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.