1. Two-Focus Fluorescence Correlation　 Spectroscopy: A New Tool for Accurate and Absolute Diffusion Measurements
Jörg Enderlein et al., ChemPhysChem, 8, 433–443 (2007)
Miyasaka Lab.
Hiroaki YAMAUCHI

2. Contents Introduction ・Background Experimental Method
・Fluorescence Correlation Spectroscopy
Experimental Method
・Experimental Setup
・Analysis
Results and Discussion
Summary

3. Background Translational diffusion of molecules in solution
Stokes-Einstein relation
D : Diffusion coefficient r : Stokes radius kB : Boltzmann’s constant T : Temperature h : viscosity of the medium
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)

4. Fluorescence Correlation Spectroscopy
FCS setup
sample
excitation light
fluorescence
objective
Laser beam
Laser
Detection volume DM
Fluctuation of fluorescence PH
DM : dichroic mirror
PH : pinhole
APD : avalanche photodiode
〈I〉
Intensity
APD
Time

5. Fluorescence Correlation Spectroscopy
Fluctuation of fluorescence
Autocorrelation function
d I(t)
d I(t+t)
d I(tn)
d I(tn+t) t
t+t tn
tn+t
Intensity
Time
G (t) t
<I>
Fitting model
N : average number of molecules
tD : diffusion time
w : wxy / wz
tt : triplet lifetime
p : fraction of dye molecules in triplet state wz
wxy
Diffusion Coefficient

6. Fluorescence Correlation Spectroscopy
In the case that quenching occurs by molecular interaction
kAB A B
Fluorescent
kBA
Non-fluorescent

7. Fluorescence Correlation Spectroscopy
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 wz
wxy
However, the result of measurement is sensitively affected in experimental condition such as refractive index mismatch and excitation intensity

8. Experimental Setup objective lens Pulsed diode laser
linearly polarized
640 nm wavelength
50 ps pulse duration
Both lasers are pulsed alternately with an overall repetition rate of 40 MHz.
(diameter 200mm)
avalanche photodiode

9. Analysis constant Cross-correlation function１ 2
25ns
constant
Laser1
Laser2
G (t) t
G (t) t
G (t) t
Each focus autocorrelation function
Cross-correlation function

10. Analysis Cross-correlation function d Constant offset z y x
g∞(d) : constant offset
U(r) : molecule detection function (MDF)
D : diffusion coefficient
c : concentration of the molecules
e1,2 : two factors describing the overall excitation
power and detection efficiency
　 : unit vector along x
d : lateral shift value x y z d
Constant offset
Ibg : the background intensity

11. Analysis MDF w(z) : width of Gaussian distribution
k(z)/w2(z) : amplitude of Gaussian distribution
lex : excitation wavelength
lem : 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

12. Two-parameter model of the MDF
Fluorescent intensity scan of a fluorescent bead
Distance between adjacent scan planes is 0.5 mm.
Each scan consisted of 200×200 pixels2 of 50×50 nm2 size.
Total excitation power is below 1 mW per focus.
W2(z)
W1(z)
effective radius
W(z)
k(z)
Two-parameter model of the MDF fits amazingly well.

13. Viscosity-Dependent Diffusion
NMR
2fFCS
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.

14. Excitation Intensity Dependence
photobleaching
constant
The diffusion coefficient of 2fFCS is constant up to 40 mW.
The value of w0 increases with increasing excitation intensity.
2fFCS is insensitivity with optical saturation.

15. 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.