assaying single molecule molecular interactions
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www.fcsxpert.com February 19, 2008
Workshop on
Assaying and Measuring Molecular Dynamics and Interactions in Solution by Fluorescence
Correlation Spectroscopy (FCS)
David Wolf and Dylan Bulseco
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What is FCS?Molecules Move Randomly in Solution
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This Random Motion Causes a Fluctuation in the Number of Molecules in the Confocal Volume
•FCS measures the fluctuations in fluorescence intensity as molecules diffuse in and out of the laser beam
0 20 40 60 80 100940
960
980
1000
1020
1040
1060
Inte
nsity
(cou
nts
per 1
00 n
s)
Time (usec)
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What is FCS?
• Physical processes are in a state of dynamic equilibrium.• FCS uses confocal optics to confine the volume of measurement
to a small confocal volume• In a small volume concentration fluctuates about its mean• FCS measures the fluctuations in fluorescence intensity that
result from these concentration fluctuations. • FCS measures concentration fluctuations, which result from
random diffusion or directed flow in and out of the confocal volume as well as processes which are independent of volume.
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Examples of Processes which Cause Fluctuations
• Diffusion• Directed flow (hydrodynamic and
electrophoretic)• Chemical Equilibrium• Intersystem crossing between singlet and
triplet states• Nonradiative fluorescence resonance energy
transfer (FRET)
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How FCS Works: Hardware
•FCS uses confocal optics to measure the motion of fluorescently labeled molecules in a small volume
Focused laser illumination
Pinhole confines measurement to confocal volume
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What is Correlation?
Suppose that you are measuring two physical parameters. These might, for instance, be intensities, I1 and I2 , at two wavelengths and you want to know if the two signals are correlated with one another.
You might start by plotting I1 and I2 against time.
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I1 and I2 as a Function of Time
0 1 2 3 4 5 6 7 8 9 10 110
20
40
60
80
100
20
40
60
80
100
120
140
Inte
nsity
1
Seconds
Intensity 1
Inte
nsity
2
Intensity 2
131.8390.254
118.3783.310
98.5278.116
94.7568.245
78.9361.131
73.0745.223
58.1541.948
53.7729.903
40.1121.228
27.949.012
I2I1
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What is Our Sense of this Data?
The two intensities appear to be closely related (correlated) with one another. Despite small fluctuations they are both going steadily upward.
To investigate this more closely (mathematically) we plot I1 vs. I2.
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Correlation Between the Two Intensities
0 20 40 60 80 100
20
40
60
80
100
120
140
R=0.98
Inte
nsity
2
Intensity 1
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What is Correlation?
We see that the two intensities are highly correlated with one another. This is reflected in the fact that there are only slight deviations from a straight line relationship. The correlation coefficient, a measure of this deviation, is 0.98 which is close to 1.0, which would indicate perfect correlation.
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What is the Correlation Function?
Let’s consider a slightly different problem. We look at a single intensity, I, which goes up and down but never really goes anywhere for long. We then ask the question if the intensity isgoing up now, how long will it continue to go up?
Mathematically, the question can be expressed as, if the intensity is rising or falling now, what is the probability that it will still be rising or falling some time in the future?
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Intensity as a Function of Time
0 20 40 60 80 100
9.8
9.9
10.0
10.1
10.2
10.3
Inte
nsity
Time (seconds)
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The Intensity is Perfectly Correlated with Itself (no surprise)
9.8 9.9 10.0 10.1 10.2 10.3
9.8
9.9
10.0
10.1
10.2
10.3
Inte
nsity
Intensity
R=1.0
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What is the Correlation Function?
It is no surprise that intensity is correlated with itself. However, let’s ask the slightly more interesting question whether the intensity at any point in time is correlated with itself a second later in time.
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Correlation Between Intensity and Itself a Second Later
9.8 9.9 10.0 10.1 10.2 10.3
9.8
9.9
10.0
10.1
10.2
10.3
Inte
nsity
one
sec
ond
late
r
Intensity
R-0.97
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What is the Correlation Function?
The intensity is still highly correlated with itself a second later.
Let’s see what happens if we continue this process with successively longer lags between the two times of measurement.
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Correlation Between Intensity and Itself Six Seconds Later
9.8 9.9 10.0 10.1 10.2 10.39.8
9.9
10.0
10.1
10.2
10.3
Inte
nsity
Six
Sec
onds
Lat
er
Intensity
R-0.92
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Correlation Between the Intensity and Itself 48 Seconds Later
9.8 9.9 10.0 10.1 10.2 10.3
9.8
9.9
10.0
10.1
10.2
10.3
Inte
nsity
48
Seco
nds
Late
r
Intensity
R-0.50
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Correlation Between the intensity and Itself 96 Seconds Later
9.8 9.9 10.0 10.1 10.2 10.3
9.8
9.9
10.0
10.1
10.2
10.3In
tens
ity 9
6 S
econ
ds L
ater
Intensity
R-0.00
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The Correlation Coefficient is a Decaying Function of Time
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Correlation Decays with a Characteristic Time Constant
0 10 20 30 40 50 60 70 80 90 100 110
0.0
0.2
0.4
0.6
0.8
1.0
Cor
rew
latio
n C
oeffi
cien
tR
(Δt)
Shift in Seconds
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What is the Autocorrelation Function?
The correlation coefficient expresses the probability that if the signal is rising or falling now that it will be still rising or falling sometime later.
This probability goes from 1 at time 0, to 0 at time infinity.
Since we are considering the correlation between intensity and itself, we refer to this as the autocorrelation function.
If we perform the same analysis comparing fluctuations in intensity at some wavelength with, say, intensity at a second wavelength we would refer to this as a cross-correlation function.
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It is important to recognize that in physics and biology the fluctuations are not really random. Some underlying process with a characteristic time scale is driving them.
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How FCS Works: Analysis•In single channel FCS we measure the autocorrelation function ofthe intensity fluctuations.•In multi-channel FCS we additionally measure the cross-correlation between the intensity fluctuations in the different channels.•The autocorrelation function provides two measures of molecular size and motion
•Number of molecules in the confocal volume (particle number)•Diffusion time for these molecules
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Particle Number (From t = 0 value)*
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 1030.981.001.021.041.061.081.101.121.141.161.181.20
G(τ
)
τ (s)
*The smaller the particle number the larger the intercept
N=5
N=25
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Molecular Size (from the rate of decay)*
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12G
(τ)
τ (s)
*The faster the diffusion the faster the rate of decay
τ=300 ms
τ=0.03 ms
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Detection of Molecular Complexing by FCS
No cross-correlationFast autocorrelationFluorescent labels
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Detection of Molecular Complexing by FCS
No cross-correlationSlow autocorrelation
Fluorescent labels boundto different targets
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Detection of Molecular Complexing by FCS
Slow cross-correlationSlow autocorrelation
Fluorescent labels boundto same target
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Simplified FCS Data From theQuantumXpertTM
Autocorrelation Functions
Cross-correlation Functions
Intensity Fluctuations
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FCS: From Molecules to Bacteria
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FCS: From Molecules to Bacteria
•The QuantumXpert can measure diffusion over seven orders of magnitude
•Assuming a spherical geometry D = kT/6πηr
•At low viscosity τ = w2/4D should depend linearly radius, MW1/3, and viscosity
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G(t) for Different Molecular Weights
1E-5 1E-4 1E-3 0.01 0.1 1 100
1
2
3
4
5
Nor
mal
ized
G(t)
Time (sec)
R6G HSA IgG QDots Beads
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Linear Dependence of τ on r
1E-8 1E-7 1E-6 1E-5 1E-4
100000
1000000
1E7
1E8
1E9
r = (MW/((6.02x1023)(4/3)πρ*)1/3 (cm)
1/D
(s/c
m2 )
Experimental Theoretical
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Micromolecular Diffusion – R6G in Water/Glycerol Mixtures
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Micromolecular vs Macromolecular Diffusion
• If one has an aqueous solution and adds to that a solute, such as alginate, which increases viscosity and where the diffusantr > the size of the solute then the molecular diffusion will follow the same laws as macromolecular diffusion
• If one has an aqueous solution and adds to that a solute which increases viscosity and where the diffusant r < the size of the solute then the molecule will diffuse as if it were in water
• Example mixtures of alginate and water
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Macromolecular Diffusion in Aqueous Alginate Solutions
• Alginate is causing the increased viscosity• If we use a 0.1 um radius bead we can
measure macroscopic viscosity because the bead is much greater in size than the alginate (MW equivalent is ~100 M da)
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Macroscopic Diffusion (0.1 um fluorescent beads)
0 1000 2000 3000 4000 5000 6000 7000 80000
3
6
9
12
15
18
21
Tau
(se
c)
Viscosity (cP)
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Macroscopic Diffusion (0.1 um fluorescent beads)
• Using FCS with 0.1 μm fluorescent beads we can measure viscosities in excess of 7000 cP
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Micromolecular Diffusion- Different Size Molecules in alginate/water mixtures
1E-7 1E-6 1E-5100000
1000000
1E7
1E8
1E9
1E10
r = (MW/((6.02E23)(4/3)πρ))1/3 (cm)
1/D
(s/c
m2 )
1 cp 400 cp 700 cp 1700 cp 3700 cp7000 cp
Alginate MW = 131 Kda
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Micromolecular Diffusion- Different Size Molecule in Alginate Hydrogels
FCS enables the measurement of micromoleculardiffusion in hydrogels even though such gels do not exhibit macromolecular diffusion or classic viscosity
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Micromolecular Diffusion- Different Size Molecule in Alginate Hydrogels
0 1 2 3 4 5 60
200000
400000
600000
800000
1000000
1200000
1400000
1600000
1800000
2000000
2200000 Gelled Alginate - Composite
1/D
(s/c
m2 )
% Alginate
Rhod 1/D Dimer 1/D IgG 1/D
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Micromolecular Diffusion- Different Size Molecule in Alginate Hydrogels
1E-7 1E-6-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Mas
s C
ondu
ctan
ce (D
/D0)
r(cm)
1.75 % 2.63 % 3.50 % 4.38 % 5.25 %
Alginate MW = 131 kDa
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QuantumXpertTM by Sensor Technologies
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QuantumXpertTM - FCS Simplified
• Easy to use• Push-button acquisition• Intuitive menu driven analysis • Convenient assay kits
• Bench-top (49 cm x 37 cm x 12 cm)
• Inexpensive• No user alignment required
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FCS provides unique measurement capabilities of polymer solutions and hydrogels
• Enables viscosity measurements to be performed in volumes as small as 10 μl
• Enables viscosity measurements to be made in both polymer solutions and hydrogels
• Enables not only macroscopic viscosity measurements but also measurements of molecular diffusion• Quantitates molecular transport rates• Determines critical molecular size cutoffs
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QuantumXpertTM - FCS Simplified
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What Kind of Information can I get from FCS?
• Translational Diffusion Rates• Chemical Kinetics Rates• Degree of Molecular Aggregation • Complex Stoichiometry• Ligand Binding • Enzymatic Activity • Nucleic Acid Interactions • Dynamic changes in protein conformation
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FCS provides unique measurement capabilities of polymer solutions and hydrogels
• Enables viscosity measurements to be performed in volumes as small as 10 μl
• Enables viscosity measurements to be made in both polymer solutions and hydrogels
• Enables not only macroscopic viscosity measurements but also measurements of molecular diffusion• Quantitates molecular transport rates• Determines critical molecular size cutoffs
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Macroscopic vs. Microscopic Diffusion
• Most techniques measure viscosity on a macroscopic scale with some very large probe (i.e. a rotating blade or falling ball)
• There is also motion on a microscopic scale (molecular diffusion)
• The two may be quite different• Empirically the distinction occurs when the characteristic
probe size is > 5X the molecular dimensions of the molecular species causing the viscosity
• Only microscopic motion occurs in the gelled state
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QuantumXpertTM
• An integrated system for FCS assays:• Hardware• Software• Application-specific kits
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Strepavidin System
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0 50 100 150 200 25030000
40000
50000
60000
70000
80000
90000
100000
Biotin Biotinylated-IgG
Fluo
resc
ence
Inte
nsity
(cps
)
[Biotin] or [Biotinylated IgG] nM
Intensity
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10-5 10-4 10-3 10-2 10-1 100 101 1020.99
1.00
1.01
1.02
1.03
1.04
G(t)
τ (s)
1 pM Biotinylated IgG 1 nM Biotinylated IgG
Autocorrelation Curves
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Particle Number
0 5 10 15 20
0
50
100
150
200
250
300
Np
Biotinylated-IgG (nM)
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PCH
0 5 10 15 20 25 301E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
P(E
vent
s)
Events
0 Biotinylated IgG 0 Biotin 1 nM Biotin-IgG 1 nM Biotin
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Diffusion Times
0 5 10 15 20
0
50
100
150
200
250
300
350
TauD
2 (m
s)
[Biotin-IgG] nM
0 50 100 150 200 250
0
50
100
150
200
250
300
350
TauD
2 (m
s)
Np
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Detection Using Two FCS Channels
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10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103
1.000
1.001
1.002
1.003
1.004
1.005
1.006
Ab Alone
Ab + HB101
G(τ
)
τ
0 20 40 60 80 100 120150000
200000
250000
300000
Ab Alone
Ab + HB101
Inte
nsity
Time (sec)
Bacterial Detection Using One FCS Channel Signal Extraction From High Background
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Bacillus subtilis: Antibody Probes
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103
1.0
1.5
2.0
2.5
3.0
3.5
G(τ
)
τ
0 25 50 75 100 125 150 175 200 225 250 275 300
0150003000045000
0 25 50 75 100 125 150 175 200 225 250 275 3000
250005000075000
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Bacillus subtilis: DNA Probes
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103
1.0
1.1
1.2
1.3
G(τ
)
τ
0 25 50 75 100 125 150 175 200 225 250 275 300 325
0200000400000600000
0 25 50 75 100 125 150 175 200 225 250 275 300 3250
250000500000750000
1000000
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Bacillus subtilis spores: Antibody Probes
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102
1
2
3
4
5
G(τ
)
τ
0 25 50 75 100 1250
1000020000300004000050000
0 25 50 75 100 1250
250005000075000
100000
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FCS Applications in Solution
•Protein-protein interactions
•Protein-nucleic acid interactions
•Ligand-receptor binding
•Enzyme activation and kinetics
•Compound aggregation
•Protein folding
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www.FCSXpert.com
•Product specifications•FCS Classroom
•FCS Tutorials•FCS Applications•Data Analysis Notes•Sample Data•Reference List
•FCS Forum
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FCS vs. FRAP vs. FRET
√√√Binding Kinetics
√Complex Stoichiometry
√√Complexing
√Concentration
√Mobile Fraction
√MulticomponentDiffusion
√√Diffusion Rates
FCSFRETFRAPParameter
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FCS vs. FRAP and FRET: What Information They Provide
• FCS• Diffusion rates on a 1 um distance scale• Number of molecules (concentration)• Molecular complexing• Complex stoichiometry• Binding kinetics
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