two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion...
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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.
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