Fluorescence correlation spectroscopy (FCS) allows one to measure diffusive properties of fluorescent molecules, and is closely related to FRAP. Instead of measuring time-dependent concentration profiles and modeling the kinetics as continuum diffusion, FCS follows the steady state fluctuations in number density of a very dilute fluorescent probe molecule in the small volume observed in a confocal microscope. We measure the fluctuating changes in fluorescence intensity emitted from probe molecules as they diffuse into and out of the focal volume. Average concentration of sample: C 0 = <10 –9 M – 10 –7 M. This corresponds to an average of ~0.1-100 molecules in the focal volume, although this number varies with diffusion into and out of the volume. The fluctuating fluorescence trajectory is proportional to the time-dependent number density or concentration: \[ F(t) \propto C(t) \nonumber \] How big are the fluctuations? For a Gaussian random process, we expect \(\dfrac{\delta N_{rms}}{N} \sim \dfrac{1}{\sqrt{N}} \) The observed concentration at any point in time can be expressed as time-dependent fluctuations about an average value: \(C(t) = \overline{C} + \delta C(t)\). To describe the experimental observable, we model the time-dependence of δC(t) from the diffusion equation: \[ \dfrac{\partial \delta C}{\partial t} = D \nabla^2 \delta C \nonumber \] \[ \langle \delta C(r,0) \delta C(r',t) \rangle = \dfrac{C_0}{(4\pi Dt)^{3/2}} e^{-(r-r')^2/4Dt} \nonumber \] The concentration fluctuations can be related to the fluorescence intensity fluctuations as \[ F(t) = AW(r) C(r,t) \nonumber \] W(r): Spatial optical profile of excitation and detection A: Other experimental excitation and detection parameters Calculate FCS correlation function for fluorescence intensity fluctuations. \(F(t) = \langle F \rangle -\delta F(t) \) \[ G(t) = \dfrac{\langle \delta F(0) \delta F(t) \rangle}{\langle \delta F \rangle^2} \nonumber \] For the case of a Gaussian beam with a waist size w 0 : \[ G(t) \sim \dfrac{B}{1+t/\tau_{FCS}} \nonumber \] Where the amplitude is \(B = 4\pi A^2I_0^2\overline{\delta C^2_0} w_0^2\), and the correlation time is related to the diffusion constant by: \[ \tau_{FCS} = \dfrac{w_0^2}{4D} \nonumber \] ___________________________________ Readings P. Schwille and E. Haustein, "Fluorescence Correlation Spectroscopy: An Introduction to its Concepts and Applications" in Biophysics Textbook Online.