Supercoiled knotted DNA: theory and simulations

Only recently have experimentalists been able to detect and measure the incidence of various types of knots in eukaryotic DNA, and specifically in yeast minichromosomes. Both the abundance and the complexity of these knots have a precise dependence on intrinsic properties of the DNA (such as its length) as well as on extrinsic ones, such as the degree of supercoiling that can be introduced by tighty-regulated molecular machines, or enzymes. Interestingly, it has also been shown that the same supercoiling level affects to varying degrees the electrophoretic migration velocity of two chiral enantiomers of the same knot species. The aim of this thesis is to use coarse-grained structural models and simulations to advance our understanding of how knotting and supercoiling affect the properties of yeast minichromosomes. In particular, we developed a minimalistic coarse-grained model of circular DNA filament as an elastic rod, and set up Monte Carlo simulations to sample the configurational space populated at canonical equilibrium. We considered both knotted and unknotted filaments, with and without supercoiling, or nicked. For each combination of topological (knotting) or geometrical (supercoiling, nicking) entanglement, we systematiclly profiled various observables, such as the gyration radius, asphericity, anisotropy, twist and writhe and used them to clarify the extent to which minimalistic physical models can account for the recent experimental measurements, and illuminate their interpretation.