Nanoscopic Approach to Quantification of Equilibrium and Rate Constants of Complex Formation at Single-Molecule Level

Equilibrium and rate constants are key descriptors of complex-formation processes in a variety of chemical and biological reactions. However, these parameters are difficult to quantify, especially in the locally confined, heterogeneous, and dynamically changing living matter. Herein, we address this challenge by combining stimulated emission depletion (STED) nanoscopy with fluorescence correlation spectroscopy (FCS). STED reduces the length-scale of observation to tens of nanometres (2D)/attoliters (3D) and the time-scale to microseconds, with direct, gradual control. This allows one to distinguish diffusional and binding processes of complex-formation, even at reaction rates higher by an order of magnitude than in confocal FCS. We provide analytical autocorrelation formulas for probes undergoing diffusion-reaction processes under STED condition. We support the theoretical analysis of experimental STED-FCS data on a model system of dye-micelle, where we retrieve the equilibrium and rates constants. Our work paves a promising way toward quantitative characterization of molecular interactions in vivo.