Biology can be hard to intuit, in part because it operates across vastly different scales, from single atoms all the way up to entire ecosystems. Students of biology therefore often first meet its agents and mechanisms through metaphors: molecules are charged balls connected by sticks! evolution designs organisms to maximize their fitness! mitochondria are the powerhouses of the cell! While metaphors give us qualitative handles to grasp, they often oversimplify complex ideas.

This is because most metaphors fail to address specifics — especially regarding numbers. Consider another common bio-metaphor: DNA is the blueprint of the cell. That’s useful for conceptual understanding, but how big is this blueprint? Is it as big as a novel or an encyclopedia? How much space does it take up? It’s possible to look up or calculate the answers to these questions; the human genome is 6.2 billion base pairs, which takes up about 10 cubic microns.¹ But how big is that compared to the total volume of a cell? Is it most of it or just a tiny fraction?

To answer questions like these, you need more quantitative metaphors. Whereas a standard metaphor says that mitochondria are the powerhouses of the cell, a quantitative metaphor says how big a battery a mitochondrion would be, say, if a cell were a toaster. If qualitative metaphors are like containers, then quantitative metaphors are closer to yardsticks.

And these yardsticks are exceptionally useful down at the scales where biology operates. We all know cells are small. But so are proteins, nucleic acids, and water molecules. We often think of everything “small” as equally small, but that is not the case. Proteins are titanic, hulking machines compared to water molecules, and the mRNA that encodes a protein is orders of magnitude larger still!

To make the sizes and shapes of various biomolecules concrete, let’s imagine that each water molecule within a cell has been blown up to the size of a grain of sand.² If this were the case, then …

Proteins

Proteins come in a variety of shapes and sizes, but a typical protein would now be a knobby ball the size of a blueberry.³
The largest human protein, titin, would be a floppy spring 3-4 mm in diameter. Coiled loosely, it would be about as long as a golden retriever end-to-end but could stretch out to the height of a double-garage door.
An antibody would consist of three blobby arms, each roughly

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