  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, mechano-sensing 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 2-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 P-selectin
and antigen extraction to illustrate how these singularities provide an
intuitive framework for explaining known behaviors and predicting new
behaviors.
