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. This is not the case for DNA, which is constantly topologically re-arranged within the cell nucleus.
Inspired by this, here I propose to study entangled systems of polymers which can selectively alter their topology and architecture in time and may expend energy to do so. I argue that solutions of **topologically active (living) polymers** can display unconventional viscoelastic behaviours and can be conveniently realised using solutions of DNA functionalised by certain families of proteins,
In this talk, I will present my first excursion into this field and present 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.
This is the simplest example of a potentially very broad family of systems in which the material properties of the complex fluid is affected by topological operations performed by energy-consuming proteins on DNA. Beyond the design of unconventional flow behaviour, these systems may shed new light on the workings of certain vitally important classes of proteins.