Polymer physics principles are increasingly acknowledged and applied to understand the behaviour of genome organisation and biopolymers in vivo. In spite of this they heavily rely on the assumption that polymers do not change topology (or architecture) in time, i.e. if they start as a linear chain of segments or a circular one, they remain so. This is not the case for DNA, which is constantly topologically re-arranged within the cell nucleus. In fact, Topoisomerase, SMC and other protein complexes are vital for the cell's health.

Inspired by this here I propose a twist to classic polymer science: investigating systems of polymers which can selectively alter their topology and architecture in time and may expend energy to do so. Solutions of topologically active (living) polymers display unconventional viscoelastic behaviours and can be conveniently realised using solutions of DNA functionalised by certain families of proteins.

In this talk I will give an overview of my interests to date and then present my first excursion into the field of topologically active polymers and some recent results on the microrheology of entangled DNA undergoing digestion by restriction enzymes.

I will present theories, simulations and experiments using particle tracking microrheology showing that we can harness this non-equilibrium process to yield time-varying viscoelastic behaviours that may find application in controlled drug delivery.