Transition State Theory for Dissociation of Dynamic Bonding Networks

Cell adhesion, molecular recognition, biomolecular folding and unfolding, dynamic cross-linking in soft materials, and many other phenomena involve formation or dissociation of multiple chemical bonds. Here, we study the overall time scale required to break or form <i>N</i> bonds. Strictly speaking, this time scale depends on the initial conditions, e.g., the number and which bonds are formed/broken, and its estimation requires kinetic details about forming and breaking of each individual bond influenced by the larger network of other bonds. We show, however, that a simple estimate, analogous to transition-state theory in chemical kinetics, accurately predicts the mean first passage time to form or break all the bonds in terms of single-bond properties and thermodynamic properties of the network. As the thermodynamics of bond networks can often be described by well-studied statistical-mechanical models, such as the Ising model and its extensions, our theory provides a link between the global dynamics and thermodynamics of multibond arrays and networks.