Cellular and molecular scales

Read

Although you have already had classes in biology and chemistry, and know well about atoms, molecules, and cells, many of you have not had the opportunity to develop a good sense of relative scale. At the cellular and molecular level, the appropriate distances are measured in nanometers $(\text{nm} = 10^{-9} \text{ m})$, micrometers $(\text{μm} = 10^{-6} \text{ m}$), and millimeters $(mm = 10^{-3} \text{m})$. While millimeters should be familiar to you -- the lead for a mechanical pencil is about 1 mm in diameter — it's hard to get a sense for the others. In this problem, we'll try to develop a sense of the scales down to 10 million times smaller than a mm by making comparisons.

Let's start with atoms. The atoms that we work with in biology — mostly hydrogen, carbon, nitrogen, oxygen, sodium, potassium, and calcium are typically about 0.1 nm  in diameter, . (H only has a diameter of about 0.075 nm, while C, N, and O had diameters about 0.15 nm.) This sets the bottom scale we will be working with.

Do

We want to get a sense of scale for the following items relevant in biology:

• A small but important biomolecule (ATP)
• A  protein molecule (say myosin)
• A small virus (say T-5)
• A small prokaryotic cell (a bacterium — say, e. coli)
• A typical mammalian cell (say a human neutrophil or white blood cell) 
• A cluster of cells that are visible without a microscope (say, volvox)

For each of these look up their approximate size (diameter) on the web and enter them into the table below. This takes us up from atoms to "barely visible" biological organisms.

Your next task is to "scale them all up". If an atom were a million times bigger, so that it is visible — say 1 mm in diameter rather than 1 nm $(10^{-3} \text{ m instead of }10^{-9} \text{ m })$ — then how big would the other objects in your table be? Calculate the scale, then identify a macroscopic object of about that scale so you can get a mental picture of relative sizes.

Joe Redish 5/27/13