Biopolymers' dynamics and elasticity: investigating the role of excluded volume by coarse-grained models

In this Thesis we discuss, from a statistical mechanical perspective, how excluded volume effects influence the mechanical and dynamical behaviours of biopolymers. It has long been recognized that steric constraints can affect dramatically the physical properties of polymers in thermal equilibrium [1, 2]. Though the presence of steric hindrance in polymer models typically makes them intractable by exact analytical means, the theoretical progress made in the past three decades turned polymer thermodynamics in a very mature and well-established research field. In recent years completely new avenues for polymer physics and chemistry were provided by a variety of experimental advancements capable of probing the mechanical and kinetic behaviours of single polymeric molecules. This stimulated the development of new models capable of accounting, in a quantitative manner, for the experimental observations. In particular, the models that we have introduced and discussed in this thesis address two major topics stimulated by the latest single-molecule and micromanipulation techniques. The first one is related to the elastic behaviour of linear polymers that are stretched by pulling at both ends. The second one, instead, is focused on the kinetics and thermodynamics of loop formation in polymers. Though both problems have been computationally and theoretically tackled before, the models used lacked almost invariably, the treatment of the steric effects. We explicitly consider and model such effects and discuss the qualitatively new emerging behaviour. In the rest of the introduction we shall provide a phenomenological background for both problems and motivations for the approach by means of . which we have investigated the two problems.