The two broad categories of structural components of the cell are filaments, the focus of Part I of this text, and sheets, which we treat in Part II. In principle, two-dimensional sheets may display more complex mechanical behavior than one-dimensional filaments, including resistance to both out-of-plane bending and in-plane shear. As examples, the plasma membrane is a two-dimensional fluid having no resistance to in-plane shear, whereas the cell wall possesses shear rigidity as a result of its fixed internal cross-links. In this first chapter of Part II, we introduce the chemical composition of the membranes, walls and lamina that are of mechanical importance to the cell and its environment. Our theoretical framework is continuum mechanics, within which we describe the elasticity and failure of membranes, with an emphasis on experiment. However, the softness of biomembranes means that their thermally induced undulations are important, as will be explored in Chapters 8 and 9, both of which are more mathematical than Chapter 7. More extensive reviews of biomembranes than those provided here can be found in Evans and Skalak (1980), Cevc and Marsh (1987) and Sackmann (1990).

Membranes, walls and lamina

The design principles of Chapter 1 argue that the cell’s membranes should be very thin, perhaps even just a few molecules in thickness, if their sole purpose is to isolate the cell’s contents. The membrane need not contribute to the cell’s mechanical strength, as this attribute can be provided by the cytoskeleton or cell wall. Are there materials in nature that meet these design specifications? Evidence for the existence of monolayers just a single molecule thick goes back to Lord Rayleigh, in an experiment that would be environmentally frowned upon today. He poured a known volume of oil onto a calm lake and observed, by reflection, the area covered by the oil. Dividing the volume of the oil by the area over which it spread gave him the thickness of the layer – a good estimate of the size of a single oil molecule.