The adherens junctions between epithelial cells involve a protein complex formed by E-cadherin, xcexb2-catenin, xcexb1-catenin and F-actin. The stability of this complex was a puzzle for many years, since in vitro studies could reconstitute various stable subsets of the individual proteins, but never the entirety. The missing ingredient turned out to be mechanical tension: a recent experiment that applied physiological forces to the complex with an optical tweezer dramatically increased its lifetime, a phenomenon known as catch bonding. However, in the absence of a crystal structure for the full complex, the microscopic details of the catch bond mechanism remain mysterious. Building on structural clues that point to xcexb1-catenin as the force transducer, we present a quantitative theoretical model for how the catch bond arises, fully accounting for the experimental lifetime distributions. The underlying hypothesis is that force induces a rotational transition between two conformations of xcexb1-catenin, overcoming a significant energy barrier due to a network of salt bridges. This transition allosterically regulates the energies at the interface between xcexb1-catenin and F-actin. The model allows us to predict these energetic changes, as well as highlighting the importance of the salt bridge rotational barrier. By stabilizing one of the xcexb1-catenin states, this barrier could play a role in how the complex responds to additional in vivo binding partners like vinculin. Since significant conformational energy barriers are a common feature of other adhesion systems that exhibit catch bonds, our model can be adapted into a general theoretical framework for integrating structure and function in a variety of force-regulated protein complexes.