Quantitative characterisation of membrane-protein reversible association using FCS.

Functionally meaningful reversible protein-membrane interactions mediate many biological events. Fluorescence Correlation Spectroscopy (FCS) is increasingly used to quantitatively study the non-reversible binding of proteins to membranes using lipid vesicles in solution. However, the lack of a complete description of the protein-membrane phase and statistical equilibria in the case of reversible protein-membrane partitioning has hampered the application of FCS to quantify the partition coefficient (K). In this work we further extend the theory that describes non-reversible partitioning to account for spontaneous protein-membrane dissociation and reassociation to the same or a different lipid vesicle. We derive the probability distribution of proteins on lipid vesicles for reversible binding and demonstrate that FCS is a suitable technique for accurate K quantification of membrane-protein reversible association. We also establish the limits to K determination by FCS studying the Cramer-Rao bound on the variance of the retrieved parameters. We validate the mathematical formulation against reaction-diffusion simulations to study phase and statistical equilibria and compare the K obtained from a computational FCS titration experiment to the experimental ground truth. Finally, we demonstrate the application of our methodology studying the association of anti-HIV broadly neutralizing antibody (10E8-3R) to the membrane.