4.3 Getting bigger or smaller



“… consider a giant man sixty feet high – about the height of Giant Pope and Giant Pagan in the illustrated Pilgrim’s Progress of my childhood. These monsters were not only ten times as high as Christian [a normal human], but ten times as wide and ten times as thick, so that their total weight was a thousand times his, or about eighty to ninety tons. Unfortunately, the cross sections of their bones were only a hundred times those of Christian, so that every square inch of giant bone had to support ten times the weight borne by a square inch of human bone. As the human thighbone breaks under about ten times the human weight, Pope and Pagan would have broken their thighs every time they took a step.”

The above is a quote by the geneticist J. B. S. Haldane in his 1928 essay On being the right size, discussing the giants ‘Pope’ and ‘Pagan’ who feature in the novel Pilgrims Progress by John Bunyan (1678). Haldane’s essay makes the point that structures in biology are ultimately constrained by the laws of physics. However, a common theme found in science fiction movies and speculative fiction is where people are made very small or an animal is made terrifyingly huge. Almost always, scientific feasibility is suspended for the sake of the story.

Consider the size of mammalian cells. Although there are a few exceptions (e.g. some specialised nerve cells and egg cells) almost all fall with a range of 5–50 µm. Even for animals which differ in size by several orders of magnitude the difference in size reflects the number of cells not the size of the cells. So, what constrains almost all cells to this microscopic size?

Cells need to have constant interaction with their environment as dissolved gases and small molecules must be constantly absorbed and waste molecules must be excreted. These substances need to pass through the plasma membrane, which means that the internal regions of the cell are reliant on the cell surface. That is, what is important for the cell to function is a large enough surface-area-to-volume ratio. But as cells become larger their volume increases at a faster rate than their surface area.

Imagine a spherical cell with a diameter of 10 µm. Its surface area is calculated by 4πr2, so is approximately 300 µm2. The volume is calculated by 4/3πr3, so is approximately 500 µm3. Therefore, the surface-area-to-volume ratio is 0.6. However, if the diameter is increased to 100 µm (a 10-fold increase), the surface area is approximately 30,000 µm2 (a 100-fold increase) and the volume is 500,000 µm3 (a 1,000-fold increase). The surface-area-to-volume ratio has thus decreased to 0.06.

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