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.