Fluorescence Correlation Spectroscopy and Photon Counting Histograms in Finite, Bounded Domains.

Analysis of fluctuations arising as fluorescent particles pass through a focused laser beam has enabled quantitative characterization of a broad range of molecular kinetic processes. Two key mathematical frameworks that have enabled these quantifications are fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis. Although these frameworks are effective and accurate when the focused laser beam is well approximated by an infinite Gaussian beam with a waist that is small compared to the size of the region over which the fluorescent particles can diffuse, they cannot be applied to situations in which this region is bounded at the nanoscale. We therefore derived general forms of the FCS and PCH frameworks for bounded systems. The finite-domain form of FCS differs from the classical form in its boundary and initial conditions and requires development of a new Fourier space solution for fitting data. Our finite-domain FCS predicts simulated data accurately and reduces to a previous model for the special case when the system is much larger than the Gaussian beam and can be considered to be infinite. We also derived the PCH form for the bounded systems. Our approach enables estimation of the concentration of diffusing fluorophores within a finite domain for the first time, to our knowledge. The method opens the possibility of quantification of kinetics in several systems for which this has never been possible.