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FCS in closed systems and application for membrane nanotubes

In the present study, we developed the fluorescence correlation spectroscopy theory for closed systems with either periodic or reflective boundaries. The illumination could be any arbitrary function. We tested our theory with simulated data of both boundary conditions. We also tested the theory with experimental data of membrane nanotubes, whose circular direction is a closed system. The result shows that the correlation function for nanotubes falls between 1D and 2D diffusion model. The fitting with our model gives an accurate recovery of the diffusion time and nanotube radius. We also give some examples of single molecule experiments for which our theory can be potentially useful.