lecture 7 fcs, autocorrelation, pch, cross-correlation · 1 lecture 7 fcs, autocorrelation, pch,...
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1
Lecture 7FCS, Autocorrelation, PCH,
Cross-correlationJoachim Mueller
Principles of Fluorescence Techniques Laboratory for Fluorescence Dynamics Figure and slide acknowledgements:
Enrico Gratton
Historic Experiment: 1st Application of Correlation Spectroscopy(Svedberg & Inouye, 1911) Occupancy Fluctuation
1200020013241231021111311251110233133322111224221226122142345241141311423100100421123123201111000111_211001320000010011000100023221002110000201001_333122000231221024011102_1222112231000110331110210110010103011312121010121111211_10003221012302012121321110110023312242110001203010100221734410101002112211444421211440132123314313011222123310121111222412231113322132110000410432012120011322231200_253212033233111100210022013011321131200101314322112211223234422230321421532200202142123232043112312003314223452134110412322220221
Gold particles
time
Svedberg and Inouye, Zeitschr. F. physik. Chemie 1911, 77:145
Statistical analysis of raw data required
Collected data by counting (by visual inspection) the number of particles in the observation volume as a function of time using a “ultra microscope”
7
6
5
4
3
2
1
0
Part
icle
Num
ber
5004003002001000
time (s)
• Autocorrelation not available in the original paper. It can be easily calculated today.
Particle Correlation
0 2 4 6 810 0
10 1
10 2
experim ent p red ic ted P o isson
frequ
ency
n um ber o f pa rtic les
*Histogram of particle counts *Autocorrelation
• Poisson statistics
1.55N =
( )1 1.560
NG
= =
Graph of
Raw Data:
2
What we learn from the correlation function? 2
Expectedµm70
6 sBk TD
Rπη= ≈
(Stokes-Einstein)
Svedberg claimed: Gold colloids with radius R = 3 nm
2 2 Dx Dτ∆ ≈
Slit
2µm
0 5 10 150.0
0.2
0.4
0.6
G(τ
)
τ (sec)
characteristic diffusion time
1.5sDτ ≈
Experimental facts:2µm1
sExpD⇒ ≈
200nmR⇒ ≈
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
DiffusionEnzymatic ActivityPhase Fluctuations
Conformational DynamicsRotational Motion
Protein Folding
Example of processes that could generate fluctuations
Fluorescence Correlation Spectroscopy (FCS)
objective
Coverslip
Generating Fluctuations By Motion
Sample
Observation Volume
1. The Rate of Motion
2. The Concentration of Particles
3. Changes in the Particle Fluorescence while under Observation, for example conformational transitions
What is Observed?
3
Observation Volume in 1- & 2-Photon Excitation.
1-Photon: 2-Photon:
Approximately 1 µm3
Observation Volume: Defined by the confocal pinhole size, wavelength, magnification and numerical aperture of the objective
1-photon excitation beam
Fluorescence excited everywhere along the beam
2-photon excitation beam
Fluorescence only excited at focal volume
Observation Volume: Defined by wavelength, and numerical aperture of the objective
http://www.andor.com/image_lib/lores/introduction
1-photon
2-photon
pinhole needed to define a small volume
Brad Amos MRC, Cambridge, UK
Two-Photon FCS
0.4 µm
Fluorescence signal at detectorTwo-photon effect
F
time
fluctuation
0 100 200 300 4002000
2500
3000
3500
4000
4500
5000
5500
Inte
nsity
(cps
)
time (sec)
Example:Fluorescently labeled viral particles
Data Treatment & AnalysisTime Histogram Autocorrelation
Photon Counting Histogram (PCH)
Autocorrelation Parameters: G(0) & krate
PCH Parameters: <N> & ε
0 100 200 300 4002000
2500
3000
3500
4000
4500
5000
5500
Inte
nsity
(cps
)
t im e (sec)10-4 10 -3 10 -2 10 -1 100 101
0
5
10
15
20
25
da ta fit
g(τ)
τ (sec)
prob
abili
ty
Counts per bin
4
Autocorrelation Function
)()()( tFtFtF −=δ
( ) ( ) ( ),F t Q d W C tκ= ∫ r r r
G(τ) =δF(t )δF(t + τ)
F(t ) 2
κQ = 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 observation volume
C(r,t) is a function of the fluorophore concentration over time. This is the term that contains the “physics”of the diffusion processes
Factors influencing the fluorescence signal:
Average fluorescence signal: ( )F t
Fluorescence fluctuation:
10-9 10-7 10-5 10-3 10-1
0.0
0.1
0.2
0.3
0.4
Lag time τ (s)
G(τ
)
10-9 10-7 10-5 10-3 10-1
0.0
0.1
0.2
0.3
0.4
Lag time τ (s)
G(τ
)
Calculating the Autocorrelation Function
F(t)in photon counts
t
τ
t + τ
Fluorescence Fluctuation
( ) ( )dF t F t F= −
t + τ
τtime
Average Fluorescence
F
2
( ) ( )( )
F t F tG
F
δ δ ττ
⋅ +=
t1
t2
t3
t4
t5
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Det
ecte
d In
tens
ity (k
cps)
The Autocorrelation Function
10-9 10-7 10-5 10-3 10-1
0.0
0.1
0.2
0.3
0.4
Time(s)
G(τ
)
G(τ) =δF(t )δF(t + τ)
F(t ) 2
G(0) ∝ 1/NAs time (tau) approaches 0
Diffusion
5
The Effects of Particle Concentration on theAutocorrelation Curve
<N> = 4
<N> = 2
0.5
0.4
0.3
0.2
0.1
0.0
G(t)
10 -7 10 -6 10 -5 10 -4 10 -3
Time (s)
Why Is G(0) Proportional to 1/Particle Number?
NNVarianceG 1)0( 2 ==10-9 10-7 10-5 10-3 10-1
0.0
0.1
0.2
0.3
0.4
Time(s)
G(τ
)
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:
VarianceNumberParticle =_
( )2
2
2
2
)(
)()(
)(
)()0(
tF
tFtF
tF
tFG
−==
δ
2)(
)()()(
tF
tFtFG
τδδτ
+=
G(0), Particle Brightness and Poisson Statistics
1 0 0 0 0 0 0 0 0 2 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0
Average = 0.275 Variance = 0.256
Variance = 4.09
4 0 0 0 0 0 0 0 0 8 0 4 4 4 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 4 0 0 0 4 0 0 4 0 0
Average = 1.1 0.296
296.0256.0275.0 2
2 ==∝ VarianceAverageN
Lets increase the particle brightness by 4x:
Time
∝N
6
Effect of Shape on the (2-Photon) Autocorrelation Functions:
(for simple diffusion)
For a 2-dimensional Gaussian excitation volume:
1
20
8( ) 1 DGN wγ ττ
−⎛ ⎞
= +⎜ ⎟⎝ ⎠
For a 3-dimensional Gaussian excitation volume:
11 2
2 20 0
8 8( ) 1 1D DGN w zγ τ ττ
−−⎛ ⎞ ⎛ ⎞
= + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
1-photon equation contains a 4, instead of 8
Model of observation volume
γ: shape factor (0.354 for 3DG, 0.5 for 2DG)N: average number of particles inside volumeD: Diffusion coefficientwo: radial beam waist of two-photon laser spotzo: axial beam waist of two-photon laser spot
Additional Equations:
... where N is the average particle number, τD is the diffusion time (related to D, τD=w2/8D, for two photon and τD=w2/4D for 1-photon excitation), and S is a shape parameter, equivalent to w/z in the previous equations.
3D Gaussian Confocor analysis:
Triplet state term:
)1
1( TeT
T ττ−
−+
..where T is the triplet state amplitude and τT is the triplet lifetime.
G(τ) = 1 +1N
1 +ττ
D
⎛
⎝ ⎜
⎞
⎠ ⎟
−1
⋅ 1 + S 2 ⋅τ
τD
⎛
⎝ ⎜
⎞
⎠ ⎟
− 12
2
( ) ( )( )
F t F tG
F
ττ
+ ⋅=Note: The offset of one is caused by a different definition of G(τ) :
Orders of magnitude (for 10nM solution, small molecule, water)
DiffusionVolume Device Size(µm) Molecules Time (s)milliliter cuvette 10000 6x1012 104
microliter plate well 1000 6x109 102
nanoliter microfabrication 100 6x106 1picoliter typical cell 10 6x103 10-2
femtoliter confocal volume 1 6x100 10-4
attoliter nanofabrication 0.1 6x10-3 10-6
7
The Effects of Particle Size on theAutocorrelation Curve
300 um2/s90 um2/s71 um2/s
Diffusion Constants
Fast Diffusion
Slow Diffusion
0.25
0.20
0.15
0.10
0.05
0.00
G(t)
10 -7 10 -6 10 -5 10 -4 10 -3
Time (s)
D =k ⋅T
6 ⋅π ⋅ η ⋅ r
Stokes-Einstein Equation:
3rVolumeMW ∝∝
and
Monomer --> Dimer Only a change in D by a factor of 21/3, or 1.26
FCS inside living cells
1E-5 1E-4 1E-3 0.01 0.10.0
0.2
0.4
0.6
0.8
1.0
in solution
inside nucleus
g(τ)
τ (sec)
Dsolution
Dnucleus= 3.3
Correlation Analysis
Measure the diffusion coefficient of Green Fluorescent Protein (GFP) in aqueous solution in inside the nucleus of a cell.
objectiveCoverslip
Two-PhotonSpot
Autocorrelation Adenylate Kinase -EGFPChimeric Protein in HeLa Cells
Qiao Qiao Ruan, Y. Chen, M. Glaser & W. Mantulin Dept. Biochem & Dept Physics- LFD Univ Il, USA
Examples of different Hela cells transfected with AK1-EGFP
Examples of different Hela cells transfected with AK1β -EGFP
Fluorescence Intensity
8
Time (s)
G(τ
)
EGFPsolution
EGFPcell
EGFP-AKβ in the cytosol
EGFP-AK in the cytosol
Normalized autocorrelation curve of EGFP in solution (•), EGFP in the cell (• ), AK1-EGFP in the cell(•), AK1β-EGFP in the cytoplasm of the cell(•).
Autocorrelation of EGFP & Adenylate Kinase -EGFP
Autocorrelation of Adenylate Kinase –EGFPon the Membrane
A mixture of AK1b-EGFP in the cytoplasm and membrane of the cell.
Clearly more than one diffusion time
Diffusion constants (um2/s) of AK EGFP-AKβ in the cytosol -EGFP in the cell (HeLa). At the membrane, a dual diffusion rate is calculated from FCSdata. Away from the plasma membrane, single diffusion constants are found.
10 & 0.1816.69.619.68
10.137.1
11.589.549.12
Plasma MembraneCytosol
Autocorrelation Adenylate Kinaseβ -EGFP
13/0.127.97.98.88.2
11.414.4
1212.311.2
D D
9
Multiple SpeciesCase 1: Species differ in their diffusion constant D
Autocorrelation function can be used:
(2D-Gaussian Shape)G(τ)sample = fi
2 ⋅ G(0) i ⋅ 1 +8Dτw2DG
2
⎛
⎝ ⎜
⎞
⎠ ⎟
−1
i=1
M
∑
G(0)sample = fi2 ⋅G(0)i∑
G(0)sample is no longer γ/N !
! fi is the fractional fluorescence intensity of species i.
Antibody - Hapten Interactions
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.
Binding siteBinding site
carb2
120
100
80
60
40
20
0
Frac
tion
Liga
nd B
ound
10-10
10-9
10-8
10-7
10-6
[Antibody] free (M)
Digoxin-Fl•IgG(99% bound)
Digoxin-Fl
Digoxin-Fl•IgG(50% Bound)
Autocorrelation curves:
Anti-Digoxin Antibody (IgG)Binding to Digoxin-Fluorescein
Binding titration from the autocorrelation analyses:
triplet state
Fb =m ⋅ Sfree
Kd + Sfree
+ c
Kd=12 nM
S. Tetin, K. Swift, & , E, Matayoshi , 2003
10
Two Binding Site Model
1.20
1.15
1.10
1.05
1.00
0.95
G(0
)
0.001 0.01 0.1 1 10 100 1000Binding sites
IgG + 2 Ligand-Fl IgG•Ligand-Fl + Ligand-Fl IgG•2Ligand-Fl
[Ligand]=1, G(0)=1/N, Kd=1.0
IgG•2Ligand
IgG•Ligand
No quenching
50% quenching
1.0
0.8
0.6
0.4
0.2
0.0
Frac
tion
Bou
nd
0.001 0.01 0.1 1 10 100 1000Binding sites
Kd
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
The autocorrelation function is not suitable for analysis of this kind of data without additional information.
We need a different type of analysis
21 DD ≈assuming that
The quantity G(0) becomes the only parameter to distinguish species, but we know that:
G(0)sample = fi
2 ⋅G(0)i∑
Multiple Species
11
Photon Counting Histogram (PCH)
Aim: To resolve species from differences in their molecular brightness
Single Species:
p(k) = PCH(ε, N )
Sources of Non-Poissonian Noise
Detector NoiseDiffusing Particles in an Inhomogeneous
Excitation Beam*Particle Number Fluctuations*Multiple Species*
Poisson Distributionfor particle number:
p(N ) =N N ⋅ e− N
N!
p(k) is the probability of observing k photon counts
But distribution of photon counts is Non-Poissonian:
Photon Counting Histogram (PCH)
Aim: To resolve species from differences in their molecular brightness
Single Species:
p(k) = PCH(ε, N )
Sources of Non-Poissonian Noise• Detector Noise• Diffusing Particles in an Inhomogeneous Excitation Beam*• Particle Number Fluctuations*• Multiple Species*
where p(k) is the probability of observing k photon counts
Molecular brightness ε : The average photon count rate of a single fluorophore
PCH: probability distribution function p(k)
16000cpsmN 0.3
ε =
=
Note: PCH is Non-Poissonian!
Photon Counts
freq
uenc
y
PCH Example: Differences in Brightness
(εn=1.0) (εn=2.2) (εn=3.7)
Increasing Brightness
12
Single Species PCH: Concentration
5.5 nM Fluorescein
Fit:ε = 16,000 cpsmN = 0.3
550 nM Fluorescein
Fit:ε = 16,000 cpsmN = 33
As particle concentration increases the PCH approaches a Poisson distribution
Photon Counting Histogram: Multiple Species
Snapshots of the excitation volume
Time
Inte
nsity
Binary Mixture: p(k) = PCH (ε1 , N1 ) ⊗ PCH(ε2 , N2 )
Brightness
Concentration
Photon Counting Histogram: Multiple Species
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.
p(k) = PCH(ε1 , N1 ) ⊗ PCH(ε2 , N2 )
13
-10-8-6-4-20
log(
PCH
)
0 5 10 15k
-2
0
2
resi
dual
s/σ
-8-6
-4
-20
log(
PCH
)
0 5 10 15k
-2
0
2
resi
dual
s/σ
Singly labeled proteins Mixture of singly ordoubly labeled proteins
Resolve a protein mixture with a brightness ratio of two
Alcohol dehydrogenase labeling experiments
+
c 1ε 1N 2ε 2N
Sample A 0.190.1826.2+
− 0.0040.0040.540+
− ----- -----
Sample B 0.61.225.1+
− 007.0002.0155.0 +
− 101056+
− 008.0003.0006.0 +
−
Both species havesame• color
• fluorescence lifetime• diffusion coefficient
• polarization
kcpsm kcpsm
0
1x104
2x104
3x104
EGFPsolution
EGFPcytoplasm
EGFPnucleus
autofluorescencenucleus
autofluorescencecytoplasm
Mol
ecul
ar B
right
ness
(cps
m)
The molecular brightness of EGFP is a factor ten higher than that of the autofluorescence in HeLa cells
Excitation=895nm
PCH in cells: Brightness of EGFP
Chen Y, Mueller JD, Ruan Q, Gratton E (2002) Biophysical Journal, 82, 133 .
Brightness Encodes Stoichiometry
EGFP
Protein
F
time
ε
Sample Fluorescence Brightness
N1
F
time
2ε
N2
+ F
time
2ε
N2N1
ε
14
100 10000
2500
5000
7500
10000
EGFP Brightness EGFP
ε app (
cpsm
)
Concentration [nM]
104 105 106
Brightness of EGFP2 is twice the brightness of EGFP
Brightness and Stoichiometry
Intensity (cps)
EGFP
100 10000
2500
5000
7500
100002 x EGFP Brightness
EGFP Brightness EGFP EGFP2
ε app (
cpsm
)
Concentration [nM]
104 105 106
EGFP2
Chen Y, Wei LN, Mueller JD, PNAS (2003) 100, 15492-15497
Distinguish Homo- and Hetero-interactions in living cells
Apparent Brightness
BA
A B
A B A B A B+ A A
ε ε
ε 0
2ε
ε
ε
ε 2ε
2ε2 905nmγλ =
2 965nmγλ =
ECFP: EYFP:
• 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!
0 4000 8000 120000.0
0.5
1.0
1.5
2.0
2.5
3.0
- RXR agonist + RXR agonist
ε app/ε
mon
omer
total protein concentration [nM]0 1000 2000 3000 4000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
- RXR agonist + RXR agonist
ε app/ε
mon
omer
RXRLBD-YFP [nM]
PCH analysis of a heterodimer in living cells
We expect: RARRXR
2 965nmγλ =2 905nmγλ =
The nuclear receptors RAR and RXR form a tight heterodimer in vitro. We investigate their stoichiometry in the nucleus of COS cells.
Chen Y, Li-Na Wei, Mueller JD, Biophys. J., (2005) 88, 4366-4377
15
Two Channel Detection:Cross-correlation
Each detector observesthe same particles
Sample Excitation Volume
Detector 1 Detector 2
Beam Splitter1. Isolate correlated
signals.2. Corrects for PMT noise
Removal of Detector Noise by Cross-correlation
11.5 nM Fluorescein
Detector 1
Detector 2
Cross-correlation
Detector after-pulsing
)()(
)()()(
tFtF
tdFtdFG
ji
jiij ⋅
+⋅=
ττ
Detector 1: Fi
Detector 2: Fj
t
τ
Calculating the Cross-correlation Function
t + τ
time
time
16
Thus, for a 3-dimensional Gaussian excitation volume one uses:
21
212
1
212
1212
8181)(
−−
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟
⎟⎠
⎞⎜⎜⎝
⎛+=
zD
wD
NG ττγτ
Cross-correlation Calculations
One uses the same fitting functions you would use for the standard autocorrelation curves.
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
Each detector observesparticles with a particular color
The cross-correlation ONLY if particles are observed in both channels
The cross-correlation signal:
Sample
Red filter Green filter
Only the green-red molecules are observed!!
Experimental Concerns: Excitation Focusing & Emission Collection
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)
We assume exact match of the observation volumes in our calculations which is difficult to obtain experimentally.
17
Two-color Cross-correlation
Gij(τ) =dFi (t) ⋅dFj (t + τ)
Fi(t) ⋅ Fj (t)
)(12 τG
Equations are similar to those for the cross
correlation using a simple beam splitter:
Information Content Signal
Correlated signal from particles having both colors.
Autocorrelation from channel 1 on the green particles.
Autocorrelation from channel 2 on the red particles.
)(1 τG
)(2 τG
G12(τ)
log τ
A + B uncorrelated
A + B uncorrelated, but crosstalk
A + B correlated
Spectral CrosstalkUncorrelated
Correlated
Uncorrelated+Crosstalk Ch.2 Ch.1
450 500 550 600 650 7000
20
40
60
80
100
Wavelength (nm)
%T
Uncorrelated
Two-Color FCS: Correct for Spectral Overlap
2211111 )( NfNftF +=2221122 )( NfNftF +=
Ch.2 Ch.1
450 500 550 600 650 7000
20
40
60
80
100
Wavelength (nm)
%T
For two uncorrelated species, the amplitude of the cross-correlation is proportional to:
11 12 1 21 22 212 2 2
11 12 1 11 22 21 12 1 2 21 22 2
(0)( )
uncorrelated f f N f f NG
f f N f f f f N N f f N
⎡ ⎤+∝ ⎢ ⎥
+ + +⎢ ⎥⎣ ⎦
fij: fractional intensity of species i in channel j
G12uncorrelated(0)
log τ
A + B uncorrelated, but crosstalk
A + B correlatedG12
correlated(0)
∆G12
18
Does SSTR1 exist as a monomer after ligand binding whileSSTR5 exists as a dimer/oligomer?
Somatostatin
Fluorescein Isothiocyanate (FITC)
Somatostatin
Texas Red (TR)
Cell Membrane
R1
R5 R5
R1
Three Different CHO-K1 cell lines: wt R1, HA-R5, and wt R1/HA-R5Hypothesis: R1- monomer ; R5 - dimer/oligomer; R1R5 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 VictoriaHospital, Montreal, QC, Canada H3A 1A1; †Department of Chemistry and Physics, Clarkson University, Potsdam, NY 13699
Green Ch. Red Ch.
SSTR1 CHO-K1 cells with SST-fitc + SST-tr
• Very little labeled SST inside cell nucleus• Non-homogeneous distribution of SST• Impossible to distinguish co-localization from molecular interaction
10-5
10-4
10-3
10-2
10-1
-2
0
2
4
6
8
10
τ(s)
G(τ
)
G1 G2 G12
Minimum
MonomerA
10-5
10-4
10-3
10-2
10-1
0
2
4
6
8
τ(s)
G(τ
)
G1 G2 G12Maximum
DimerB
= 0.22G12(0)G1(0)
= 0.71G12(0)G1(0)
19
10-4 10-2 100
0.00
0.02
0.04
0.06
τ(s)
G(τ
)
G1 G2 G1 2
10-5
10-4
10-3
10-2
10-1
-0.04
0.00
0.04
0.08
0.12
0.16
τ(s)
G(τ
)
G1 G2 G1 2
Experimentally derived auto- and cross-correlation curves from live R1 and R5/R1 expressing CHO-K1 cells using dual-color two-photon FCS.
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.
R1 R1/R5
Patel, R.C., et al., Ligand binding to somatostatin receptors induces receptor-specific oligomer formation in live cells. PNAS, 2002. 99(5): p. 3294-3299
- 4 Ca2+ + 4 Ca2+
CFP YFP
calmodulin M13
CFP
YFP“High” FRET
“Low” FRET
trypsin
CFP YFP+
NO FRET
(a)
(b)
(c)
Molecular Dynamics
What if the distance/orientation is not constant?
• Fluorescence fluctuation can result from FRET or Quenching
• FCS can determine the rate at which this occurs
• This will yield hard to get information (in the µs to ms range) on the internal motion of biomolecules
450 500 550 600 6500
10000
20000
30000
40000
50000
60000
Fluo
resc
ence
Inte
nsity
(cps
)
Wavelength (nm)
trypsin-cleaved cameleon
CFP cameleon
Ca2+-depleted cameleon
Ca2+-saturated YFP
20
A)
10-3 10-2 10-1 100 101
0
40
80
120
160
200
τ (s)
G( τ)
B)
. 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.
10-5 10-4 10-3 10-2 10-1 100-0.02
0.00
0.02
0.04
0.06
0.08
0.10
G(τ
)
τ (s)
Donor Ch. Autocorrelation Acceptor Ch. Autocorrelation Cross-correlation
Crystallization And Preliminary X-Ray Analysis Of Two New Crystal Forms Of Calmodulin, B.Rupp, D.Marshakand S.Parkin, Acta Crystallogr. D 52, 411 (1996)
Ca2+ Saturated
Are the fast kinetics (~20 µs) due to conformational changes or to fluorophore blinking?
In vitro Cameleon Data
Cross-CorrelationDual-Color PCH
Fluo
resc
ence
F(t)
<FA>δFA
Time t
<FB>δFB
Time t
Fluo
resc
ence
F(t)
Dual-color PCH analysis (1)
21
Tsample
Sign
al A
Tsample
Sign
al B
Brightness in each channel: εA, εB
Average number of molecules: N
Tsample
Sign
al A
Tsample
Sign
al B
Brightness in each channel: εA, εBAverage number of molecules: N
Dual-color PCH analysis (2)
Single Species: ( , ) ( , , )A B A Bp k k PCH Nε ε=
Dual-Color PCHfluctuations
2 channels
2 species model χ2 = 1.01
2000 3000 4000 5000 6000 7000 8000 9000100002000
3000
4000
5000
6000
7000
8000
9000
10000
EYFP alone ECFP alone species 1 from fit species 2 from fit
ε A (c
psm
)
εB (cpsm)
1 species modelχ2 = 17.93
ECFP & EYFP mixture resolved with single histogram.
Resolve Mixture of ECFP and EYFP in vitro
Note: Cross-correlation analysis cannot resolve a mixture of ECFP & EYFP with a single measurement!
Chen Y, Tekmen M, Hillesheim L, Skinner J, Wu B, Mueller JD, Biophys. J. (2005), 88 2177-2192