Multiscale rheology and dynamics of topologically-active DNA solutions and composites*

Topologically-novel polymers, such as rings with no free ends, give rise to complex scale-dependent rheological properties in entangled polymer solutions blends and composites. At the same time, non-equilibrium biopolymer networks, which undergo bulk rheological changes driven by macromolecular restructuring, are the topic of intense investigation. Yet, how macromolecular dynamics give rise to bulk viscoelasticity in such complex polymeric systems, and how local stresses are propagated and distributed across scales, are long-standing open questions. Here we present the design and rheological characterization of solutions of ring and linear DNA, as well as their composites with dextran crowders and stiff microtubules, that are pushed out of equilibrium by enzymatically-driven topological conversion of DNA. We use a robust characterization platform to elucidate the time-varying polymer dynamics and rheological properties of our engineered 'topologically-active' complex fluids across orders of spatiotemporal scales - from single polymers to the bulk over milliseconds to hours. Specifically, we couple particle-tracking and differential dynamic microscopy with optical tweezers microrheology and bulk rheology to reveal key discoveries including: viscous thickening and gated thinning of circular DNA solutions undergoing linearization and fragmentation; discrete state-switching of bulk rheological properties of topologically-active DNA-dextran composites; and emergent nonlinear stress responses of DNA-microtubule composites in which affine alignment, superdiffusivity, and elastic memory are maximized when the strain rate is resonant with the entanglement rate.