Protein Oligomerization Equilibria and Kinetics Investigated by Fluorescence Correlation Spectroscopy: A Mathematical Treatment

Fluorescence correlation spectroscopy (FCS) is a technique that is increasingly being used to investigate protein oligomerization equilibria and dynamics. Each individual FCS decay is characterized by its amplitude and a characteristic diffusion time, both of which are sensitive to the degree of dissociation of the protein. Here, we provide a mathematical treatment that relates these observables with the parameters of interest: the equilibrium constants of the different protein dissociation steps and their corresponding dissociation and association kinetic rate constants. We focused on the two most common types of protein homooligomers (dimers and tetramers) and on the experimental variables relevant for the design of the experiment (protein concentration, fractional concentration of labeled protein). The analysis of the theoretical expectations for proteins with different dissociation constants is a key aspect of experiment design and data analysis and cannot be performed without a physically accurate treatment of the system. In particular, we show that the analysis of FCS data using some commonly used empirical models may result in a serious misinterpretation of the experimental results.