Polymers diffusion and translocation

Recent trends in the analysis of diffusion processes in complex environments, such as the diffusion of a polymer in a crowded biological cell, focus on non-Gaussian traits for the probability density function of the diffusing coordinate. One possibility of modelling such processes is by allowing the diffusion coefficient to fluctuate in time, as a consequence of a second source of randomness, besides the one affecting the diffusing coordinate. In terms of probability theory, this mechanism is called subordination, since the randomness of the diffusing coordinate is subordinated to that of the diffusion coefficient. Additionally, the ability of polymers to undergo significant conformational changes makes them ideal candidates for large entropic variations. This characteristic trait will be employed in the analysis of the traslocation process, which, along with simple diffusion, governs much of the polymer dynamics in biological cells. In fact, it is a paramount biological paradigm for the transmission of information at the cellular level. In this thesis, after reviewing the Langevin equations of motion, we will explore the diffusion of polymers not only under standard conditions (Brownian diffusion), but also in a medium full of other monomers (Brownian non-Gaussian diffusion). Finally, the translocation process will be illustrated by means of thermodinamic and stochastic tools.