Concurrent Rupture of Two Molecular Bonds in Series: Implications for Dynamic Force Spectroscopy

Abstract

The immobilization of receptor–ligand molecules in dynamic force spectroscopy (DFS) often relies on an extra noncovalent linkage to solid surfaces, resulting in two barrier-crossing diffusion processes in series and concurrent bond dissociations. One outstanding theoretical issue is whether the linkage between the immobilizer and biomolecule is sufficiently strong during repeated force ramping in the measurements and how it might influence the interpretation on receptor–ligand kinetics. Following the classical framework by Kramers, we regard each dissociation process as a flux of probabilistic bond configuration outward over an energy barrier in the coordinated energy landscape, and solve the two coupled boundary value problems in the form of Smoluchowski equation. Strong kinetic and mechanical coupling is observed between the two molecular bonds in series, with the results showing that involving a noncovalent linkage in DFS can obscure the unbinding characteristics of the receptor–ligand bond. Our approach provides a quantitative assessment to the hidden effects of having a fragile molecular anchorage in DFS and allows the corrected interpretation on receptor–ligand dissociation kinetics in the case.