Physics meets Biology: Size!

Photo courtesy of Brendan Wood

One interesting thing about my new job is that my colleagues are not biologists, but physicists. To some extent, physics was quite absent from my biology curriculum; of course, as a freshman in biology I attended physics classes, but they were usually disconnected from the scope of biology (with some notable exceptions, such as mentioned in this post). If you think about it, there are reasons for this. Physics – and chemistry as well, for the matter – are fundamentally different from biology in the sense that each individual atom or molecule is undistinguishable from another one of the same kind, whereas in biology, in the words of Ernst Mayr, each individual is unique. The uniqueness of individuals stands at the core of evolution, since natural selection requires it to operate. 

Despite this observation, it is undeniable that biological organisms live and evolve in the physical world. In that respect, a lot of what organisms can or cannot do is under direct control of physical laws. If I want to jump, I’d better hope that my muscles can counteract the force of gravitation… Physics is thus intricately associated to biology, and when biologists forget this fact it can lead to absurd hypotheses or ideas that could be refuted by a wave of a hand.

With this in mind, I have decided to do some more reading about the influence of physics on biology. And one very savory topic is the one of size!

The most obvious differences between different animals are differences of size, but for some reason the zoologists have paid singularly little attention to them. In a large textbook of zoology before me I find no indication that the eagle is larger than the sparrow, or the hippopotamus bigger than the hare, though some grudging admissions are made in the case of the mouse and the whale. But yet it is easy to show that a hare could not be as large as a hippopotamus, or a whale as small as a herring. For every type of animal there is a most convenient size, and a large change in size inevitably carries with it a change of form.

J. B. S. Haldane, On being the right size (1926)¹

In his delightful short piece, J. B. S. Haldane points out some of the constraints that physics imposes on living beings. One of the most striking examples is the relationship between surface and volume: if a given animal could be made ten times bigger by a magic wand, its volume would be multiplied by a factor of 1,000, whereas a section of its body would be multiplied only by a factor of 100… For this reason, its bones would have to become 10 times more resistant… or break under the weight excess. (Sorry, Godzilla, but you would probably break your leg at the first step.) This observation of the weight/strength relationship was actually made by Galileo, as I learned in John T. Bonner’s very nice book, Why Size Matters (2006). In an illustration from his Dialogues Concerning Two New Sciences, Galileo shows how a bone should increase in thickness more than in lenght to keep performing the same function in larger animals.

Illustration from Galileo Galilei

Bonner expresses this rule by stating that the strength varies as the weight at the power of 2/3. This explaines why, for instance, the rhino has short thick legs while those of the gazelle are slender. The difference is of course even more important between animals whose respective size differs by orders of magnitude. Take, for instance, the ant and the ape shown on top of this post. If both were to fall from the top of a building, the fate of the ape would be seriously compromised, while the ant would probably be unharmed. Conversely, being immerged in water is unremarkable for human beings, while insects can easily be trapped by the surface tension of water, and drown!

Published at Princeton University Press

There are strict limits to what living beings can be, and these limits are physical… This doesn’t mean, however, that biology cannot find ways around it! Take, for instance, diffusion: Bonner explains that diffusion occurs through surfaces, and therefore any increase in weight has to be accompanied by a sufficient increase of exchange surface. By modifiying its shape, an organism can increase its exchange surface more rapidly than its weight! Haldane notes (op. cit.):

A man, for example, has a hundred square yards of lung. Similarly, the gut, instead of being smooth and straight, becomes coiled and develops a velvety surface, and other organs increase in complication. The higher animals are not larger than the lower because they are more complicated. They are more complicated because they are larger.

Not only are larger organisms more complicated, but they also live longer! This becomes obvious when the average size of living beings is plotted against their generation time, as shown in the figure below, from J. T. Bonner's book:

Figure 32 from Why Size Matters, reproduced with permission of the author

So the solution to eternal life might be to grow in infinite proportions and slow down the metabolism accordingly! (I guess there wouldn't be much to enjoy in this state, but, well, you can't have it both ways!)

Next time, I will dive into the size that interests me most, the size of microbes! 

Notes

          1. For anyone looking for good examples of popular science writing, I warmly recommend reading J. B. S. Haldane. He is one of the greatest writers I have ever read. Haldane wrote a lot of short science articles for newspapers, and most are available in collections.

References:

• Haldane J. B. S. (1926). On being the right size. In Possible Worlds (2001), Transaction Publishers, 312 pages.
• Bonner J. T. (2006). Why size matters: From Bacteria to Blue Whales. Princeton University Press, 176 pages.