Analytic Solution to the Autocorrelation Function for Lateral Diffusion and Rare Strong Adsorption

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Abstract
An analytic expression is derived to describe the autocorrelation function for fluorophors interacting with heterogeneous chemical interfaces, where both lateral diffusion and reversible strong adsorption occur. The expression is accurate when the rate of strong adsorption is low compared to the rates of both diffusion and desorption, enabling analysis by nonlinear regression. Simulations of single molecules are employed to investigate the applicability of the analytic equation for interpretation of chemical equilibrium and kinetics of single fluorescent molecules undergoing both lateral diffusion and varying amounts of specific adsorption at chemical interfaces. The simulations show that the analytic equation accurately describes the autocorrelation decay, and the equation begins to deviate, as expected, when the adsorption rate becomes large. The results show that a smaller beam size enhances the ability to extract sorption kinetics from the autocorrelation decay, and that a larger beam size enhances the ability to obtain information about the diffusion coefficient with minimal interference from sorption processes. The expression provides a tool for choosing between fluorescence correlation spectroscopy and single-molecule sorting in studies of heterogeneous surfaces.