Lecture 5 FCS, Autocorrelation, PCH, Cross-correlation Enrico Gratton

1
Lecture 5FCS, Autocorrelation, PCH,
Cross-correlation Enrico Gratton
Principles of Fluorescence Techniques
Laboratory for Fluorescence Dynamics
2
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
3
First Application of Correlation
Spectroscopy (Svedberg Inouye, 1911) Occupancy
Fluctuation
Experimental data on colloidal gold particles
12000200132412310211113112511102331333221112242212
2612214 234524114131142310010042112312320111100011
1_2110013200000 10011000100023221002110000201001_3
33122000231221024011102_ 1222112231000110331110210
110010103011312121010121111211_10 0032210123020121
21321110110023312242110001203010100221734 41010100
2112211444421211440132123314313011222123310121111
222412231113322132110000410432012120011322231200_2
53212033 23311110021002201301132111312001013143221
1221122323442230 321421532200202142123232043112312
003314223452134110412322 220221
Collected data by counting (by visual inspection)
the number of particles in the observation
volume as a function of time using a ultra
microscope
4
Particle Correlation
Histogram of particle counts Poisson
behavior Autocorrelation not available in the
original paper. It can be easily calculated
today.
They estimated the particle size to be 6 nm.
Comments to this paper conclude that scattering
will not be suitable to observe single molecules,
but fluorescence could
5
In FCS Fluctuations are in the Fluorescence
Signal
Example of processes that could generate
fluctuations
6
Generating Fluctuations By Motion
What is Observed?
1. The Rate of Motion 2. The Concentration of
Particles 3. Changes in the Particle
Fluorescence while under Observation, for example
conformational transitions
Observation Volume
Sample Space
7
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
Defined by the wavelength and numerical aperture
of the objective
8
1-photon
Need a pinhole to define a small volume
2-photon
Brad Amos MRC, Cambridge, UK
9
Data Treatment Analysis
Time Histogram
Autocorrelation
Autocorrelation Parameters G(0) kaction
Photon Counting Histogram (PCH)
PCH Parameters ltNgt e
10
Autocorrelation Function
Factors influencing the fluorescence signal
kQ quantum yield and detector sensitivity (how
bright is our probe). This term could contain
the fluctuation of the fluorescence intensity due
to internal processes
C(r,t) is a function of the fluorophore
concentration over time. This is the term that
contains the physics of the diffusion processes
W(r) describes our observation volume
11
The Autocorrelation Function
t3
t5
t4
t2
t1
G(0) ? 1/N As time (tau) approaches 0
Diffusion
12
Calculating the Autocorrelation Function
Photon Counts
time
?
Average Fluorescence
t t
t
13
The Effects of Particle Concentration on
the Autocorrelation Curve
14
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
15
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
Time
Average 0.275
Variance 0.256
Lets increase the particle brightness by 4x
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
Variance 4.09
0.296
16
What about the excitation (or observation) volume
shape?
17
Effect of Shape on the (Two-Photon)
Autocorrelation Functions
For a 2-dimensional Gaussian excitation volume
1-photon equation contains a 4, instead of 8
For a 3-dimensional Gaussian excitation volume
18
Additional Equations
3D Gaussian Confocor analysis
... where N is the average particle number, tD is
the diffusion time (related to D, tDw2/8D, for
two photon and tDw2/4D for 1-photon excitation),
and S is a shape parameter, equivalent to w/z in
the previous equations.
Triplet state term
..where T is the triplet state amplitude and tT
is the triplet lifetime.
19
Orders of magnitude (for 1 µM solution, small
molecule, water) Volume Device Size(µm)
Molecules Time milliliter cuvette 10000 6x10
14 104 microliter plate well
1000 6x1011 102 nanoliter microfabrication
100 6x108 1 picoliter typical cell
10 6x105 10-2 femtoliter confocal volume
1 6x102 10-4 attoliter nanofabrication
0.1 6x10-1 10-6
20
The Effects of Particle Size on
the Autocorrelation Curve
Stokes-Einstein Equation
and
Monomer --gt Dimer Only a change in D by a factor
of 21/3, or 1.26
21
Autocorrelation Adenylate Kinase -EGFP Chimeric
Protein in HeLa Cells
Examples of different Hela cells transfected with
AK1-EGFP
Fluorescence Intensity
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
22
Autocorrelation of EGFP Adenylate Kinase -EGFP
EGFP-AK in the cytosol
G(t)
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().
23
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.
24
Autocorrelation Adenylate Kinaseb -EGFP
Plasma Membrane
Cytosol
D
D
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.
25
Multiple Species
Case 1 Species vary by a difference in
diffusion constant, D.
Autocorrelation function can be used
(2D-Gaussian Shape)

!
26
Antibody - Hapten Interactions
Binding site
Binding site
carb2
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.
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).
27
Anti-Digoxin Antibody (IgG) Binding to
Digoxin-Fluorescein
triplet state
Digoxin-FlIgG (99 bound)
Autocorrelation curves
Digoxin-FlIgG (50 Bound)
Digoxin-Fl
Binding titration from the autocorrelation
analyses
Kd12 nM
S. Tetin, K. Swift, , E, Matayoshi , 2003
28
Two Binding Site Model
IgG2Ligand-Fl
Ligand-Fl
IgG 2 Ligand-Fl
IgGLigand-Fl
50 quenching
Kd
IgGLigand
No quenching
IgG2Ligand
Ligand1, G(0)1/N, Kd1.0
29
Digoxin-FL Binding to IgG G(0) Profile
Y. Chen , Ph.D. Dissertation Chen et. al.,
Biophys. J (2000) 79 1074
30
Case 2 Species vary by a difference in brightness
assuming that
The quantity Go becomes the only parameter to
distinguish species, but we know that
The autocorrelation function is not suitable for
analysis of this kind of data without additional
information.
We need a different type of analysis
31
Photon Counting Histogram (PCH)
Aim
To resolve species from differences in their
molecular brightness
Poisson Distribution
Single Species
Where p(k) is the probability of observing k
photon counts
32
PCH Example Differences in Brightness
frequency
(en1.0)
(en2.2)
(en3.7)
Increasing Brightness
Photon Counts
33
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
34
Photon Counting Histogram Multispecies
Binary Mixture
Molecular Brightness
Concentration
Snapshots of the excitation volume
Intensity
Time
35
Photon Counting Histogram Multispecies
Sample 2 many but dim (23 nM fluorescein at pH
6.3)
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.
36
Examination of a Protein Dimer with FCS
Secreted Phospholipase A2
Sanchez, S. A., Y. Chen, J. D. Mueller, E.
Gratton, T. L. Hazlett. (2001) Biochemistry, 40,
6903-6911.
37
sPLA2 Interfacial Binding
sPLA2 Self-Association
sPLA2 Membrane Binding
Interfacial sPLA2Self-Association
38
Lipid Interfaces
Choline Group
Multibilayers (MLVs)
Vesicles (SUVs, LUVs GUVs)
12 Carbon Tail
Micelles
Dodecylphosphocholine (DPC) Micellar Lipid Analog
(CMC 1.1 mM)
39
In Solution a Tight Dimer
Fluorescein-sPLA2
Steady-State Anisotropy
Fluorescence Correlation Spectroscopy
Fl-sPLA2
Fl-sPLA2
measured predicted (by sedimentation)
Time-Resolved Anisotropy
Rotational correlation time 1 12.8 ns
(0.43) Rotational correlation time 2 0.50 ns
(0.57)
Why this large discrepancy?
40
In Solution Fluorescein-sPLA2 /- Urea
1. Autocorrelation
sPLA2 G(0)0.021 D 72 um2/s
Increasing Particles
sPLA2 3M Urea G(0)0.009 D 95 um2/s
2. PCH analysis
sPLA2 e 0.6 N 3.29 sPLA2
3M Urea e 0.6 N 8.48
Increasing Particles
Adjusted for viscosity differences
Change in number of particles, little change in
brightness!
41
The Critical Question Is sPLA2 a Dimer in the
Presence of Interfacial Lipid?
What Could We Expect to Find in the FCS Data?
Monomer Lipid
Micellar Lipid
C.atrox sPLA2
Ddimer N particles
(Poor Substrate)
(Preferred Substrate)
Upon dissociation, the mass could increase due to
lipid binding. Better count the number of
particles!
Observing Fluorescein-labeled sPLA2
42
FCS on Fluorescein - sPLA2 in Buffer (RED) and
with DPC Micelles ( BLUE )
1. Autocorrelation Analysis
DPC increase in particles
sPLA2 G0 0.0137 D 75
um2/s sPLA2 20 mM DPC G0 0.0069
D 55 um2/s
2. PCH Analysis
sPLA2 e 0.41 N
6.5 sPLA2 20 mM DPC e 0.45
N 12.2
DPC increase in particles
43
Fluorescein-sPLA2 Interaction with DPC
N
Ca2
EDTA
(Dmicelle57 um2/s)
D 55-60 um2/s
12
10
(Ddimer 75 um2/s)
N
D 73 um2/s
8

• The PLA2 dimer dissociates in the presence of
  micelles.
• Active enzyme form in a micellar system is
  monomeric.

6
0.01
0.1
1
10
DPC (mM)
44
Schematic of sPLA2 - Dodecylphosphocholine
Interactions
Monomer-Lipid Association
sPLA2
sPLA2-Micelle
Co-Micelle
45
Two Channel Detection Cross-correlation
Sample Excitation Volume
Beam Splitter

1. Increases signal to noise by isolating correlated
   signals.
2. Corrects for PMT noise

Detector 1
Detector 2
Each detector observes the same particles
46
Removal of Detector Noise by Cross-correlation
Detector 1
11.5 nM Fluorescein
Detector 2
Detector after-pulsing
Cross-correlation
47
Calculating the Cross-correlation Function
Detector 1 Fi
time
?
t t
t
Detector 2 Fj
time
48
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
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.
49
Two-Color Cross-correlation
The cross-correlation ONLY if particles are
observed in both channels
Sample
Green filter
Red filter
Each detector observes particles with a
particular color
The cross-correlation signal
Only the green-red molecules are observed!!
50
Two-color Cross-correlation
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.
51
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)
52
Two-Color Fluctuation Correlation Spectroscopy
Uncorrelated
Interconverting
For two uncorrelated species, the amplitude of
the cross-correlation is proportional to
53
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
Three Different CHO-K1 cell lines wt R1, HA-R5,
and wt R1/HA-R5
Hypothesis R1- monomer R5 - dimer/oligomer
R1R5 dimer/oligomer
54
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

55
Monomer
A
Dimer
B
56
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
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 receptor-specific
oligomer formation in live cells. PNAS, 2002.
99(5) p. 3294-3299
57
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
  ms to ms range) on the internal motion of
  biomolecules

58
(No Transcript)
59



60
In vitro Cameleon Data
Ca2 Saturated
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 ?s) due to
conformational changes or to fluorophore blinking?
61
Autocorrelation Adenylate Kinaseb -EGFP
Plasma Membrane
Cytosol
D
D
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 costants are found.
62
FRET Efficiency Distribution in Low Mg
Low-FRET Conformation
High-FRET Conformation
FRET Efficiency
63
What is scanning FCS? How is it
implemented? What kind of information scanning
FCS provides that cannot be obtained with
single-point FCS?
Definition Simultaneous FCS measurements at
multiple sample positions Simultaneous
multiplexing Principle Return to the same
location before the particle leaves the volume of
observation
64
Scenarios for Scanning FCS application

• Explore spatial-temporal correlation.
• Detection and characterization of membrane
  rafts.

Visible raft-like domains
How to see the invisible rafts? Probe must be
selective for rafts Probe concentration must be
large to properly paint the rafts If the rafts
are stationary, measurement at only one position
will not provide the number of rafts in a
pixel If we know the number, we can determine
the average size
GUV made from integral membrane fragment
Nano scale
Macro scale
65
Chamber Design
66
Lipid Extract GUV Morphology
BBM LIPID EXTRACT GUVs
BBM and BLM Lipid Extract GUVs exhibit formation
of lipid domains. GUVs composed of BBM and BLM
natural lipid extracts. Micron-sized
non-fluorescent circular domains appear on the
surface of the GUVs. Domain formation occurs at
43 C for the BBM and at 38C for the BLM.
67
Integral Membrane GUV Morphology
Integral BBM GUV
Integral BLM GUV
Integral BBM and BLM GUVs exhibit domain
formation. GUVs composed of integral membrane
fragments. On the surface of the GUVs appear
micron-sized non-fluorescent domains which are
irregularly shaped. Domain formation occurs at
43 C for the BBM and at 41.5C for the BLM.
68
Measure the molecular weight of DNA (Weissman,
Proc. Natl. Acad, Sci, USA 73 2776
(1976)) Measure the Diffusion of Fluorescent
Beads and DNA (Koppel and others. Biophysical J.
Vol 66 502, 1994)

• Advantages
• Improved signal to noise ratio

69
Data analysis
Time
Measure association/dissociation equilibrium in
protein systems (Berland et al, Biophys. J. 1996)
70
Fitting Model for Scanning FCS
Calculation of the Autocorrelation Function
Fitting Model
D5mm2/s
71
Conventional FCS (vs) Scanning FCS in solution
Autocorrelation curve of fluorescein labeled
beads in suspension.
72
FCS of fluorescent antibody (labeled with Alexa
488) in solution
Free fluorophore
D21.4?1.3mm2/sec
D20.6?1.1mm2/sec
Scanning FCS
Point FCS
73
Scanning FCS on GUV
POPC
Scanning FCS
Laurdan labeled GUV, surface
FCS at one point
Scanning frequency is 1 ms per orbit We have a
bandwidth sufficient to observe diffusion of a
small molecule such as Laurdan or prodan in a
fluid membrane (POPOC)
74
Advantage of scanning FCS for membrane and
cellular studies

• Less photo damage
• Easy to locate membrane border
• Multiple points simultaneously
• Distinguish moving from immobile fraction
• Spatial cross correlation
• Velocity direction and gradients

75
Protein interactions on GUVs can not be detected
by imaging
Addition of fluorescent antibody to GUV
background
The GUVs were made from rat kidney brush-border
membrane extract containing all the integral
membrane proteins. The antibody against one
specific membrane protein (NaPi II) was labeled
with Alexa 488, no enhanced fluorescence was
observed on the GUV membrane bilayers. Performing
FCS measurements on the bilayers was difficult
due to the lack of contrast.
76
Protein interactions on GUVs can be detected by
Scanning FCS
Time One line is 1 ms
Autocorrelation time (log axis)
Hyperspace Vertical axis is time, horizontal
axis is location along the orbit
Autocorrelation at different positions
77
Diffusion coefficient of the antibody obtained
from scanning FCS
D124 mm2/sec D20.11 mm2/sec
D20 mm2/sec
In solution
On GUVs
Inside GUVs
78
Membrane Undulation Detected by Scanning FCS
Example of spatial correlation
Membrane labeled with Laurdan
Autocorrelation curve
Time
Mid section of GUV
FCS-hyperspace
79
Protein Interactions on GUVs Detected by Scanning
FCS
Intensity Autocorrelation
The GUV is made out of whole membrane extract
from the basolateral membrane (BLM) of OKP cells.
The antibody labeled with Alexa488 was against
NaPi II cotransporter. This protein was suppose
to be present in the BLM. This experiment proved
that our GUV generation method also incorporated
the membrane proteins. It is relatively close to
the natural composition of the plasma membrane.
time
80
Conclusions Scanning FCS is feasible both in
solution, in model membranes and in cells When
the characteristic times for diffusion (or
reactions) are about 1 ms or longer, it could be
convenient to perform scanning FCS Scanning FCS
provides autocorrelation functions at many
positions in the sample in a multiplexing
way Scanning FCS offers the possibility to
distinguish processes such as true diffusion and
flow from local movements Scanning FCS allows to
clearly distinguish the location (and movements)
of membranes proteins and membrane domain while
performing FCS measurements Scanning FCS can be
used to determine with nanometer precision the
positions of particles (molecules) and membranes