Microreologia di una rete di polimeri attivi e fuori dall'equilibrio, studio teorico e numerico di polimeri semiflessibili nel citoscheletro = Microrheology of Non Equilibrium and Active Polymer Network, Theoretical and Numerical Study of Semi-flexible Polymers in Cytoskeleton.

We investigate the behavior of active semi-flexible polymer networks, using in-silico and theoretical methods. We first study the mechanics and thermal fluctuations of a single semi-flexible polymer at equilibrium, exhibiting distinct power-law dynamical regimes in longitudinal and transverse directions of the polymer, and compare our simulations with the free software Cytosim. We then introduce the polymerization and depolymerization at both ends (treadmilling) and we adopt a theoretical framework developed by Liverpool by considering the local connectivity constraint instead of the local inextensibility constraint, and we show preliminary results on the resulting Langevin equation: the polymer motion is thus described by two coupled Langevin equations, one for the local position, the other for the local orientation. Order zero approximation of the equations gives properties of the center of mass and mean orientation of the polymer. Secondly, we study viscoelastic properties of networks of semi-flexible polymers, using simulations of a micro bead in a network of polymers. We derive well-known results from fluctuation-dissipation theorem, such as a sub-diffusive power-law for the mean-square displacement (MSD) of the micro bead, linked with the single semi-flexible transverse power-law. We then consider treadmilling of the polymers in the networks, at two different velocities. This out of equilibrium process leads to two results: the MSD power-law becomes diffusive, which corresponds to a fluidization of the network; increasing the treadmilling velocity decreases the viscosity of the network.