Analytical Form of the Fluorescence Correlation Spectroscopy Autocorrelation Function in Chemically Reactive Systems

Fluorescence correlation spectroscopy (FCS) applied to chemically reactive systems provides information about chemical reaction equilibrium constants and diffusion coefficients of reactants. These physical quantities are determined from the FCS-measured autocorrelation function, G(t), as a function of time, t. In most of the studied cases, the analytical form of G(t) is well-known for reactions that are much faster than the diffusion time of reactants across the focal volume probed by FCS or when they are much slower than the diffusion time. Here, we develop an analytical form of G(t) for reactions occurring at an intermediate time scale comparable to the diffusion time. G(t) depends on the reaction rates in such reactions. We focus on reversibly binding a fluorescently labeled small molecule to a macromolecule in a diluted solution in thermodynamic equilibrium. Our approach allows the analysis of FCS data over a wide range of diffusion coefficients, reaction rate constants, and brightness levels of fluorescent labels. Our G(t) is valid even when the fluorescent label changes its brightness upon binding. The easy-to-implement analytical form of the autocorrelation function greatly helps experimentalists study chemical reactions, determining the equilibrium constants of reactions and the reaction rates.