Figure 2. Discoidal and filamentous structures offer a better scaling of surface area with volume than spheres.
Graph showing the dependence of the surface-to-volume ratio on volume of spherical (black line) and cylindrical (yellow, cyan, green and orange lines) compartments. Arrows on the black line indicate the arbitrary division of small (<2 µm diameter) and big (>2 µm diameter) vesicles. Base diameters of the cylinders were fixed at 0.8 µm (yellow) and 0.3 µm (cyan) to represent cell-size filaments and lipid nanotubes, respectively. For green and orange lines, cylinder heights were fixed at 1 µm and 0.3 µm, respectively, to represent discoidal cells. Arrows on the x-axis indicate volumes of several organisms: P. ubique (0.01 µm3, [63]), E. coli (1.1 µm3; BNID:100004), haploid Saccharomyces cerevisiae (37 µm3; BNID:100430) and HeLa (940 µm3; BNID:106664) cells. The surface-to-volume ratio for a sphere is given by the equation: A/V = 3/(3V/4π)1/3; for a cylinder with a fixed base diameter the equation is as follows: A/V = (4/d + 2/πd2)/V; for a cylinder with a fixed height: A/V = (2π(V/hπ)1/2h + V/2. V is the volume, d is the cylinder base diameter and h is the cylinder height.