On the interpretation of kinetics and thermodynamics probed by single-molecule experiments

Single-molecule pulling experiments are widely used to extract both thermodynamic and kinetic data on ligand-receptor pairs, typically by fitting different models to the probability distribution of rupture forces of the corresponding bond. Here, a theoretical model is presented that shows how a measurement of the number of binding and unbinding events as a function of the observation time can also give access to both the binding (k_on) and the unbinding (k_off) rates of bonds, which combined provide a well-defined bond free-energy ΔG^bond. The connection between ΔG^bond and the ligand-receptor binding constant measured by typical binding essays is critically discussed. The role played by the molecular construct used to tether ligands and receptors to a surface is considered, highlighting the various approximations necessary to derive general expressions that connect its structure to its contribution, termed ΔG^cnf, to the bond free-energy. In this way, the validity and the assumptions underpinning widely employed formulas and experimental protocols used to extract binding constants from single-molecule experiments are assessed. Finally, the role of ΔG^cnf in processes mediated by ligand-receptor binding is briefly considered, and an experiment to unambiguously measure this quantity proposed.