Simplifying topological entanglements by entropic competition of slip-links

Topological entanglements are abundant, and often detrimental, in polymeric systems in biology and materials science. Here we theoretically investigate the topological simplification of knots by diffusing slip-links (SLs), which may represent biological or synthetic molecules, such as proteins on the genome or cyclodextrines in slide-ring gels. We find that SLs entropically compete with knots and can localise them, greatly facilitating their downstream simplification by transient strand-crossing. We further show that the efficiency of knot localisation strongly depends on the topology of the SL network and, informed by our findings, discuss potential strategies to control the topology of biological and synthetic materials.