Two-Focus Fluorescence Correlation 　Spectroscopy: A New Tool for Accurate andAbsolute Diffusion Measurements

Jörg Enderlein et al., ChemPhysChem, 8, 433–443 (2007)

Miyasaka Lab.

Hiroaki YAMAUCHI

Contents

Introduction・ Background・ Fluorescence Correlation

Spectroscopy

Experimental Method・ Experimental Setup・ Analysis

Results and Discussion

Summary

Background

Translational diffusion of molecules in solution

Stokes-Einstein relation

r

TkD B

6

Any change in Stokes radius will change the associated diffusion coefficient of the molecules.

It is necessary to measure the diffusion coefficient with a high accuracy.(ex. For monitoring conformational changes in proteins)

D : Diffusion coefficient r : Stokes radius kB : Boltzmann’s constant T : Temperature : viscosity of the medium

Fluorescence Correlation Spectroscopy

Laser beam

objective

sample

Detection volume

Inte

nsity

Time

〈 I〉

Fluctuation of fluorescence

APD

Laser

DM : dichroic mirror

PH : pinhole

APD : avalanche photodiode

DM

PH

FCS setup

excitation light

fluorescence

N : average number of molecules

D : diffusion time

w : wxy / wz

t : triplet lifetime

p : fraction of dye molecules in triplet state

Fluorescence Correlation Spectroscopy

Autocorrelation function

T

DD

p

p

NG

exp1

1

111

15.0

2

1Fitting model

2

)()()(

tI

tItIG

G ()

Fluctuation of fluorescence

I(t)I(t+)

I(tn)

I(tn+)

t t+ tn tn+

Inte

nsity

Time

<I>

D

xywD4

2

Diffusion Coefficient

wz

wxy

Fluorescence Correlation Spectroscopy

1

2

121

/

11

1)( 1exp1

BAABK

BAAB

Dz

xy

DK

kk

kkK

w

w

NG K

In the case that quenching occurs by molecular interaction

A B kAB

kBAFluorescent Non-fluorescent

Molecule Detection Function (MDF)Molecule Detection Function (MDF)

Position-dependent probability to excite and detect a fluorescence photon from a molecule at a given position within the sample

standard assumption

three-dimensional Gaussian profile

However, the result of measurement is sensitively affected in experimental condition such as refractive index mismatch and excitation intensity

wz

wxy

2

2

2

22 22exp

zxy w

z

w

yx

Fluorescence Correlation Spectroscopy

D

xywD4

2

Experimental Setup

Pulsed diode laserlinearly polarized640 nm wavelength50 ps pulse duration

Both lasers are pulsed alternately with an overall repetition rate of 40 MHz.

avalanche photodiode

(diameter 200m)

objective lens

AnalysisG

()

G ()

G

()

Each focus autocorrelation function Cross-correlation function

constant

Laser1 Laser2

１ 2 １ 2 １ 2 １ 225ns

Analysis

g∞() : constant offset U(r) : molecule detection function (MDF) D : diffusion coefficient c : concentration of the molecules1,2 : two factors describing the overall excitation power and detection efficiency 　 : unit vector along x : lateral shift value

Cross-correlation function

Ibg : the background intensity

Constant offset xy

z

Analysis

MDF MDF

w(z) : width of Gaussian distribution(z)/w2(z) : amplitude of Gaussian distribution

ex : excitation wavelengthem : center emission wavelength n : refractive index of the immersion medium a : radius of the confocal aperture divided by magnification w0 , R0 : two (generally unknown) model parameters

Two-parameter model of the MDF

Distance between adjacent scan planes is 0.5 m.

Each scan consisted of 200×200 pixels2 of 50×50 nm2 size.

Total excitation power is below 1 W per focus.

Two-parameter model of the MDF fits amazingly well.

(z)W(z)

Fluorescent intensity scan of a fluorescent bead

W1(z)

W2(z)

effective radius

Viscosity-Dependent Diffusion

2fFCS

NMR

Agreement between the diffusion coefficient of NMR and 2fFCS

Increasing refractive mismatch leads to increasing w0 and R0

2fFCS is insensitivity with refractive index mismatch.

Excitation Intensity Dependence

The diffusion coefficient of 2fFCS is constant up to 40 W.

The value of w0 increases with increasing excitation intensity.

2fFCS is insensitivity with optical saturation.

constant

photobleaching

Summary

The authors have proposed a new FCS setup and analytical method for accurate measurement of diffusion coefficients.

They demonstrated that 2fFCS is robust against refractive index changes of the sample medium and optical saturation.

The 2fFCS can be used as an ideal tool to study protein folding/unfolding dynamics thunks to its high accuracy in measurement of diffusion coefficient.