Why Are Cells Small?

A human body is built from 30 trillion cells — excluding microbes — that each<br>arise from a lone, fertilized egg. These cells come in a multiplicity of shapes and sizes,<br>with internal volumes spanning five orders of magnitude. The smallest human cell, a sperm,<br>has a volume of just<br>30 µm³,<br>whereas an oocyte has a volume of<br>4,000,000 µm³,<br>making it the largest cell in the human body.1

What accounts for this huge range? A simplistic answer is that evolution has made each cell<br>the size best suited to its function. Maybe sperm are small because the body needs to make<br>many of them, and tiny cells cost less energy to make. (Sperm consist of little more than<br>DNA and a few mitochondria, which are necessary for providing energy to spin their whip-like<br>tails.) By contrast, an oocyte needs massive reserves of mitochondria and nutrients to<br>support early embryonic growth. In short, every cell is as large or small as it needs to be<br>— within reason.

But we can derive far more satisfying answers from physics.

The first major limit on a cell’s size is its surface area-to-volume<br>ratio . Assuming that a cell is roughly spherical in shape, its internal volume<br>grows proportionally to the cube of its radius, whereas its surface area grows<br>proportionally to the square of that radius. In other words, a cell’s<br>volume grows much faster than its surface area.

This ratio has big consequences for cell survival. The cell’s membrane funnels<br>nutrients into the cell and secretes waste. It’s also where the energy in a<br>prokaryotic cell — like E. coli — gets made. If the interior grows<br>too large relative to the membrane, the cell will not be able to produce enough energy or<br>excrete waste quickly enough to maintain all the ‘stuff’ inside, and metabolism<br>will slow down.

A second constraint is diffusion , or the tendency for molecules to<br>migrate from areas of high concentration to areas of lower concentration. This migration<br>dictates how quickly enzymes find substrates, or how signaling molecules reach receptors,<br>and how often ribosomes collide with messenger RNAs. Inside a cell, nearly everything<br>happens by chance encounters amongst molecules! As a cell’s volume grows, though,<br>the chance that these encounters will happen decreases (assuming the total numbers of<br>molecules stay constant).

A molecule’s diffusion rate changes based on various factors. The cytoplasm<br>is extremely crowded, for example, and so molecules spend lots of time ricocheting off obstacles,<br>delaying their arrival at a distant location. Every protein in a cell collides with about<br>10 billion water molecules per second on average. The vast majority of proteins in a bacterium have diffusion coefficients of only 5 to 10 µm2<br>per second (a measure of how quickly molecules spread through space). Some molecules also aggregate or stick to charged surfaces, further slowing<br>their movement.2<br>In general, large molecules diffuse slower than small ones.

Metabolites in E. coli can diffuse from one side of the cell to the other in<br>milliseconds, which means collisions — and cellular outcomes — happen<br>quickly. A typical protein takes just<br>0.01 seconds<br>to traverse a bacterium’s diameter (about 1 micrometer), but the same<br>protein would take around four minutes to move one millimeter and more than six<br>hours to move one centimeter. This is, in part, why cells are so tiny.

With these constraints in mind, we can begin to speculate as to why various cells are<br>shaped the way they are.

Red blood cells are tiny and shaped like biconcave discs to aid with diffusion; by<br>abandoning a spherical shape and evolving more toward a ‘donut,’ they increase<br>their surface area without compromising their compact volume. This, in turn, enhances their<br>ability to exchange oxygen with cells in the body. Their small size (just 8 micrometers<br>across) also helps them move through narrow capillaries.

Simulating Diffusion<br>Cells must make tradeoffs between many different constraints, from energy demands to volume to surface area and nutrient import. It can feel overwhelming to track all these things at once! Fortunately, we don't even need to appeal to complicated mathematics to wrap our head around these constraints, and why cells make the decisions they do.

Everything in biology runs on collisions between molecules. The "magic" of life cannot happen without these collisions. So let's imagine the simplest possible scenario: a cell with one molecule and one target. Hit the "Run" button to see how long it takes for the two to collide.

Of course, real cells are not empty! Every molecule in every cell collides with billions of water molecules per second, not to mention all the RNA, DNA, and proteins floating around. Below is the same simulation, but now there are barriers between the molecule and its target. Run the simulation to see how this increases the time it takes for the two to collide.

A bigger cell can do more things than a small one. It can carry more proteins, which means it can execute...