Regulation of topological entanglement in ring polymers
Entanglement abundance and complexity can be both beneficial and detrimental to the biological and mechanical function of polymers. In living organisms, for instance, DNA entanglement is so impactful that its proliferation might have catastrophic consequences, such as mutation and death. Even though entanglement regulation is therefore necessary to keep the behaviour of both biological and synthetic polymer systems under control, how it is practically achieved is currently not well understood for many systems. To fill this void, by formulating analytic predictions and performing computer simulations, we study the equilibrium properties of sets of geometrically and topologically constrained ring polymers, and model how entanglement abundance and complexity is regulated in both biological and synthetic polymer systems. We find that a complex of rings undergoing recombination under confinement is distinguished by the presence of a topological gelation transition, which can be controlled by the stiffness or the concentration of the rings. Furthermore, we show that an efficient and controlled way to resolve entanglement by transient cross stranding is having it compete entropically with a slip-linked polymer network. Finally, we study multicomponent polymer links where the monomers can be distributed among the components in all possible ways, and show that, asymptotically, due to entropy maximisation, one of the rings grows at the expense of the others, which behave as roots sliding along the contour of the growing component.