A closed form for fluorescence correlation spectroscopy experiments in submicrometer structures

Fluorescence correlation spectroscopy (FCS) is a powerful technique for measuring low concentrations of fluorescent molecules and their diffusion coefficients in an open detection volume. However, in several practical cases, when FCS measurements are carried out in small compartments like microchannels, neglecting boundary effects could lead to erroneous results. Here, a close form solution is proposed to explicitly account for the presence of walls located at a distance comparable with the characteristic detection volume lengths. We derive a one-dimensional diffusion constrained model and then generalize the solution to the two- and the three-dimensional constrained cases. We further indicate within which limits the standard autocorrelation function (ACF) model gives reliable results in microconfinement. Our model relies just on the assumption of elastic hits at the system walls and succeeds in describing the ACF of fluorescent probes confined along one direction. Through the analysis of FCS experimental data, we are able to predict the correct shape of the ACF in channels of micrometric and submicrometric width and measure the extent of lateral confinement. In addition, it permits the investigation of microstructured material features such as cages and cavities having dimensions on the micrometric range. On the basis of the proposed model, we also show in which conditions confinement could generate an apparent time dependent probe mobility, thus allowing a proper interpretation of the transport process taking place in submicrometric compartments.