filaments of the cytoskeleton
represent very thin nanorods: Actin filaments
have a helical structure with a thickness of 8 nm, microtubuli resemble
hollow cylinders with a thickness of 25 nm. Because of their
bending stiffness, these filaments assume
essentially straight conformations at low temperatures and in the absence of external
forces. However, they undergo pronounced thermally excited shape fluctuations at
room temperature and can be bent by relatively small external forces. Thus, as far as their
elastic properties are concerned, cytoskeletal filaments behave in the same way as
semi-flexible polymers, which may be regarded as "one-dimensional membranes".
Both nature and chemical synthesis provide a large variety of such
polymers. In contrast to cytoskeletal filaments, which are formed by the
self-assembly of proteins in aqueous solution, semi-flexible polymers
are chain-like macromolecules, in which the monomers or subunits
are connected by covalent bonds. Two prominent examples for
such polymers are DNA molecules and polysaccharides.
The interplay between elastic properties, external forces, and thermal fluctuations
of semi-flexible polymers and filaments involves the following aspects:
For reviews of these and related aspects, see
Modelling semi-flexible polymers
Buckling, Bundling, and Pattern formation.