Statics and dynamics of DNA knotting

Source abstract

Abstract Knots and entanglement in polymers and biopolymers such as DNA and proteins constitute a timely topic that spans various scientific disciplines ranging from physics to chemistry, biology and mathematics. Although in the past many advancements have been made in understanding the equilibrium knotting probability and knot complexity of long polymer chains in solutions, many questions have been addressed in recent years by both experimental and theoretical means—for instance, how the knotting probability depends on the quality of the solvent, the elastic properties of the molecule and its degree of confinement. How knots form, evolve and eventually disappear in a fluctuating chain. Are the equilibrium and non-equilibrium properties of knotted molecules affected by the knot swelling/shrinking dynamics? Moreover, thanks to the great advance in nanotechnology and micromanipulation techniques, nowadays knots can be ‘manually’ tied in a single DNA molecule, followed during their motion along the chains, forced to pass through nanopores, or stretched by external forces or elongational flows. All these experimental approaches allow access to new information on the interplay of topology and polymer physics, and this has opened new perspectives in the field. Here, we provide an overview of the current knowledge of this topic, stressing the main results obtained, including the recent developments in experimental and computational approaches. Since almost all experiments on knotting involve DNA, the review will be mainly focused on the topological properties of this fascinating and biologically relevant molecule.