Statistics of living polymer rings

Living polymers are macromolecules that can undergo several structural changes. In particular they can break and reform on experimental time scales. A striking example of living polymer is an ensemble of DNA fragments in presence of site-specific recombinase, i.e. enzymes such as integrase and gyrase that, by binding at specific DNA sites can separate and re-join the DNA in different manners. Site-specific recombinease are naturally present, for example, during viral infection when the viral genome has to be integrated into the DNA of the hosting cell. This process is also used in synthetic biology to assemble DNA parts into devices and to modify these devices, once made, get new biological function. In this thesis we will study the statistics of a simple coarse-grained model of living polymer rings in equilibrium with the solvent. First we focurs our attention on the effect of volume confinment on the polymer rings. Then, In the ensemble considered, the rings will be allowed to assemble and disassemble and the student will look, both numerically and analytically, at the equilibrium distribution of the number of rings with a given contour length as a function either of the monomer density or on the rate constants of breakage and recombination processes.