Braiding transitions and plectonemic structures in multiple-stranded chains manipulated by magnetic tweezers

Thanks to the recent advance in micromanipulation techniques based for instance on optical and magnetic tweezers, it is nowadays possible to probe the mechanical response and the configurational transitions of soft structures made by multiple linear polymers, such as ds-DNA filaments, that wrap one to another in a braided fashion. In particular, by using magnetic tweezers one can look at the braided/plectonemic (or buckling) transition of these structures as a function of the extensional force and torsion injected on the system. Recent theoretical and experimental studies have focused on structures made by only two filaments. The aim of this thesis is to extend these investigations to the case of multiple (i.e. more then two) strands where the reciprocal position of the rooted monomers at the tweezeers' plates and the detection of plectonemic structures are interesting novel issues to be explored. Geometric quenches between three-stranded and two-stranded configurations are also explored by introducing a cut along the additional third strand and simulating the system relaxing to equilibrium. The analytical approach is based on the elastic rod model of a chain with bend and twist rigidities, while numerical simulation are performed on a coarse-grained model of three stranded chains whose stochastic dynamics is integrated using LAMMPS code. The study of such new configurations highlights the presence of a buckling transition similar to the one found with two strands, in which the coexistence of plectonemic and non formations is more pronounced than what previously observed. For such phase transition the geometric properties of the system influence directly the critical points positioning.