfilled. The ratio R depends on several parameters, in particular on the purity of
receptor and ligand, on quenching of receptor and ligand upon binding, on non-specific
binding, and on the fluorescence yields of ligand, receptor, and ligand receptor complex
(as measured in the setup).
Although equation 19 and 21 describe the CCF for the general case they contain too
many parameters to be of practical use. To be able to use these equations as many
parameters as possible should be determined independently. Therefore, in the next
section we will discuss simplifications of the equations as applicable to the biotinstreptavidin system. It will be shown in the Results and Discussion section how the
different parameters influence the detection threshold for binding.
SW-FCCS, Hwang and Wohland
11
The biotin-streptavidin ligand-receptor system
The biotin-streptavidin ligand-receptor system is a well studied model system for
ligand receptor interactions. In our case we use fluorescein labeled biotin (BF) and
tetramethylrhodamine labeled straptavidin (TMRSA). There are several points in this
system that considerably simplify the expression for the fluorescence intensity (Eqs. 18
and 20) and thus the CCF (eqs. 19 and 21):
i) The fluorescence of TMRSA is not dependent on BF binding and no FRET was
observed (data not shown).
ii) We assume an average count rate per particle for the TMR labeled streptavidin
although different amounts of labels could be present at each molecule.
iii) There is at most one fluorophore per ligand.
iv) The fluorescence of BF is quenched by 75% upon binding
19,20
but it is not
dependent on the number of BF ligands bound to TMRSA or unlabeled streptavidin.
Thus, a complex with n* fluorescent ligands will have just n* times the fluorescence of a
complex with only 1 fluorescent ligand. In addition, the quenching is the same in both
detectors and can be described by the factor qL = 0.25 (this implies that there is no shift in
the emission spectrum of the ligand fluorophore). With these four assumptions the
fluorescence of all compounds can be described by the following parameters: The
fluorescence yield of TMR label in each channel  R ,i , the fluorescence yield of
fluorescein in each channel  L ,i , and the quenching of fluorescein upon binding qL. Thus
the fluorescence yields in eq. 18 can be expressed as:
free fluorescent ligand:  n ,0 ,i  1,0 ,i   L ,i
(24)
free fluorescent receptor: 0 ,m ,i  m R ,i
(25)
SW-FCCS, Hwang and Wohland
12
non-fluorescent ligands bound to fluorescent receptor: 0 ,m ,i  m R ,i
(26)
fluorescent ligands bound to non-fluorescent receptor:  n ,0 ,i  q L n L ,i
(27)
ligands receptor complex:  n ,m ,i  q L n L ,i  m R ,i 
(28)
The fluorescence intensity in the different channels can thus be written as:
Fi t    L ,i c1,0
nt
  q L n L ,i c~n ,0 
n1
M
 m R ,i c~0 ,m 
m1
nt
 m R ,i c0 ,m    q L n L ,i  m R ,i c~n ,m
M
m1
M
(29)
n1 m1
To simplify the equations we can combine the 3rd and 4th terms since the fluorescene
yield of receptor fluorophores is independent of the state of binding. In addition, we
define the fluorescence yield of the complexes with fluorescent receptor and fluorescent
ligands:
~n ,m ,i  q L n L ,1  m R ,1 
(30)
We can thus write the fluorescence intensity in channel i as:
Fi t    L ,i c1,0
nt
  q L n L ,i c~n ,0 
n 1
 m R ,i c0 ,m
M
m1
n
t
 c~0 ,m    ~n ,m ,i c~n ,m
M
(31)
n 1 m1
Putting these equations into the CCF we get
G x 0 
 L,1 L , 2 c1,0   q L2 n 2 L ,1 L , 2 c~n ,0   m R ,1 R , 2 c 0,m  c~0,m    ~n ,m,1~n ,m, 2 c~n ,m
nt
M
n 1
m 1
nt
M
n 1 m 1
nt
nt M
M

~
~
~ ~  
 L ,1c1, 0   q L n L ,1 c n , 0   m R ,1 c 0, m  c 0, m     n , m,1 c n , m  *
n 1
m 1
n 1 m 1
 
Veff N A 
nt
nt M
M

~
~
~ ~ 
  L , 2 c1, 0   q L n L , 2 c n , 0   m R , 2 c 0, m  c 0, m     n, m , 2 c n , m  
n 1
m 1
n 1 m 1
 
 
In our experiments the competitor (unlabeled biotin) has no influence on the
fluorescence yields of the labeled particles. For the negative control we thus have
(32).
SW-FCCS, Hwang and Wohland
G 0  
 L ,1 L ,2 * Lt 
13
M
 m 2 R ,1 R ,2 p R M , m* Rt
m 1
(33).



Veff N A  L ,1 * Lt   m R ,1 p R M , m * Rt  L ,2 * Lt   m R ,2 p R M , m * Rt 
m 1
m 1



M
M
It should be noted that most assumptions can be verified directly from the intensity
traces recorded in the two detection channels. The values Li, Ri, and qL can be measured
from samples by comparing the signals in the two detectors. The concentrations c1, 0 ,
c 0 , m , c~0 , m , c~n , 0 , and c~n ,m can be numerically calculated from Eqs. 12-16 in dependence on
the total receptor and ligand concentrations.
The parameters which are unknown and have to be measured are the Kd, the effective
observation volume Veff and the relative concentrations of fluorescent and non-fluorescent
receptors and ligands. However, the extent of labeling of the interaction partners is
usually unknown. While for BF it is safe to assume that it has either one or no ligand
attached, streptaviding can have up to 6 labels attached (number of lysines plus Nterminus). The extent of labeling in the case of TMRSA is given by the manufacturer as
4.2 mole dye per mole streptavidin but there is no information available about the exact
distribution of labels. However, we will show in the simulations that the distribution of
labels on TMRSA plays a minor role in our measurements in which the TMRSA
concentration is kept constant, and the assumption of an average count rate for TMRSA
is justifiable.
The CCF of Eq. 32 contains several contributions: 1) The first three sums in the
numerator are contributions of particles that contain either only ligand fluorophores or
only receptor fluorophores. These contributions are similar to the autocorrelation of these
particles and are caused by the cross talk of the signal into both detectors. 2) The fourth
SW-FCCS, Hwang and Wohland
14
sum in the numerator is the contribution of particles that actually contain both
fluorophores of ligands and receptors and represent actual binding interactions. The
contribution of the different particles depends solely on the product of their fluorescence
yields in the two detectors. Thus the condition for a successful distinction between the
different contributions to the CCF is only that Cn*1Cn*2 is sufficiently different from
L1L2, R1R2, and n*2 qL2 L1 L 2 . This implies that even when the same label is used on
both ligand and receptor, a distinction is possible between the different contributions to
the CCF, provided that the fluorescence characteristics of the complex are different from
the characteristics of the ligand and receptor alone (see as well 9).
Calculations of SW-FCCS limits
For calculations of limits of the Kd which can be determined with SW-FCCS, the ratio
R was calculated in dependence of different parameters. Since the solution for the binding
curve (and the detection threshold R) is constant for constant ratios of Lt/Rt and Kd/Rt, all
results are given in terms of these dimensionless parameters.
According to Eq. 23 the ratio R must be at least 1 to allow the distinction between
positive and negative control. In Table 2 we show the maximum values for Kd/Rt at which
R = 1 and report the corresponding value of Lt/Rt at which this maximum is reached (see
supplement for graphs depicting the R = 1 line for different conditions). With the
knowledge that FCS measurements can be performed at fluorophore concentrations
between about 0.1 nM and 1 M, one can directly calculate possible Kds accessible by
this technique and the ideal receptor and ligand concentrations to be employed. In these
calculations we assumed
SW-FCCS, Hwang and Wohland
15
i)
a standard deviation of Δ = 10% for all measurements.
ii)
that quenching upon binding is always equal in both detection channels.
iii)
that there is no quenching for negative controls.
Condition i) was found to be generally fulfilled in the measurements. In FCS the
amplitude can often be determined with a much lower standard deviation. Condition ii)
might improve or worsen the resolution limit since it can result in larger or smaller
differences for the fluorescence yield products for the different species. Condition iii)
would in general worsen the resolution limit since more quenching means lower signal to
noise ratio in the SW-FCCS measurements.
One has to differentiate between two different cases:
1) If
Lt
R
R
 1 , then Rtmax  t * 10 6 M and Rtmin  t * 10 10 M .
Rt
Lt
Lt
2) If
Lt
 1 , then Rtmax  10 6 M and Rtmin  10 10 M .
Rt
The maximum and minimum Kds can be calculated by
K dm ax 
K d m ax
Rt and
Rt
(34)
K dmin 
K d min
Rt
Rt
(35).
Materials and Methods
The SW-FCCS optical setup consists of an Ar-Kr ion laser (Melles Griot, Singapore)
set at an excitation wavelength of 488nm and laser power at 100μW. The laser beam is
expanded 4 times with two achromat lenses, f = 20 mm and f = 80 mm (Linos,
SW-FCCS, Hwang and Wohland
16
Heidelberg, Germany), and coupled into a microscope Axiovert 200 (Carl Zeiss,
Singapore). The excitation beam is reflected by a dichroic mirror 505DRLP (Omega
Optical, Brattleboro, USA) and focused by a water immersion objective, C-Apochromat
63x/1.2NA (Carl Zeiss, Singapore) into a small spot. The fluorescence of the sample is
collected back by the same objective and transmitted through the same dichroic mirror. A
50 μm pinhole (Linos) is placed at the image plane of the emission beam to spatially filter
out light not coming from the focus. A second dichroic mirror 560DRLP (Omega) is
placed after the pinhole to split the emission wavelengths into two detection channels.
The two beams are then refocused by achromats onto two separate avalanche photodiodes
(SPCM-AQR-14, Pacer Components, Berkshire, UK). Bandpass filters, 510AF23 and
580DF30 (Omega), are placed in-front of the green and red detectors, respectively, to
further restrict the wavelengths of the emitted fluorescence. The intensity signals are
auto- and cross-correlated simultaneously with a measurement time of 30 seconds by an
external hardware correlator Flex-02-12D (correlator.com, Zhejiang, China). The
correlation curves are fitted with the Levenberg-Marquardt algorithm using software Igor
Pro (Wavemetrics Inc., Oregon, USA). Calibrations of the setup were performed with
fluorescein (Molecular Probes, Eugene, USA) in both channels and the geometry
parameter K, describing the ratio of the extension of the confocal volume along compared
to perpendicular to the optical axis, was fixed between 2 - 4 for the curve fittings,
depending on the calibrations.
Tetramethylrhodamine-streptavidin conjugate (Molecular Probes, Eugene, USA) was
diluted to 12 sample solutions of 5nM. Each solution was incubated at least ½ hour with
increasing concentrations of biotin-fluorescein (Molecular Probes) from 0-50nM to
SW-FCCS, Hwang and Wohland
17
obtain mixtures with BF/TMRSA ratios between 0-10. Negative controls at the same
concentration ratios were prepared by saturating all binding sites of TMRSA with 1μM of
excess D-biotin (Amersham Biosciences Ltd., Singapore) before adding BF. All solutions
were prepared in phosphate buffered solution at pH 7.4 (Sigma-Aldrich, Singapore).
Results and discussion
To study the influence of the dissociation constant, impurities, cross-talk and labeling
we assume in general the following, if not noted otherwise: i) Interactions have a 1:1
stoichiometry since this is the situation where FCS cannot measure molecular
interactions, especially when there is no accompanying change in fluorescence yield. ii)
All fluorophores have the following fluorescence yields: L1 = 27000 Hz, L2 = 3000 Hz,
R1 = 3000 Hz, R2 = 27000 Hz. iii) Receptors and ligands carry only one fluorophore.
iv) No quenching occurs for the fluorophores upon binding. v) All receptors and ligands
are active and carry one fluorophores (no impurities). In the following calculation we will
now determine the influence of each of these conditions on the CCF by varying one of
the conditions at a time while keeping the others at their values stated here.
Influence of the dissociation constant on SW-FCCS
The amplitudes of the CCF were calculated as a function of ligand receptor ratio Lt/Rt
for dissociation constants 10-15 M < Kd < 10-7 M. The negative control decreases steadily
with an increasing ratio Lt/Rt since the receptor concentration remains constant and the
ligand concentration increases. The CCF changes only due to the cross-talk of the ligand
in the two channels, the behavior is similar to FCS (Eq. 33).
SW-FCCS, Hwang and Wohland
18
The CCFs of the positive control have two different parts. In the first part for small
values of Lt/Rt, i.e. unsaturated binding, not every receptor has yet one ligand bound and
the amplitude of the CCF changes due to increasing binding. As soon as all receptor
binding sites are occupied, at saturating binding conditions, contributions to the CCF are
made by increasing numbers of ligands. Again the increase in free ligand concentration
leads to a decrease of the CCF amplitude. The CCF converges to the negative control due
to the cross-talk of the ligand in the two channels. This separation of the CCF for positive
and negative control is obvious for small Kds and can also be seen in the experimental
data (Fig. 1). For increasing Kds, i.e. smaller affinities, this difference slowly vanishes
and thus determines the maximum Kd measurable (Fig. 2).
Influence of impurities on SW-FCCS
Different impurities can be present in a sample. The receptor can be either active or
inactive, and the receptor can either be fluorescently labeled or unlabeled. To make the
influence of the individual impurities clear, we assume that only one impurity is present
at a time and represents 50% of the total ligand or receptor concentration. The graphs for
two different Kds (10-15 M and 10-9 M) and the three kinds of impurities are shown in Fig.
3.
Impurities lead in general to a reduction in the difference between negative and
positive control and thus reduce the sensitivity of the method (see as well Table 2).
Fluorescent but inactive ligands and receptors shift the apparent separation of unsaturated
binding to saturated binding to higher or lower values of Lt/Rt, respectively, and thus lead
to misinterpretation of binding stoichiometries. In addition, for increasing concentrations
SW-FCCS, Hwang and Wohland
19
of fluorescent non-active ligands, the initial slope of the binding curve becomes steeper
(Fig. 3 A).
Non-fluorescent but active ligands and receptors have almost no influence on the
point of separation of unsaturated to saturated binding. However, non-fluorescent but
active receptors change the initial slope of the CCF and thus its amplitude. From the
experimental data in Fig. 1 it can be seen that impurities can be part of an explanation of
the strong initial decrease of the amplitude of the CCF, and these impurities must be
either fluorescent, inactive ligands or non-fluorescent, active receptors.
Non-fluorescent inactive impurities shift the point of separation of unsaturated to
saturated binding and influence the absolute amplitudes. Due to the different influences
of the impurities it is at least theoretically possible to analyze their fractions from
experimental data. If this is practical will largely depend on the signal to noise ratio and
whether the exact labeling conditions are known for receptor and ligand.
Influence of cross-talk and quenching on SW-FCCS
Cross-talk is a serious problem in FCCS and SW-FCCS since it increases the
contributions of singly labeled species and reduces the difference between the
fluorescence yield products of singly and doubly labeled species. The influence of cross
talk of the ligand fluorophores into the channel for the detection of the receptor
fluorophore on the binding curves is shown in Fig. 4. The question for SW-FCCS is
therefore, how large can cross talk, i.e. overlap between emission spectra, be without
compromising binding measurements. The answer will depend on the binding affinity to
be measured. In Fig. 5 we have depicted the values for K d Rt and Lt Rt versus the
SW-FCCS, Hwang and Wohland
20
percentage of cross talk of either the ligand fluorophore only, the receptor fluorophore
only, or both fluorophores simultaneously. 50% cross talk means that both detection
channels detect the same amount of fluorescence from a fluorophore. Thus in cases with
more than 50% cross talk of one of the fluorophores it would be better to measure with a
single detector. From these graphs one can directly evaluate whether a measurement of
an expected K d is possible by calculating the maximum measurable dissociation
constant, K dmax , from the values of K d Rt and Lt Rt at the measured level of cross talk.
Influence of receptor labeling on SW-FCCS
The number of labels per receptor and ligand can have a strong influence on the
correlation curves in FCS as well as in FCCS. This is due to the fact that the amplitude of
the autocorrelation function (ACF) is proportional to the square of the fluorescence yield
per particle. Similarly, the amplitude of the CCF is proportional to the product of the
fluorescence yield per particle in the two detection channels. Thus a particle with two
labels instead of one can contribute four times more to the ACF than a particle with only
one label.
The influence of labeling on measurements will have to be determined for every
individual system. This is often a problem since the exact distribution of labels is not
known and is usually for commercial products not available. Especially proteins, which
usually contain several possible labeling sites, are usually not fully labeled, since the
extent of labeling increases the probability of precipitation of the protein. Thus in most
protein systems we do not know the distribution of labels. However, often two conditions
can help reducing this influence. Firstly, the ligand is usually well known and labeling
SW-FCCS, Hwang and Wohland
21
can be controlled so that a single label is attached to this molecule (e.g. peptide synthesis,
small molecule ligands, ligands with a fluorescent protein attached). Secondly, the
concentration of the receptor Rt which contains an unknown distribution of labels can be
held constant while the ligand concentration Lt is varied. In this case we can show that the
influence of the unknown label distribution is relatively small and does influence the
detection of binding only marginally.
For this purpose, we have calculated the expected amplitudes of the CCF for two Kds
(10-15 and 10-9 M) and for a receptor that has either 2 or 4 possible binding sites and thus
can carry either 1 or 2 or between 1 and 4 fluorophores, respectively. We assume that all
fluorophores, independent of binding site, contribute equally to the fluorescence signal.
Although this assumption is in general not true, the calculations show that the extent of
labeling of the receptor and thus its fluorescence yield does not influence the CCFs
strongly. All calculations were done for standard fluorophores (fluorescence yields L1 =
27000 Hz, L2 = 3000 Hz, R1 = 3000 Hz, R2 = 27000 Hz; binding stoichiometry 1:1; no
quenching of ligand and receptor qL = qR = 1; the ligands carry one fluorophore; the
receptors can carry several fluorophores). The results of these calculations are shown in
Fig. 6.
From Fig. 6 it can be seen that the influence of labeling on the CCF is strongest at
low ratios of Lt/Rt. But this is as well the region where the distinction between positive
and negative control is most difficult since the differences are small. This effect can be
seen especially well in the calculations for a Kd of 10-9 M, where at Lt/Rt < 1, the
difference between positive and negative control is very small. In the region 1 < Lt/Rt < 4
SW-FCCS, Hwang and Wohland
22
where the differences between positive and negative control are large, the influence of the
labeling distribution is small.
SW-FCCS with spectrally similar fluorophores on the biotin-streptavidin system
Binding of BF to TMRSA was measured at constant TMRSA concentration (5 nM)
and increasing BF concentrations. The resulting CCF amplitudes are depicted in Fig. 1 as
function of [BF]/[TMRSA]. The background corrected intensities detected in the
different channels are given in Table 1 for solutions of 1 nM, which result typically in
0.22 ± 0.01 particles per observation volume in our system. From this all necessary
number of counts per particle n,m,i can be calculated.
At low ratios of [BF]/[TMRSA], the binding curve decreases until a ratio between 3-4
where full binding is attained and stoichiometry of binding can be determined. Beyond
this point, the binding curve decreases steeply towards the negative control due to the
saturation of binding sites of streptavidin. A proper fit of the data is difficult since Eqs.
32 and 33 contain to many unknown parameters. Especially, the unknown stoichiometry
of labeling of streptavidin, and the uncertainty in the purity of the sample are difficult to
assess. We thus make two assumptions. Firstly, we assume that 90% of the ligand
consists of active labeled ligands and 10 % are fluorescent inactive impurities. This is in
line with the 90 purity level given by the manufacturer. Secondly, we assume for
TMRSA an average fluorescence yield, as measured (Table 1), and neglect the
distribution of labels.
With these two assumptions and all the fluorescence yields measured, we can model
the data as shown in Fig. 1. The best fit with the lowest 2 has the following values: {Veff
SW-FCCS, Hwang and Wohland
23
= 0.33×10-15 L; Kd = 10-15 M; fluorescent active receptor: 0.7; fluorescent inactive
receptor: 0.1; non-fluorescent active receptor: 0.2}. This confirms the simulations which
showed that non-fluorescent active receptor (and fluorescent inactive ligands as fixed by
us) is responsible for the steep initial slope in the binding curve. To give an idea of how
accurate the fitting parameters are, we have varied the parameters and determined the
minimum and maximum values they can vary without changing the 2 value by more
than 50 %. We have indicated the range of the models by the shaded area in Fig. 1. The
parameter ranges are: Veff = [0.33 - 0.42]×10-15 L; Kd: [10-15 - 5×10-10] M; fluorescent
active receptor = [0.7-0.85]; fluorescent inactive receptor = [0.0-0.1]; non-fluorescent
active receptor = [0.1-0.2]. The effective volume Veff is close to the expected value of
0.37×10-15 L, as calculated from the 0.22 particles per observation volume. The Kd has a
very large range due to the small differences for the binding curves at low Kds. As shown
in Fig. 2, the difference in the binding curve between a Kd of 10-15 M and a Kd of 10-10 M
is smaller than between a Kd of 10-10 M and a Kd of 10-9 M. This is mainly due to the fact
that we measure in the nanomolar range, far away from the actual Kd. The fractions for
the fluorescent active receptors compared to the fluorescent inactive and the nonfluorescent active receptors are a bit low. Only 70-85 % of the receptors are fluorescent
and active. However, the manufacturer claims only that 90 % of the labeled sample is
active and that is consistent with our data.
The model shows systematic deviations from the data to smaller values at low
[BF]/[TMRSA] ratios. This could be due to the fact that we have not taken account of the
distribution of labels on the receptor. As shown in Fig. 6 it is at precisely the low ligand
SW-FCCS, Hwang and Wohland
24
to receptor ratios that the curves deviate most strongly from curves that assume only one
average label.
Comparison of sensitivities of different fluorophore pair systems
To give a general idea how different fluorophores will influence SW-FCCS
measurements we compare the values for two fluorophore pairs that represent different
extremes: fluorescein - quantum red (Flu-QR) and fluorescein - tetramethylrhodamine
(Flu-TMR). The system with Flu-QR can be excited at 488 nm, and due to the large
Stokes’ shift of QR (emission mainly at 670 nm) the emission of the two fluorophores
can be easily separated. Binding measurements have been shown previously with SWFCCS on this system 16. The emission maxima of Flu-TMR, as used in this work, are not
that well separated and excitation is not as efficient for the longer wavelength emitting
dye TMR.
In Table 2 we have calculated the maximum values of K d Rt and the corresponding
value of Lt Rt for these two fluorophore pairs. The values have been calculated for
different conditions. We chose to show extreme values of 80% quenching of either ligand
or receptor, and for 20% fluorescent non-active impurities of both ligand and receptor
(for more detailed sets of values see graphs in the supplement). These conditions were
chosen to be representative of typical situations.
In the Flu-QR system the ratio K d Rt ranges from 0.77 to 377 with values of Lt Rt
of 1.99 and 113, respectively. This translates into measurable K dmax between 0.4 – 3.3
M and shows that this system can be used for the measurement of even weak
interactions. In the case of Flu-TMR the ratio in K d Rt can be well below 1, and in
SW-FCCS, Hwang and Wohland
25
general for 1:1 binding stoichiometry is between 0.02 and 0.22 with Lt Rt between 0.47
and 1. Therefore, the measurable K dmax is in the range of 20 - 220 nM or lower. For a
binding stoichiometry of 4:1, the values increase to K d Rt = 4.5 at Lt Rt = 5.5,
resulting in a measurable K dmax of 0.8 M.
Possible fluorophore pairs for SW-FCCS
The preceding discussion shows that ideal fluorophore pairs for SW-FCCS minimize
cross talk due to large differences in Stokes shift but have strong absorptions at the same
wavelength. This is fulfilled best for quantum dots and energy transfer dyes which can all
be excited at 488 nm but have largely different emission spectra. However, these labels
suffer from serious disadvantages. Quantum dots are large and often of similar size or
larger than the molecule to be labeled. In addition they can show aggregation, making
measurements very difficult
16
. Therefore other labels, preferably small organic dyes or
fluorescent proteins, have to be found. The choice of fluorescein and TMR is a borderline
case and improvement over FCS with two equal labels is small. This is mainly due to the
quenching of fluorescein upon binding and the limited absorption of TMR at 488 nm.
However, new fluorophores on the market with large Stokes’ shifts could offer new
perspectives for SW-FCCS. Possible candidates are so-called MegaStokes dyes
(www.dyomics.com) which can be excited at 488 nm but have fluorescence peak
emission between 530 and 670 nm. These fluorophores could be used together with
standard fluorophores that can be excited at 488 nm (fluorescein, GFP). A problem with
these dyes is that their emission spectra get broader with longer emission wavelength,
possibly increasing problems of cross talk. Another possibility would be combinations of
SW-FCCS, Hwang and Wohland
26
fluorescent proteins several of which can be excited pair wise at 488 nm but emit at
different wavelength. For instance, green and red fluorescent proteins can be excited
efficiently at 488 nm and FCS curves can be measured efficiently in vivo (in
preparation). Fluorescent proteins would not only offer the advantage that measurements
can be performed in vivo but labeling is precisely controlled thus eliminating the need to
determine fluorophore distributions on the interaction partners. With these different
fluorophore combinations SW-FCCS could be used for screening and as well for the
determination of dimerization of proteins in vivo.
A comparison between FCS and SW-FCCS
In general, binding can be measured by fluorescence spectroscopy if the fluorescence
yield changes upon binding. However, if there are no changes in fluorescence yield
binding can be measured using FCS. For a stoichiometry unequal to 1:1, binding can be
determined by a change in amplitude of the ACF
21
. Otherwise binding can be measured
by a change in the diffusion coefficient under the condition that the mass change upon
binding is at least a factor 4-8 7,22.
In the cases of 1:1 binding with mass changes smaller than a factor 4-8 and no
accompanying fluorescence yield changes, binding cannot be measured anymore by FCS.
To be able to measure binding under these conditions both binding partners have to be
labeled. This can be done by either using the same label for both binding partners and
detect fluorescence in one channel which is autocorrelated (FCS). Or it can be achieved
by using different labels each of which is detected in a different channel. The detection
channels can then be cross-correlated (SW-FCCS).
SW-FCCS, Hwang and Wohland
27
The contribution of a particle to the ACF depends on the square of the fluorescence
yield (X) in the single detection channel. In the best case a complex of a ligand and
receptor would thus have double the fluorescence yield and contribute 4 times as much to
the ACF than the unbound particles. In our case, BF is quenched by 75% upon binding.
An FCS experiment with both interaction partners labeled would thus increase the square
of the fluorescence yield by only 1.252 ≈ 1.56. SW-FCCS therefore improves upon FCS
only when the quantum yield products from the two detectors are larger than this
threshold. For the case when QR or quantum dots are used in combination with BF it was
shown that SW-FCCS is a definite improvement 16.
In Table 1 we report the fluorescence yield products for the TMRSA and BF system
for a 1:1 stoichiometry. For higher stoichiometries the comparison is even more
favorable. The fluorescence yield product for the two detection channels of the bound
TMRSA-BF complex (C1C2) is actually more than 4 times larger than that for BF
(X1X2). In addition, since BF is quenched by 75% upon binding an FCS experiment
with both interaction partners labeled would increase the square of the fluorescence yield
(C) of the single detection channel not by a factor 4 but by only 1.252 ≈ 1.56. So in this
comparison SW-FCCS is a definite improvement over FCS since it increases the
contribution of the bound complex almost 3 times more than FCS. However, when
comparing C1C2 of the TMRSA-BF complex to X1X2 of TMRSA, the improvement is
much less than a factor 4. In this case an FCS experiment with double labeling using
TMR would have a better signal than SW-FCCS using TMR and fluorescein.
Responsible for this effect is the strong quenching by 75% of fluorescein upon binding.
Therefore, one has to choose carefully the pairs of fluorophores that are to be used in a
SW-FCCS, Hwang and Wohland
28
SW-FCCS experiment so that an improvement over FCS is achieved. However, the
extension of labels for SW-FCCS to organic dyes with only narrowly separated emission
spectra makes a wide range of labels accessible for experiment optimization.
Conclusions
In this work we have shown that dual-color fluorescence cross-correlation
spectroscopy can be performed by using a single laser wavelength (SW-FCCS) for
excitation of fluorophores that have only small differences in emission spectra. This
extends the applicability of SW-FCCS from the previously reported long Stokes’ shift
fluorophores to the more routinely used small organic dyes. The advantage of this method
lies in its simplicity since it is not necessary anymore to align several lasers to the same
focal spot, and its broad applicability since there are much fewer restrictions for
fluorophore pairs that can be used compared to FCCS using two-photon excitation.
Although, depending on the fluorophores, the detection of interactions can be restricted to
very low dissociation constants, i.e. very strong binders, (~ 1 nM), the method is
applicable in most cases to dissociation constants up to about 1 M. Thus this method
could be of value not only for research but as well for high-throughput screening of
biomolecular interactions.
Acknowledgements
LCH is a recipient of a National University of Singapore PhD scholarship. TW
gratefully acknowledges funding from the Academic Research Fund of the National
University of Singapore.
SW-FCCS, Hwang and Wohland
29
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SW-FCCS, Hwang and Wohland
31
Table Captions
Table 1: Fluorescence intensities of the different particles in the detection channels 1
and 2 for standard solutions of 1 nM. The average number of particles per observation
volume in our setup for a 1 nM solution is 0.22 ± 0.01. From this number the values in
brackets,the counts per particle and second, are calculated. The residual fluorescence
after binding for the different particles is given by qX.
Table 2: Maximum Kd/Rt values with corresponding Lt/Rt values, for a value of the
detection threshold R = 1. Values are given for two fluorophore combinations: BF/QR
and BF/TMRSA. With these values maximum and minimum detectable Kds can be
calculated by Eqs. 34 and 35. All values were calculated using the spectroscopic data of
Table 1 and using Eqs. 23, 32 and 33.
SW-FCCS, Hwang and Wohland
32
Molecule
IG [Hz]
IR [Hz]
qX
Flu
10700 (48600)
2700 (12300)
-
TMR
<50 (<300)
800 (3600)
-
BF
5700 (25900)
1200 (5500)
0.25
TMRSA
300 (1400)
1500 (6800)
1.0
QRSA
700 (3200)
15700 (71400)
1.0
QD655SA
500 (2300)
43000 (195500)
1.0
Hwang and Wohland
SW-FCCS
Table 1
SW-FCCS, Hwang and Wohland
Stoichiometry
33
No quenching,
80%
quenching 80%
no impurities
of ligand (green)
quenching Rec. imp. 20 %,
of receptor (red)
Lig imp. 20 %
fluorescein/quantum-red
Lt/Rt
Kd/Rt
Lt/Rt
Kd/Rt
Lt/Rt
Kd/Rt
Lt/Rt
Kd/Rt
1:1
41
43.5
1.99
0.77
39.2
9.0
33
22.0
1:4
113
377
33
33
85.0
153.0
104.0
224.0
fluorescein/tetramethylrhodamine
Lt/Rt
Kd/Rt
Lt/Rt
Kd/Rt
Lt/Rt
Kd/Rt
1:1
0.47
0.22
0.85
0.02
1.0
0.04
0.61
0.03
1:4
5.5
4.5
2.9
1.2
5.3
4.5
4.9
2.5
Hwang and Wohland
SW-FCCS
Table 2
Lt/Rt
Kd/Rt
SW-FCCS, Hwang and Wohland
34
Figure Captions
Fig. 1: Binding experiments of BF to TMRSA. Depicted is the amplitude of the crosscorrelation function versus the BF to TMRSA concentration ratio. The concentration of
TMRSA was 5 nM in all experiments. The positive control (full circles) is shown with
the best fitting model as a solid line (Veff = 0.33×10-15 L; Kd = 10-15 M; * Lt = 0.9, * Lt =
0.1; * Rt = 0.7; * Rt = 0.1; 0 Rt = 0.2). The negative control (open circles) is shown with
the best fitting model as a dashed line (Veff = 0.42×10-15 L; * Lt = 0.9, * Lt = 0.1; * Rt =
0.7; * Rt = 0.1; 0 Rt = 0.2). The shaded areas show the borders of the models which can
fit the data with a change of 2 of less than 50 % of its minimum value. The model
parameters have the following ranges: Veff = [0.33 - 0.42]×10-15 L; Kd: [10-15 - 5×10-10]
M; * Lt = 0.9, * Lt = 0.1; * Rt = [0.7-0.85]; * Rt = [0.0-0.1]; 0 Rt = [0.1-0.2]. The two
vertical grey lines delimit the [BF]/[TMRSA] concentration region in which the detection
threshold for binding R  1 (Eqs. 22 - 23).
Fig.2: Influence of the Kd on the CCF. The amplitude of the CCF is shown versus the
ligand to receptor concentration ratio. The curves were calculated for a standard
fluorophore pair (fluorescence yields L1 = 27000 Hz, L2 = 3000 Hz, R1 = 3000 Hz, R2
= 27000 Hz; binding stoichiometry 1:1; no quenching of ligand and receptor qL = qR = 1).
Fig.3: Influence of impurities on the CCF. The amplitude of the CCF is shown versus the
ligand to receptor concentration ratio. The curves were calculated for a standard
fluorophores pair (fluorescence yields L1 = 27000 Hz, L2 = 3000 Hz, R1 = 3000 Hz,
SW-FCCS, Hwang and Wohland
35
R2 = 27000 Hz; binding stoichiometry 1:1; no quenching of ligand and receptor qL = qR
= 1) and for two different Kds (A, C, E: Kd = 10-15 M; B, D, F: Kd = 10-9 M). A, B:
fluorescent inactive impurities. C,D: non-fluorescent active impurities. E, F: nonfluorescent inactive impurities. Curves for calculations assuming no impurities are given
in solid lines. Curves for ligand impurities are given as dotted lines. Curves for receptor
impurities are given as dashed lines.
Fig.4: Influence of cross talk on the CCF. The amplitude of the CCF is shown versus the
ligand to receptor concentration ratio. The curves were calculated for three different
levels of cross talk of the ligand fluorophores into the channel of the receptor
fluorophores (fluorescence yield L1+L2= 30000 Hz distributed over the two channels
depending on cross talk). The receptor fluorophores was assumed to have a cross talk of
10% into the first channel (R1 = 3000 Hz, R2 = 27000 Hz;). The binding stoichiometry
is 1:1 and no quenching of ligand and receptor were used qL = qR = 1.
Fig.5: Sensitivity of SW-FCCS depending on increasing cross talk of ligand fluorophores
(dotted lines), receptor fluorophores (dashed lines), or both fluorophores simultaneously
(solid lines). For these calculations a 1:1 binding stoichiometry and no quenching upon
binding were assumed. For the ligand and receptor curves the cross talk of one
fluorophore was fixed at 10% while the cross talk of the other flurophore was varied
between 10 and 50%. At 50% cross talk for a fluorophore the fluorescence intensity
detected in the two detection channels is equal. For the ligand and receptor curves the
cross talk of both fluorophores was varied simultaneously between 10 and 90 %. The
SW-FCCS, Hwang and Wohland
36
fluorophores were assumed to result in 30000 counts per second and particle over all
detection channels. A) The values of Kd/Rt are depicted versus percentage of cross talk.
B) The values of Lt/Rt are depicted versus percentage of cross talk. Maximum
measureable Kds can be calculated from the data according to Eq. 22.
Fig.6: The influence of receptor labeling on the cross-correlation amplitudes. The graphs
depict the cross-correlation amplitudes for a standard fluorophore pair (fluorescence
yields L1 = 27000 Hz, L2 = 3000 Hz, R1 = 3000 Hz, R2 = 27000 Hz; binding
stoichiometry 1:1; no quenching of ligand and receptor qL = qR = 1). The ligand carries
one fluorophores and the receptor can carry either 1-2 fluorophores (A, C) or 1-4
fluorophores (B, D). The ratios of receptors carrying 1 to n fluorophores are given in the
legends as F1:F2:…:Fn. A and B depict the curves for a Kd = 10-15 M. C and D depict the
curves for a Kd = 10-9 M.