Lecture 7
FCS, Autocorrelation, PCH,
Cross-correlation
Joachim Mueller
Principles of Fluorescence Techniques
Laboratory for Fluorescence Dynamics
Figure and slide acknowledgements:
Enrico Gratton
Fluorescence Parameters & Methods
1. Excitation & Emission Spectra
• Local environment polarity, fluorophore concentration
2. Anisotropy & Polarization
• Rotational diffusion
3. Quenching
• Solvent accessibility
• Character of the local environment
4. Fluorescence Lifetime
• Dynamic processes (nanosecond timescale)
5. Resonance Energy Transfer
• Probe-to-probe distance measurements
6. Fluorescence microscopy
• localization
7. Fluorescence Correlation Spectroscopy
• Translational & rotational diffusion
• Concentration
• Dynamics
Historic Experiment: 1st Application of Correlation Spectroscopy
(Svedberg & Inouye, 1911) Occupancy Fluctuation
time
Gold particles
1200020013241231021111311251110233133322111224221226122142345241141311423
100100421123123201111000111_211001320000010011000100023221002110000201001
_333122000231221024011102_12221122310001103311102101100101030113121210101
21111211_1000322101230201212132111011002331224211000120301010022173441010
1002112211444421211440132123314313011222123310121111222412231113322132110
000410432012120011322231200_253212033233111100210022013011321131200101314
322112211223234422230321421532200202142123232043112312003314223452134110
412322220221
Svedberg and Inouye, Zeitschr. F. physik. Chemie 1911, 77:145
Collected data by counting (by visual inspection) the number of particles in the observation volume as a
function of time using a “ultra microscope”
Statistical analysis of raw data required
Particle Correlation
7
6
4
3
A
2
1
0
0
number of molecules
Particle Number
5
4
100
200
300
400
500
time (s)
0
0
200
400
*Histogram
of particle
counts
time (sec)
• Poisson
statistics
2
C
0.6
0.4
G ()
frequency
10
1
10
N  1.55
0.2
experiment
predicted Poisson
0
10
800
*Autocorrelation
600
• Autocorrelation not
available in the
original paper. It can
be easily calculated
today.
0.0
0
2
4
6
8
0
5
10
 (sec)
number of particles
15
N 
1
 1.56
G  0
Historical Science Investigator
Svedberg claimed: Gold colloids with radius R = 3 nm
DExpected
kBT
μm2

 70
6 R
s
Experimental facts:
0.6
characteristic diffusion time
 D  1.5s
Slit
0.4
x
2
 2 D D
μm2
1
s
 R  200 nm
G()
2 μm
 DExp
(StokesEinstein)
0.2
0.0
0
5
10
15
 (sec)
Conclusion: Bad sample preparation
The ultramicroscope was invented in 1903 (Siedentopf and Zsigmondy). They already
concluded that scattering will not be suitable to observe single molecules, but
fluorescence could.
In FCS
Fluctuations are in the Fluorescence Signal
Diffusion
Enzymatic Activity
Phase Fluctuations
Conformational Dynamics
Rotational Motion
Protein Folding
Example of processes that could generate fluctuations
Generating Fluctuations By Motion
What is Observed?
1. The Rate of Motion
2. The Concentration
of Particles
Observation
Volume
Sample Space
3. Changes in the Particle
Fluorescence while under
Observation, for example
conformational transitions
Defining Our Observation Volume:
One- & Two-Photon Excitation.
2 - Photon
1 - Photon
Defined by the pinhole size,
wavelength, magnification and
numerical aperture of the
objective
Approximately 1 um3
Defined by the wavelength
and numerical aperture of the
objective
1-photon
Need a pinhole to
define a small volume
2-photon
Brad Amos
MRC, Cambridge, UK
Data Treatment & Analysis
Time Histogram
50
0.04
0.035
Auto Correlation
40
Counts
Autocorrelation
30
20
10
0.03
Fit
0.025
Data
0.02
0.015
0.01
0.005
0
0
20
40
60
80
100
Time
0
0.01
0.10
1.00
10.00
Time (ms)
Photon Counting Histogram (PCH)
Autocorrelation Parameters:
G(0) & kaction
Number of Occurances
1000000
100000
10000
1000
PCH Parameters: <N> & e
100
10
1
0
5
10
Counts per Bin
15
100.00
Autocorrelation Function
G( ) 
F(t)F(t   )
F(t)
2
F (t )  F (t )  F (t )
Factors influencing the fluorescence signal:
F (t )  Q  dr W (r )C (r, t )
Q = quantum yield and detector
sensitivity (how bright is our
probe). This term could contain
the fluctuation of the
fluorescence intensity due to
internal processes
W(r) describes our
C(r,t) is a function of the
fluorophore concentration
over time. This is the term
that contains the “physics”
observation volume
of the diffusion processes
Calculating the Autocorrelation Function
Fluorescence
Fluctuation
dF (t )  F (t )  F
3
26x10
24
Fluorescence
F(t)
22
20
in
18
photon
counts 16
time
14
12
0
5
10
Time
20
25
Average
Fluorescence

t
15
30
35
F
t+
G ( ) 
 F (t )   F (t   )
F
2
The Autocorrelation Function
t3
Detected Intensity (kcps)
t5
t4
t2
t1
19.8
19.6
19.4
19.2
19.0
18.8
0
5
10
15
20
25
30
35
Time (s)
G(0)  1/N
0.4
As time (tau) approaches 0
0.3
G()
Diffusion
0.2
G( ) 
0.1
0.0
10
-9
10
-7
10
-5
Time(s)
10
-3
10
-1
F(t)F(t   )
F(t)
2
The Effects of Particle Concentration on the
Autocorrelation Curve
0.5
0.4
<N> = 2
G(t)
0.3
0.2
0.1
<N> = 4
0.0
10
-7
10
-6
10
-5
10
Time (s)
-4
10
-3
Why Is G(0) Proportional to 1/Particle Number?
A Poisson distribution describes the statistics of particle occupancy fluctuations.
In a Poissonian system the variance is proportional to the average number of
fluctuating species:
Particle _ Number  Variance
G ( ) 
0.4
F (t )F (t   )
F (t )
G()
0.3
0.2
G(0) 
F (t )
F (t )
0.1
2
2

2
F (t ) 
F (t )
F (t )
0.0
10
-9
10
-7
10
-5
Time(s)
10
-3
10
-1
G ( 0) 
Variance
N
2

1
N
2

2
G(0), Particle Brightness and Poisson Statistics
1000000002011100000010000000101000100100
Time
Average = 0.275
Variance = 0.256
2
0
.
275
N  Average2 Variance 
 0.296
0.256
Lets increase the particle brightness by 4x:
4000000008044400000040000000404000400400
Average = 1.1 Variance = 4.09
N 
0.296
What about the excitation (or observation) volume shape?
Effect of Shape on
the (Two-Photon) Autocorrelation Functions:
For a 2-dimensional Gaussian excitation volume:
1
 
8D  
G( )  1  2 
N  w 2 DG 
1-photon equation contains a 4, instead of 8
For a 3-dimensional Gaussian excitation volume:
1
  8D  
G( )  1  2 
N  w3 DG 
1
 8D 
1  2 
 z3 DG 
2
Additional Equations:
3D Gaussian Confocor analysis:
1

1 
  
 
2
G( )  1  1    1  S  
N   D  
 D 
1
2
... where N is the average particle number, D is the diffusion time (related
to D, D=w2/8D, for two photon and D=w2/4D for 1-photon excitation),
and S is a shape parameter, equivalent to w/z in the previous equations.
Note: The offset of one is caused by a different definition of G() : G ( ) 
F (t   )  F (t )
F
Triplet state term:
2

T T
(1 
e )
1 T
..where T is the triplet state amplitude and T is the triplet lifetime.
Orders of magnitude (for 1 μM solution, small molecule, water)
Volume
milliliter
microliter
nanoliter
picoliter
femtoliter
attoliter
Device
Size(μm)
Molecules
cuvette
10000
6x1014
plate well
1000
6x1011
microfabrication
100
6x108
typical cell
10
6x105
confocal volume
1
6x102
nanofabrication
0.1
6x10-1
Time
104
102
1
10-2
10-4
10-6
The Effects of Particle Size on the
Autocorrelation Curve
Diffusion Constants
0.25
300 um2/s
90 um2/s
71 um2/s
0.20
Slow Diffusion
0.15
G(t)
Fast Diffusion
0.10
Stokes-Einstein Equation:
k T
D
6    r
and
MW  Volume  r 3
0.05
0.00
10
-7
10
-6
-5
10
10
Time (s)
-4
10
-3
Monomer --> Dimer
Only a change in D by a factor of 21/3, or 1.26
FCS inside living cells
Correlation Analysis
Two-Photon
Spot
1.0
Dsolution
Dnucleus
0.8
= 3.3
inside nucleus
g()
0.6
0.4
Coverslip
in solution
objective
0.2
0.0
1E-5
1E-4
1E-3
 (sec)
0.01
0.1
Measure the diffusion coefficient of Green Fluorescent Protein
(GFP) in aqueous solution in inside the nucleus of a cell.
Autocorrelation Adenylate Kinase -EGFP
Chimeric Protein in HeLa Cells
Examples of different Hela cells transfected with AK1b -EGFP
Qiao Qiao Ruan, Y. Chen, M. Glaser & W. Mantulin Dept. Biochem & Dept Physics- LFD Univ Il, USA
Fluorescence Intensity
Examples of different Hela cells transfected with AK1-EGFP
Autocorrelation of EGFP & Adenylate Kinase -EGFP
EGFP-AK in the cytosol
EGFP-AKb in the cytosol
EGFPsolution
EGFPcell
Time (s)
Normalized autocorrelation curve of EGFP in solution (•), EGFP in the cell (• ),
AK1-EGFP in the cell(•), AK1b-EGFP in the cytoplasm of the cell(•).
Autocorrelation of Adenylate Kinase –EGFP
on the Membrane
Clearly more than one diffusion time
A mixture of AK1b-EGFP in the cytoplasm and membrane of the cell.
Autocorrelation Adenylate Kinaseb -EGFP
Cytosol
D
10 & 0.18
16.6
9.61
9.68
10.13
7.1
11.58
9.54
9.12
Plasma Membrane
D
13/0.12
7.9
7.9
8.8
8.2
11.4
14.4
12
12.3
11.2
Diffusion constants (um2/s) of AK EGFP-AKb in the cytosol -EGFP in the cell
(HeLa). At the membrane, a dual diffusion rate is calculated from FCS
data. Away from the plasma membrane, single diffusion constants are
found.
Multiple Species
Case 1: Species vary by a difference in diffusion constant, D.
Autocorrelation function can be used:
G( )sample
1
 8D 
2
  fi  G(0) i  1  2 
i 1
 w 2DG 
M
(2D-Gaussian Shape)
!
G(0)sample 
f
i
2
 G(0)i
G(0)sample is no longer /N !
fi is the fractional fluorescence
intensity of species i.
Antibody - Hapten Interactions
Binding site
Binding site
carb2
Mouse IgG: The two heavy chains are shown
in yellow and light blue. The two light chains
are shown in green and dark blue..J.Harris,
S.B.Larson, K.W.Hasel, A.McPherson, "Refined
structure of an intact IgG2a monoclonal
antibody", Biochemistry 36: 1581, (1997).
Digoxin: a cardiac glycoside used to treat
congestive heart failure. Digoxin competes
with potassium for a binding site on an
enzyme, referred to as potassium-ATPase.
Digoxin inhibits the Na-K ATPase pump in
the myocardial cell membrane.
Anti-Digoxin Antibody (IgG)
Binding to Digoxin-Fluorescein
triplet state
Digoxin-Fl•IgG
(99% bound)
Autocorrelation curves:
Digoxin-Fl•IgG
(50% Bound)
Digoxin-Fl
120
Binding titration from the
m  Sfree
Fb 
c
K d  S free
Fraction Ligand Bound
autocorrelation analyses:
100
80
Kd=12 nM
60
40
20
0
10
-10
10
-9
10
-8
[Antibody]
S. Tetin, K. Swift, & , E, Matayoshi , 2003
10
fr ee
(M)
-7
10
-6
Two Binding Site Model
IgG•2Ligand-Fl
IgG•Ligand-Fl + Ligand-Fl
IgG + 2 Ligand-Fl
1.0
1.20
50% quenching
0.8
Kd
0.6
IgG•Ligand
0.4
G(0)
Fraction Bound
1.15
1.10
1.05
0.2
IgG•2Ligand
No quenching
1.00
0.95
0.0
0.001
0.01
0.1
1
Binding sites
10
100
1000
0.001
0.01
[Ligand]=1, G(0)=1/N, Kd=1.0
0.1
1
Binding sites
10
100
1000
Digoxin-FL Binding to IgG: G(0) Profile
Y. Chen , Ph.D. Dissertation; Chen et. al., Biophys. J (2000) 79: 1074
Case 2: Species vary by a difference in brightness
assuming that
D1  D2
The quantity G(0) becomes the only parameter to distinguish species,
but we know that:
G(0)sample 
2
f
 i  G(0)i
The autocorrelation function is not suitable
for analysis of this kind of data without additional information.
We need a different type of analysis
Photon Counting Histogram (PCH)
Aim: To resolve species from differences in their molecular brightness
Molecular brightness ε : The average photon count rate of a single fluorophore
PCH:
where p(k) is the probability of
observing k photon counts
probability distribution function p(k)
Single Species:
e  16000 cpsm
p(k)  PCH(e, N )
N  0.3
Note: PCH is Non-Poissonian!
Sources of Non-Poissonian Noise
• Detector Noise
• Diffusing Particles in an Inhomogeneous Excitation Beam*
• Particle Number Fluctuations*
• Multiple Species*
frequency
PCH Example: Differences in Brightness
en=1.0)
en=2.2)
en=3.7)
Increasing Brightness
Photon Counts
Single Species PCH: Concentration
5.5 nM Fluorescein
Fit:
e = 16,000 cpsm
N = 0.3
550 nM Fluorescein
Fit:
e = 16,000 cpsm
N = 33
As particle concentration increases the PCH approaches a Poisson distribution
Photon Counting Histogram: Multispecies
Binary Mixture: p(k)  PCH (e1 , N1 )  PCH(e 2 , N2 )
Molecular
Brightness
Concentration
Intensity
Snapshots of the excitation volume
Time
Photon Counting Histogram: Multispecies
Sample 2: many but dim (23 nM fluorescein at pH 6.3)
Sample 1: fewer but brighter fluors
(10 nM Rhodamine)
Sample 3: The mixture
The occupancy fluctuations for each specie in the mixture becomes a convolution
of the individual specie histograms. The resulting histogram is then broader than
expected for a single species.
Resolve a protein mixture with a brightness ratio of two
Alcohol dehydrogenase labeling experiments
Mixture of singly or
doubly labeled proteins
Singly labeled proteins
+
log(PCH)
-2
-4
-6
-8
2
residuals/s
residuals/s
log(PCH)
0
0
-2
0
5
10
15
0
-2
-4
-6
Both species have
same
-8
-10
2
0
-2
0
5
k
c
10
k
e1
kcpsm
N1
e 2 kcpsm
Sample A
26.20.19
0.18
0.5400.004
0.004
-----
Sample B
25.10.6
1.2
0.155 00..007
002
56 10
10
N2
----0.006 00..008
003
15
• color
• fluorescence lifetime
• diffusion coefficient
• polarization
Excitation=895nm
3x10
4
2x10
4
1x10
4
0
FP
FP
EG
EG
lu
m
n
s
tio
eu
as
pl
cl
so
nu
to
nc
ce
ce
es
es
or
or
c
cy
e nu
FP
nc
lu
flu
EG
to
f
to
au
au
Molecular Brightness (cpsm)
PCH in cells: Brightness of EGFP
us
le
m
as
pl
to
e cy
The molecular brightness of EGFP is a factor ten higher than that of the
autofluorescence in HeLa cells
Chen Y, Mueller JD, Ruan Q, Gratton E (2002) Biophysical Journal, 82, 133 .
Brightness and Stoichiometry
Intensity (cps)
10
4
10
10
6
2 x EGFP Brightness
10000
eapp (cpsm)
5
EGFP2
7500
5000
EGFP
2500
EGFP Brightness
EGFP
EGFP2
0
100
1000
Concentration [nM]
Brightness of EGFP2 is twice the brightness of EGFP
Chen Y, Wei LN, Mueller JD, PNAS (2003) 100, 15492-15497
Caution: PCH analysis and dead-time effects
Molecular brightness (cpsm)
20000
10000
0
-10000
after correction
before correction
-20000
-30000
100
1000
10000
EGFP concentration (nM)
PCH analysis assumes ideal detectors. Afterpulsing and deadtime of the
photodetector change the photon count statistics and lead to biased parameters.
Improved PCH models that take non-ideal detectors into account are available:
Hillesheim L, Mueller JD, Biophys. J. (2003), 85, 1948-1958
Distinguish Homo- and Hetero-interactions in living cells
ECFP:
EYFP:
Apparent Brightness
A
B
A
B
+ B
A
A
A
2  905nm
A
B
ε
ε
2ε
ε
2ε
2  965nm
A
B
ε
0
ε
ε
2ε
• single detection channel experiment
• distinguish between CFP and YFP by excitation (not by emission)!
• brightness of CFP and YFP is identical at 905nm (with the appropriate filters)
• you can choose conditions so that the brightness is not changed by FRET between CFP
and YFP
• determine the expressed protein concentrations of each cell!
PCH analysis of a heterodimer in living cells
The nuclear receptors RAR and RXR form a tight heterodimer in vitro. We
investigate their stoichiometry in the nucleus of COS cells.
We expect:
2  905nm
3.0
2.5
2.5
2.0
2.0
1.5
1.0
- RXR agonist
+ RXR agonist
0.5
2  965nm
3.0
eapp/emonomer
eapp/emonomer
RAR
RXR
1.5
1.0
- RXR agonist
+ RXR agonist
0.5
0.0
0.0
0
4000
8000
12000
total protein concentration [nM]
0
1000
2000
3000
4000
RXRLBD-YFP [nM]
Chen Y, Li-Na Wei, Mueller JD, Biophys. J., (2005) 88, 4366-4377
Two Channel Detection:
Cross-correlation
Sample Excitation
Volume
1.
2.
Beam Splitter
Increases signal to noise
by isolating correlated
signals.
Corrects for PMT noise
Detector 1
Detector 2
Each detector observes
the same particles
Removal of Detector Noise by Cross-correlation
Detector 1
11.5 nM Fluorescein
Detector 2
Detector after-pulsing
Cross-correlation
Calculating the Cross-correlation Function
3
26x10
Fluorescence
24
Detector 1: Fi
22
20
18
16
time
14
12
0
5
10
15
Time
20
25

t
35
dFi (t )  dF j (t   )
Gij ( ) 
t+
30
Fi (t )  F j (t )
3
26x10
Fluorescence
24
Detector 2: Fj
22
20
18
16
time
14
12
0
5
10
15
Time
20
25
30
35
Cross-correlation Calculations
One uses the same fitting functions you would
use for the standard autocorrelation curves.
Thus, for a 3-dimensional Gaussian excitation volume one uses:
  8D12
G12 ( ) 
1

N12 
w2




1
 8D12
1 
2

z





1
2
G12 is commonly used to denote the cross-correlation and G1 and
G2 for the autocorrelation of the individual detectors. Sometimes
you will see Gx(0) or C(0) used for the cross-correlation.
Two-Color Cross-correlation
The cross-correlation
Sample
ONLY if particles are observed in both channels
Red filter
Each detector observes
particles with a particular color
The cross-correlation signal:
Only the green-red molecules are observed!!
Green filter
Two-color Cross-correlation
Equations are similar to those for the cross
correlation using a simple beam splitter:
Information Content
Correlated signal from
particles having both colors.
Autocorrelation from channel 1
on the green particles.
Autocorrelation from channel 2
on the red particles.
G ij ( ) 
dFi (t)  dFj (t  )
Fi (t)  Fj (t)
Signal
G12 ( )
G1 ( )
G2 ( )
Experimental Concerns: Excitation Focusing &
Emission Collection
We assume exact match of the observation volumes in our calculations
which is difficult to obtain experimentally.
Excitation side:
(1) Laser alignment
(2) Chromatic aberration
(3) Spherical aberration
Emission side:
(1) Chromatic aberrations
(2) Spherical aberrations
(3) Improper alignment of detectors or pinhole
(cropping of the beam and focal point position)
Two-Color Fluctuation Correlation Spectroscopy
Uncorrelated
Gij ( ) 
 Fi (t ) F j (t   ) 
 Fi (t )  F j (t ) 
1
100
F2 (t )  f12 N1  f 22 N2
Ch.1
80
F1 (t )  f11N1  f 21N2
60
%T
Correlated
Ch.2
40
20
0
450
500
550
600
650
700
Wavelength (nm)
Interconverting
For two uncorrelated species, the amplitude of the
cross-correlation is proportional to:

f11 f12 N1  f 21 f 22 N 2
G12 (0)  
2
 f11 f12 N1  ( f11 f 22  f 21 f12 ) N1 N 2  f 21 f 22 N 2


2

Does SSTR1 exist as a monomer after ligand binding while
SSTR5 exists as a dimer/oligomer?
Collaboration with Ramesh Patel*† and Ujendra Kumar*
*Fraser Laboratories, Departments of Medicine, Pharmacology, and Therapeutics and Neurology and Neurosurgery, McGill University, and Royal Victoria
Hospital, Montreal, QC, Canada H3A 1A1; †Department of Chemistry and Physics, Clarkson University, Potsdam, NY 13699
Fluorescein Isothiocyanate (FITC)
Texas Red (TR)
Somatostatin
Somatostatin
Cell Membrane
R1
R1
Three Different CHO-K1 cell lines: wt R1, HA-R5, and wt R1/HA-R5
Hypothesis: R1- monomer ; R5 - dimer/oligomer; R1R5 dimer/oligomer
SSTR1 CHO-K1 cells with SST-fitc + SST-tr
Green Ch.
Red Ch.
• Very little labeled SST inside cell nucleus
• Non-homogeneous distribution of SST
• Impossible to distinguish co-localization from molecular interaction
A
Monomer
10
G1
G2
G 12
8
6
G()
G12(0)
= 0.22
G1(0)
4
Minimum
2
0
-2
10
10
-4
10
-3
10
-2
10
-1
(s)
Dimer
8
G1
G2
G 12
6
G12(0)
= 0.71
G1(0)
Maximum
G()
B
-5
4
2
0
10
-5
10
-4
10
-3
(s)
10
-2
10
-1
Experimentally derived auto- and cross-correlation curves from live R1 and
R5/R1 expressing CHO-K1 cells using dual-color two-photon FCS.
R1
R1/R5
0.16
G1
G2
G1 2
G()
0.04
0.12
G( )
0.06
G1
G2
G1 2
0.02
0.08
0.04
0.00
0.00
-0.04
10
-4
10
(s)
-2
10
0
10
-5
10
-4
10
-3
10
(s)
-2
10
-1
The R5/R1 expressing cells have a greater cross-correlation relative to the
simulated boundaries than the R1 expressing cells, indicating a higher level
of dimer/oligomer formation.
Patel, R.C., et al., Ligand binding to somatostatin receptors induces receptorspecific oligomer formation in live cells. PNAS, 2002. 99(5): p. 3294-3299
Molecular Dynamics
“High” FRET
(a)
P
YF
What if the distance/orientation
is not constant?
• Fluorescence fluctuation can
result from FRET or
Quenching
CFP
- 4 Ca2+
+ 4 Ca2+
(b)
calmodulin
M13
CFP
• FCS can determine the rate
at which this occurs
• This will yield hard to get
information (in the ms to ms (c)
range) on the internal motion
of biomolecules
YFP
“Low” FRET
trypsin
CFP
+
NO FRET
YFP
Fluorescence Intensity (cps)
60000
trypsin-cleaved
cameleon
CFP
cameleon
2+
Ca -depleted
cameleon
2+
Ca -saturated
YFP
50000
40000
30000
20000
10000
0
450
500
550
Wavelength (nm)
600
650
A)
B)200
160
G()
120
80
40
0
-3
10
-2
10
-1
10
 (s)
. A) Cameleon fusion protein consisting of ECFP, calmodulin, and EYFP.
[Truong, 2001 #1293] Calmodulin undergoes a conformational change that allows the
ECFP/EYFP FRET pair to get cl ose enough for efficient energy transfer. Fluctuations
between the folded and unfolded states will yield a measurable kinetic component for the
cross-correlation. B) Simulation of how such a fluctuation would show up in the
autocorrelation and cross-correlation. Red dashed line indicates pure diffusion.
0
10
1
10
In vitro Cameleon Data
Ca2+ Saturated
0.10
Donor Ch. Autocorrelation
Acceptor Ch. Autocorrelation
Cross-correlation
0.08
G()
0.06
0.04
0.02
0.00
-0.02
10
-5
10
-4
10
-3
-2
10
10
-1
 (s)
Crystallization And Preliminary X-Ray
Analysis Of Two New Crystal Forms Of
Calmodulin, B.Rupp, D.Marshak and
S.Parkin, Acta Crystallogr. D 52, 411
(1996)
Are the fast kinetics (~20 ms) due to
conformational changes or to fluorophore
blinking?
10
0
Fluorescence F(t)
Dual-color PCH analysis (1)
FA
<FA>
Time t
Cross-Correlation
Fluorescence F(t)
Dual-Color PCH
FB
<FB>
Time t
Signal A
Tsample
Brightness in each
channel: eA, eB
Signal B
Average number of
molecules: N
Tsample
Signal A
Dual-color PCH analysis (2)
Signal B
Tsample
Tsample
Single Species: p(k A , kB )  PCH (e A , e B , N )
Brightness in each channel: eA, eB
Average number of molecules: N
Resolve Mixture of ECFP and EYFP in vitro
fluctuations
Dual-Color PCH
2 channels
2 species model
c2 = 1.01
1 species model
c2 = 17.93
10000
9000
eA (cpsm)
8000
7000
6000
5000
4000
3000
EYFP alone
ECFP alone
species 1 from fit
species 2 from fit
2000
2000 3000 4000 5000 6000 7000 8000 900010000
eB (cpsm)
Chen Y, Tekmen M, Hillesheim L, Skinner J, Wu B, Mueller JD, Biophys. J. (2005), 88 2177-2192
ECFP & EYFP mixture resolved with single histogram.
Note: Cross-correlation analysis cannot resolve a mixture of ECFP & EYFP with a single measurement!