With some notable exceptions, such as DNA, most filaments in the cell are linked together as part of a network, which may extend throughout the interior of the cell, or be associated with a membrane as an effectively two- dimensional structure such as shown inFig. 5.1. This chapter concentrates on the properties of planar networks, particularly the temperature- and stress- dependence of their geometry and elasticity. To allow sufficient time to develop the theoretical framework of elasticity, we focus in this chapter only on networks having uniform connectivity, namely those with the four-fold and six-fold connectivity found in a number of biologically important cells.

Soft networks in the cell

Two-dimensional networks arise in a variety of situations in the cell; they may be attached to its plasma or nuclear membrane, or be wrapped around a cell as its wall. Containing neither a nucleus nor other cytoskeletal components such as microtubules, for example, the human red blood cell possesses only a membrane-associated cytoskeleton. Composed of tetramers of the protein spectrin, the erythrocyte cytoskeleton is highly convoluted in vivo (see Fig. 3.17(b)), but can be stretched by about a factor of seven in area to reveal its relatively uniform four- to six-fold connectivity, as shown in Fig. 5.1(a) (Byers and Branton, 1985; Liu et al., 1987; Takeuchi et al., 1998). Roughly midway along their 200 nm contour length, the spectrin tetramers are attached to the plasma membrane by the protein ankyrin (using another protein called band 3 as an intermediary). About 120 000 tetramers cover the 140 μm2 membrane area of a typical erythrocyte, corresponding to a tetramer density of about 800 μm−2. The tetramers are attached to one another at junction complexes containing actin segments 33–37 nm long; perhaps 35 000 junction complexes, with an average separation of about 75 nm, cover the erythrocyte.