Biology and Physical Factors #6: Scaling

Large organisms don’t look anything like magnified versions of tiny organisms. Why not? Because of the (physics) principle of scaling. And it’s not just limited t0 physical structure. In So Simple a Beginning, Raghuveer Parthasarathy asks an interesting question: Why can’t a bacterium swim like a whale?

 

Swimming involves pushing the water to move. There are two aspects that make this action hard: inertia and viscosity. The ratio of these two forces is called the Reynolds number. The higher the Reynolds number, the higher the inertia. Which means the liquid appears turbulent to the act of swimming. The lower the Reynolds number, the higher the viscous force.

 

Wait, it gets trickier. The Reynolds number also depends on the size of the object trying to swim. To a tiny bacterium, the water has a low Reynolds number. But to a whale, the Reynolds number is huge. This has other consequences:

“This fact has deep consequences for how aquatic creatures can or cannot move.”

How? At high Reynolds numbers, flows are irreversible. This means that if you move an object one way through a fluid, then reverse the movement to its starting point, the liquid will not return to its original configuration. (Easier example: Mix cream with tea, turn the spoon once, then turn the spoon back to its original position. The cream and tea won’t unmix). This is the way large creatures like us experience water.

 

But at low Reynolds numbers, flows are reversible. Tiny creatures like bacterium experience water as a low Reynolds number, i.e., reversible. What is the consequence of this?

“Microorganims simply cannot swim using back-and-forth motions.”

A picture explains this a lot more clearly. Say a creature moves its appendages inwards, it would propel itself forward. 

So far so good. It now reverses the appendages motion to go back to starting position. Here is what happens. 

Notice what happened? The organism just moved backward! Worse, the speed of the movements doesn’t matter. If the appendages go back to the starting position, the organism moves back. That’s reversibility for you.

 

So microorganisms are forced to come up with other ways of moving, anything which doesn’t involve reciprocal movements. A cockscrew movement is one way. Having tiny hairs that retrace their movements imperfectly is another.

 

To summarize: the world of the whale is very different from that of the bacterium. On physical principles alone…