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The mechanics of living cells is, to a great extent, determined by the cytoskeleton, a fibrillar meshwork of biopolymers. A common feature of the basic structural elements of the cytoskeleton and the extracellular matrix is their semiexibility: behavior intermediate between that of random coils and slender rods. The cytoskeletal mechanics is determined by both the single polymer properties and the collective behavior of many filaments.
In the first part of this talk, I will present some recent developments in cell mechanics which highlight the importance of elasticity in biological function and the role of physics. In the second part of the talk, I will discuss two biologically inspired soft-matter systems studied analytically using statistical mechanics. The first is an isotropic liquid of semiflexible polymers in which permanent aligning cross-links are randomly introduced. Under certain conditions, we predict a transition from an isotropic liquid to a nematic amorphous solid (gel). The other system is a bundle of parallel aligned semiflexible polymers stretched by a pulling force. We study the effect of permanent random cross-links and find out a stiffening in the stretching elasticity of the bundle. I will conclude the talk with some thoughts on the Parsegian-Austin debate (Physics Today, July 1997), sixteen years later.