Catch-slip bonding, pathway switching, and singularities in the flow of molecular deformation

The proteins involved in cells' mechanobiological processes have evolved specialized and surprising responses to applied forces. Biochemical transformations that show catch-to-slip switching and force-induced pathway switching serve important functions in cell adhesion, mechanosensing and signaling, and protein folding. We show that these switching behaviors are generated by singularities in the flow field that describes force-induced deformation of bound and transition states. These singularities allow for a complete characterization of switching mechanisms in two-dimensional (2D) free energy landscapes, and provide a path toward elucidating novel forms of switching in higher dimensional models. Remarkably, the singularity that generates a catch-slip switch occurs in almost every 2D free energy landscape, implying that almost any bond admitting a 2D model will exhibit catch-slip behavior under appropriate force. We apply our analysis to models of selectin-ligand catch bonds and antigen extraction to illustrate how these singularities provide an intuitive framework for explaining known behaviors and predicting new behaviors.