Assaying Single Molecule Molecular Interactions

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


What is FCS?Molecules Move Randomly in Solution


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)


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.


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)


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


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.


I1 and I2 as a Function of Time

0 1 2 3 4 5 6 7 8 9 10 110

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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


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.


Correlation Between the Two Intensities

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R=0.98

Inte

nsity

2

Intensity 1


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.


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?


Intensity as a Function of Time

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Inte

nsity

Time (seconds)


The Intensity is Perfectly Correlated with Itself (no surprise)

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9.9

10.0

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Inte

nsity

Intensity

R=1.0



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.


Correlation Between Intensity and Itself a Second Later

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nsity

one

sec

ond

late

r

Intensity

R-0.97



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.


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

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Inte

nsity

Six

Sec

onds

Lat

er

Intensity

R-0.92


Correlation Between the Intensity and Itself 48 Seconds Later

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9.8

9.9

10.0

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nsity

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nds

Late

r

Intensity

R-0.50


Correlation Between the intensity and Itself 96 Seconds Later

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tens

ity 9

6 S

econ

ds L

ater

Intensity

R-0.00


The Correlation Coefficient is a Decaying Function of Time


Correlation Decays with a Characteristic Time Constant

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0.0

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1.0

Cor

rew

latio

n C

oeffi

cien

tR

(Δt)

Shift in Seconds


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.


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.


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


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


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


Detection of Molecular Complexing by FCS

No cross-correlationFast autocorrelationFluorescent labels



No cross-correlationSlow autocorrelation

Fluorescent labels boundto different targets



Slow cross-correlationSlow autocorrelation

Fluorescent labels boundto same target


Simplified FCS Data From theQuantumXpertTM

Autocorrelation Functions

Cross-correlation Functions

Intensity Fluctuations


FCS: From Molecules to Bacteria


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


G(t) for Different Molecular Weights

1E-5 1E-4 1E-3 0.01 0.1 1 100

1

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5

Nor

mal

ized

G(t)

Time (sec)

R6G HSA IgG QDots Beads


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


Micromolecular Diffusion – R6G in Water/Glycerol Mixtures


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


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)


Macroscopic Diffusion (0.1 um fluorescent beads)

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Tau

(se

c)

Viscosity (cP)


Macroscopic Diffusion (0.1 um fluorescent beads)

• Using FCS with 0.1 μm fluorescent beads we can measure viscosities in excess of 7000 cP


Micromolecular Diffusion- Different Size Molecules in alginate/water mixtures

1E-7 1E-6 1E-5100000

1000000

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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


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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2200000 Gelled Alginate - Composite

1/D

(s/c

m2 )

% Alginate

Rhod 1/D Dimer 1/D IgG 1/D



1E-7 1E-6-0.2

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Mas

s C

ondu

ctan

ce (D

/D0)

r(cm)

1.75 % 2.63 % 3.50 % 4.38 % 5.25 %

Alginate MW = 131 kDa


QuantumXpertTM by Sensor Technologies


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


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


QuantumXpertTM - FCS Simplified


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


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


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


QuantumXpertTM

• An integrated system for FCS assays:• Hardware• Software• Application-specific kits


Strepavidin System


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Biotin Biotinylated-IgG

Fluo

resc

ence

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nsity

(cps

)

[Biotin] or [Biotinylated IgG] nM

Intensity


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G(t)

τ (s)

1 pM Biotinylated IgG 1 nM Biotinylated IgG

Autocorrelation Curves


Particle Number

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Np

Biotinylated-IgG (nM)


PCH

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P(E

vent

s)

Events

0 Biotinylated IgG 0 Biotin 1 nM Biotin-IgG 1 nM Biotin


Diffusion Times

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TauD

2 (m

s)

[Biotin-IgG] nM

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Detection Using Two FCS Channels


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Ab Alone

Ab + HB101

G(τ

)

τ

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Ab Alone

Ab + HB101

Inte

nsity

Time (sec)

Bacterial Detection Using One FCS Channel Signal Extraction From High Background


Bacillus subtilis: Antibody Probes

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1.0

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G(τ

)

τ

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0150003000045000

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250005000075000


Bacillus subtilis: DNA Probes

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G(τ

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τ

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Bacillus subtilis spores: Antibody Probes

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G(τ

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τ

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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


www.FCSXpert.com

•Product specifications•FCS Classroom

•FCS Tutorials•FCS Applications•Data Analysis Notes•Sample Data•Reference List

•FCS Forum


FCS vs. FRAP vs. FRET

√√√Binding Kinetics

√Complex Stoichiometry

√√Complexing

√Concentration

√Mobile Fraction

√MulticomponentDiffusion

√√Diffusion Rates

FCSFRETFRAPParameter


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

Assaying Single Molecule Molecular Interactions

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