Fluorescence Correlation & Image Correlation Fluorescence Correlation & Image Correlation MethodsMethods

Paul Wiseman

Department of Physics

Department of Chemistry

McGill University

Montreal, Canada

Overview for TutorialOverview for Tutorial

Optical Microscopy Dynamics vs. Resolution

Fluorescence Correlation Spectroscopy (FCS)

Image Correlation Spectroscopy (ICS)

Image Cross-Correlation Spectroscopy (ICCS)

Spatio-Temporal Image Correlation Spectroscopy

Reciprocal Space Image Correlation Spectroscopy

Optical ResolutionOptical Resolution

-10 -5 5 10

-0.4

-0.2

0.2

0.4

0.6

0.8

1J0() or J0()2

Bessel Function of Order zero and its Square

-20 -10 10 20

-0.6

-0.4

-0.2

0.2

0.4

0.6

J1() or J1()2

Bessel Function of Order one and its Square

)"(Jinc"

J I I 2

2

1o

-20 -10 0 10 20

-20

-10

0

10

20

q1

light ofh wavelengt

length focal lens f

Diameter Aperture D

D

f 1.22 q

First Zero to

1

Radius

-20-10

010

20

-20

-10 0

10 20

3D PSF

z

Airy Disk in Focal Plane(cross section of PSF)

Rayleigh Resolution Criterion Circular ApertureRayleigh Resolution Criterion Circular Aperture

Obj.Lens d

Ultimate Goal of MicroscopyResolve to closely separate Point sources from the object planeWithin the image plane

Object Point~ (x) Image~ {J1(x)/x}2

RayleighResolutionCriterionq1~1.22 f/(D)

D

Angular D

1.22

Spatial D

f 1.22 L

Min

Min

Diffraction Limited Optical Resolution…Diffraction Limited Optical Resolution…

Optical Resolution ~ /2

Macromolecules ~ /50

-1 -0.5 0 0.5 1

-4

-2

0

2

4

Gaussian Beam Focus

~ 500 nm

Truly Interacting SpeciesDance Partners Versus Simply

“Colocalized”

Optical MicroscopyDynamics at the Price of Spatial Resolution

Goal: Measure the Biomolecular DanceGoal: Measure the Biomolecular Dance

Paxillin-dsRed (red) & -actinin GFP (green)in CHO CellTIRF Microscopy Total time = 50 min t =15 s

170 m

Optical Microscopy

Dynamics…At the price of Limited Spatial Resolution

Fluorescence MicrscopySpecificity

Low Detection Limits (singleMolecule)

Fluctuation Magnitudes & Fluctuation TimesFluctuation Magnitudes & Fluctuation Times

Elson and Magde ; Magde, et al. Biopolymers (1974) 13, 1-27 ; 29-61

Obj.Lens

Fluorescence Correlation Spectroscopy (FCS)

-1 -0.5 0 0.5 1

-4

-2

0

2

4

Fig. 1 Overview of Fluctuation Spectroscopy

<i>

i(t)=i(t) –<i>

Intensity Fluctuations Laser Focus ~ 1 um3

Fluorophores excited in focus

Molecular Dynamics

Number in the Focus fluctuates

i(t)

f

i i(t)

t

Fluctuation Magnitudes & Fluctuation TimesFluctuation Magnitudes & Fluctuation Times

t

i(t)

<i>=26.36

i(t) = i(t) - <i>Fluctuation Magnitude

f = Characteristic Fluctuation Time

FCS: Fluctuations & DynamicsFCS: Fluctuations & Dynamics

Focal Volume 1 m3

Fast DynamicsShort f

FCS: Fluctuations & DynamicsFCS: Fluctuations & Dynamics

Focal Volume 1 m3

Slow DynamicsLong f

FCS InstrumentationFCS Instrumentation

LaserM1

M2BE

Sample

Dichroic

Pinhole

Mirror

Filters

APD AMP

SignalAutocorrelator

PhotonDetector

Computer

TemporalACF

Correlation Function Decay Model: 2DCorrelation Function Decay Model: 2D

N. L. Thompson; Topics in Fluorescence Spectroscopy (1991) 1, 337-378

N α

M N α M g(0) τg 2R

1iii

R

1iii

2iR

1ii

For 2D System; Laser TEM00 Modei= Qi/Q1 Ratio of Fluorescent Yields

Correlation Function Amplitude: g(0)Number Density <N> per Beam AreaAggregation State

2R

1iii

R

1ii

2i

N α

N α 0g

Correlation Function Decay: Mi

Fluctuation Relaxation TermsTransport and Kinetics Properties

R

1iiM τg

Sum over all fluorescent species

PMT 3

TiSapph. laser

+L1 pinhole+L2

PMT 2 PMT 1Sample

M4

M1

M2 M3

Dichroic mirror

Filter

Dichroic mirrors

100fs, 780-920nm pulse 82MHz rep-rate

Em. Filters

Image Correlation SpectroscopyImage Correlation Spectroscopy

t=0 t=1 t=2 t=3 t=4

TIRF Microscopy ~ 100 nm z depth of fieldTIRF Microscopy ~ 100 nm z depth of field

Laser

Laser BeamFluorescence

NA 1.45Obj. Lens

Sample

CCD Camera

Dichroic &Em. Filter

ND Filters

Slow or Static Distributions?Slow or Static Distributions?

Receptor Occupation Number Varies across the Membrane

Intensity Fluctuations Laser Beam Rasters across Sample

<(i)2>/<i> 2 = 1/<N> Mean Number of “Independent” Clusters per Beam Area

A

Confocal Image

Spatial Image Correlation SpectroscopySpatial Image Correlation Spectroscopy

Petersen et al. Biophys. J. 65, 1135-1146 (1993); Wiseman and Petersen, Biophys. J. 76, 963-977 (1999)

211

i

y ,x δi ηy , ξxδi ηξ,r

N

1

i

y ,x δi 0,0r 2

2

11

Spatial AC Function WhiteNoise

i - t)y,i(x, ty,x,i

Spatial Autocorrelation Function (ACF)Spatial Autocorrelation Function (ACF)

Image i(x,y)

CorrelateImageWithItself

} lag variable pixel shift in y

}

lag variable pixel shift in x

Spatial ACFr11(,)

Correlation FunctionMathematical CorrelationOf Image with Itself

Spatial Autocorrelation Function (ACF)Spatial Autocorrelation Function (ACF)

Image i(x,y)

FFT

Inve

rse

FFT

Norm

aliza

tion

F {i(x,y)}

F {i(x,y)}*

*

Power Spectrum

F {i(x,y)}

Spatial ACFr11(,)

complexconjugate

multiplication

A

Confocal Image

Spatial Image Correlation SpectroscopySpatial Image Correlation Spectroscopy

Petersen et al. Biophys. J. 65, 1135-1146 (1993); Wiseman and Petersen, Biophys. J. 76, 963-977 (1999)

211

i

y ,x δi ηy , ξxδi ηξ,r

N

1

i

y ,x δi 0,0r 2

2

11

Spatial AC Function WhiteNoise

i - t)y,i(x, ty,x,i

Nonlinear Least Squares FittingNonlinear Least Squares Fitting

B

ω

η ξ-exp (0,0)g ηξ,g

2o

22

1111

GaussianFitting Function

N

1 0,0g11

GaussianFitting Function

<N> Independent Fluorescent Entities; Aggregation

Image Correlation Spectroscopy (ICS)Image Correlation Spectroscopy (ICS)

Temporal ACF

t t

11 i i

) t ,y i(x, t)y, i(x, ,0 ,0r

Srivastava and Petersen Methods Cell Sci. 18, 47-54 (1996)

t=0

t=1

t=2

t=3

t=n

Temporal Autocorrelationof i(x,y,t) = i(x,y,t) - <i>Through Time Series

DecayTransportDynamics

Diffusion Coeff.&

Flow Speeds

OffsetImmobilePopulation

Temporal ICSTemporal ICS

t t

11 i i

) t ,y i(x, t)y, i(x, ,0 ,0r

Time Lag = 0

t=0

t=1

t=2

t=3

t=n

t=4

= 0

Time Lag = 1

= 1

Time Lag = 2

= 2

Time Lag = 3

= 3

Time Lag = 4

= 4

Time Lag = n

= n

How to Calculate Normalized Fluctuation Autocorrelation Function

3D Diffusion Model3D Diffusion Model

0.2 m blue fluorescent spheres in sucrose/water solutions Temperature 21C, 0% sucrose, 2P Microscopy 30f/s

5 m

Wiseman et al. J. Microscopy 200, 14-25 (2000)