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

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

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)

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

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

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

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

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

Analysis constant Cross-correlation function １ 2 25ns constant Laser1 Laser2 G (t) t G (t) t G (t) t Each focus autocorrelation function Cross-correlation function

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

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

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.

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.

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.

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.