Fluorescence Workshop UMN PhysicsJune 8-10, 2006

Fluorescence Microscopy and Fluorescence Correlation Spectroscopy

Joachim Mueller

Fluorescence Microscopy

Use a microscope as a fluorometer

Advantages:

• superb optics• very high collection efficiency• imaging• allows single cell measurements• single molecule experiments

The microscope as a filter fluorometerwith focusing optics

Basic design of a fluorescent microscope

objective

red fluorescence

Filters

Selecting Filters

Anatomy of a Fluorescence Microscope

Widefield-fluorescence microscope image

Widefield fluorescence image of a 16 micron thick section of fluorescently-labeled mouse kidney. Copyright, J. Waters, 2004

Principle of Confocal MicroscopyPinhole only passes light that emanates from a thin section of the sample (indicated in red)

z

Note confocal microscopy only observes a point (a tiny subvolume to be more precise)

Laser Scanning Confocal Microscopy (LSCM):

Observed volume

Need to perform a raster scan to build up an image point by point

Two electronically driven scan mirrors move the laser spot on the sample in a raster-like fashion.

Widefield Image Confocal Image

The same specimen show on the left, taken with a confocal microscope.

Widefield fluorescence image of a 16 micron thick section of fluorescently-labeled mouse kidney.

Copyright, J. Waters, 2004

Photobleaching

The average number of excitation and emission cycles that occur for a particular fluorophore before photobleaching is dependent upon the molecular structure and the local environment. Some fluorophores bleach quickly after emitting only a few photons, while others that are more robust can undergo thousands or millions of cycles before bleaching.

Photobleaching

original image Photobleached image

6 s5 s4 s3 s2 s1 s0 s

Two-Photon Microscopy: Principle

Now consider two-photon absorption

Energy Diagram:

Fluorescence~10-9 s

Absorption~10-15 s

S0

S1

Internal Conversion~10-12 s

Radiation-less Decay

<10-9 s

Two-photon absorption is an optical nonlinear process

Two-Photon Fluorescence Simultaneous absorption of two-photons is a rare process:

Maximize two-photon effect by increasing the photon flux- spatially by focusing the light- temporally (ultrafast laser pulses)

objective

One photonbeam

two photonspot(volume: 1 fl)

Inherent 3 - dimensional optical sectioning effect!

Two-photon spectroscopy

two-photonOne-photon

2γ1γemission

wavelength

Inte

nsit

y

Two-photon absorption is spectrally well separated from the fluorescence! Note that Raman of the solvent will not occur within the fluorescence emission spectrum.

Two-photon Instrumentation

Steeringmirror

Sample

Objective

Dichroic Mirror

Short Pass Filter

Photon CountingAcquisition Card

Ti-S

apph

ire

lase

r

Data Analysis

Beam Expander

APD

Two-photon Imaging

Purkinje neurone in a living brain slice filled with fluorescein dextran imaged with two-photon excitation laser scanning microscopy (Svoboda, Cold spring Harbor Laboratories)

Two-photon image resolution is essentially the same as that of confocal microscopy. However, imaging in the presence of significant scatter (such as in thick tissue) requires two-photon excitation.

Also note that photobleaching in two-photon microscopy is strictly restricted to the excitation volume!

Denk, Nature Methods 2, 932 - 940 (2005)

Fluorescence Fluctuation SpectroscopyQ: How many fluorescent molecules are (on average) in the two-photon (or confocal) volume of the microscope?

A: That depends on the concentration. At a high concentration there are more molecules in the volume than at low concentrations.

Q: Ok, many proteins in cells have nanomolar concentrations. How many proteins ( assuming c = 1 nM ) are now in the volume?

A: Let me calculate … (Volume is 1 femtoliter, Avogadro’s number is 6x1023, c = 1 nM). The number I get is a single molecule per observation volume. Well that’s ok, fluorescence is very sensitive and can detect single molecules.

Q: Proteins in a solution (and in a cell) are typically mobile. They diffuse around. What will happen if the single molecule moves around? Also a single molecule is in the volume on average. Is there a chance that sometimes there will be two or no molecules in the volume?

A: Yes, the number of molecules will fluctuate as they diffuse in and out of the observation volume. Because two molecules produce more fluorescence than a single molecule there will be fluctuations in the fluorescence intensity.

Fluorescence Fluctuation Spectroscopy

objectiveCoverslip

F

Fluorescence intensity::

time

fluctuation

Raw data: : Photon Counts

Statistical Analysis of the Fluctuations required

0

10

20

30

40

50

0 20 40 60 80 100Time

Cou

nts

Photon counts

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.01 0.10 1.00 10.00 100.00

Time (ms)

Auto

Cor

rela

tion Fit

Data

Fluorescence Correlation Spectroscopy (FCS)

1

10

100

1000

10000

100000

1000000

0 5 10 15

Counts per Bin

Num

ber o

f Occ

uran

ces

Photon Counting Histogram (PCH)

Parameters: G(0) & kkinetics

PCH Parameters: <N> & ε

Autocorrelation

2

( ) ( )( )

dF t dF tG

Fτ

τ⋅ +

=

Autocorrelation Function:

Calculating the Autocorrelation Function

time

Average Fluorescence

F

Fluorescence Fluctuation

( ) ( )dF t F t F= −

F(t)in photon counts

τ

t + τt

2

( ) ( )( )

dF t dF tG

Fτ

τ⋅ +

=

The Autocorrelation Function

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)

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(0) ∝ 1/Nas time t

approaches 0Diffusion

2

( ) ( )( )

dF t dF tG

Fτ

τ+

=

The Effects of Particle Concentration on theAutocorrelation Curve

<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)<N> = 4

What about the excitation (or observation) volume shape?

Correlation function of diffusing molecules

For a 3-dimensional Gaussian excitation volume:

11 2

2 20 0

1 1 8 8( ) 1 18

D DGN w z

τ ττ−−

= + +

1-photon equation

contains a 4, instead of 8

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

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)

Stokes-Einstein Equation:

D =k ⋅T

6 ⋅π ⋅ η ⋅ rand

Monomer --> Dimer Only a change in D by a factor of 21/3, or 1.26

3rVolumeMW ∝∝

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.

Statistical Analysis: Brightness

Brightness ε is the average fluorescence intensity of a single particle

Illustration:

time

Sample Fluorescence Brightness

εEGFP F

Protein

Brightness Encodes Stoichiometry Sample Fluorescence Brightness

time

time

2ε

Protein

EGFPF ε

N1

F

N2

time

2ε

N2N1

ε+ F

Photon Counting Histogram (PCH)Aim: To resolve species from differences in their molecular brightness

Molecular brightness ε : The average photon count rate of a single fluorophore

where p(k) is the probability of observing k photon counts

PCH: probability distribution function p(k)

16000cpsmN 0.3ε =

=

Single Species:

p(k) = PCH(ε, N )

Note: PCH is Non-Poissonian!

Sources of Non-Poissonian Noise• Detector Noise• Diffusing Particles in an Inhomogeneous Excitation Beam*• Particle Number Fluctuations*• Multiple Species*

PCH in cells: Brightness of EGFP

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

Chen Y, Mueller JD, Ruan Q, Gratton E (2002) Biophysical Journal, 82, 133 .

Brightness and Stoichiometry

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

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

The End