Laboratoire de Physique Théorique
Toulouse - UMR 5152

The mechanics of living cells is, to a great extent, determined by the cy- toskeleton, a fibrillar network of biopolymers. A common feature of the basic structural elements of the cytoskeleton is their semiflexibility : behavior inter- mediate between random coils and slender rods. The cytoskeletal mechanics is determined by both the single polymer properties and the network-forming linking of many filaments. In the first part of this talk, I will discuss the problem of a semiflexible chain with uncorrelated quenched disorder in its arc-length-dependent spontaneous curvature. In the weakly bending approximation, we obtain analytic results for the elastic response to a stretching force applied at its end-points. I will also discuss a formally similar disordered system where a stretched filament is subject to random uncorrelated transverse forces. In the second part of the talk, I will present a semimicroscopic theory of anisotropic amorphous solids formed by random cross-linking of semiflexible polymers. In a three-dimensional model, we consider random cross-links which constrain the corresponding monomers to be parallel or antiparallel. Using the cross-link density and the polymer stiffness as control parameters, we obtain a phase diagram which contains a liquid (sol), a statistically isotropic amorphous solid (orientational glass), and a nematic gel. A two-dimensional implemen- tation of the same theoretical scheme allows us to consider cross-links which prescribe a finite angle. If the cross-linking angle is a rational fraction of 2π, we show that an amorphous solid with m-fold orientational order may emerge. Some comments will also be made on the random cross-linking of directed poly- mers.