Runaway transition in irreversible polymer condensation with cyclization

The process of polymer condensation, i.e., the formation of bonds between reactive end groups, is ubiquitous in both industry and biology. Here we study generic systems undergoing polymer condensation in competition with cyclization. Using a generalized Smoluchowski theory, molecular dynamics simulations and experiments with DNA and ATP-consuming T4 ligase, we find that this system displays a transition, from a ring-dominated regime with finite-length chains at infinite time to a linear-polymers-dominated one with chains that keep growing in time. Finally, we show that fluids prepared close to the transition may have widely different compositions and rheology at large condensation times.