This PhD is devoted to the mechanics and statistical mechanics of biofilaments and their most widespread model, the Worm-Like Chain (WLC) model, which, as it turns out, needs to be extended. We study the WLC in 2-d in the presence of obstacles closer than their persistence length. We characterize the short time motion by numerical simulations complemented by analytical calculations. Similar concepts serve to describe grafted DNAs swept by the front of a spreading vesicle whose adhesion is promoted by biotin/streptavidin bonds, which constrain the DNAs on narrow paths where they can be imaged. Microtubules (MT), here stabilized by taxol, show features which cannot be rationalized by the WLC and shall be related to their internal structure : i)lateral deflections of a clamped MT correspond to an effective persistence length growing with the MT size ii) MT adopt super-helical shapes. These two points are proven by refined image analysis. We analyze shape transitions correlated along the MT which are compatible with a model based on dimer bi-stability. Finally, a super helical chain model (HWLC) allowing for spontaneous curvature and twist is developed which extends the WLC. When confined to 2-d, the HWLC can adopt a ground state which is circular or wavy with inflection points where twist accumulates, so-called twist-kinks. In the circular case there exist close metastable states, with a small number of twist-kinks, which are hyperflexible.
