Multiscale Entanglement in Spherically Confined DNA Rings

Abstract

Knots are frequent in biological systems, and particularly in DNA, where they can be a major hindrance for biological functions. In particular it is argued that the presence of tight knots in viral genome can prevent its ejection from the capsid thus stopping the life cycle of the virus.Inspired by those problems we investigate the interplay of geometrical and topological entanglement in knotted DNA rings confined inside a spherical cavity using advanced numerical methods.We show that the complex interplay between the length of the knotted portion of DNA, the contour length of the DNA ring, and the radius of the enclosing sphere can be encompassed by a simple scaling argument based on deflection theory.Furthermore, we show that with increasing confinement the entanglement acquires a multi-scale character which can be rationalised using the same scaling argument.