# Scales in biology

#### Prerequisite

Items of interest in biology range over a huge range of length scales, ranging from thousands of kilometers for the migration range of seabirds (10,000 km = 106 m) to the size of an atom (0.1 nm = 10-9 m). That's 15 orders of magnitude!

If we want to apply our estimation skills in biological systems, we need to have some foothold ideas of about the size of biological structures. While we have direct experience with plants and animals, we typically don't have direct visual personal experiences with microscopic biological structures. Let's learn a few scales that we can use as starting points for our estimations.

The following table offers some starting scales to learn. Depending on your choice of specialty in biology, you may want to add some of your own!

Learn to keep straight the scales for fractions of a meter: millimeter (mm = 10-3 m), micron or micrometer (μm = 10-6 m), and nanometer (nm = 10-9 m). These are shown in the table to let you watch the march downward in size as powers of ten.

 Size of a typical animal cell ~10-20 microns (10 μm = 10-5 m) Size of a bacterium, chloroplast, or mitochondrion ~1 micron (1 μm =10-6 m) Size of a medium-sized virus ~0.1 micron (0.1 μm = 10-7 m) Thickness of a cell membrane ~5-10 nm (10 nm = 10-8 m) Size of an amino acid ~1 nm (1 nm = 10-9 m) Diameter of an atom ~0.2 nm (0.1 nm = 10-10 m)

Learning the numbers is a good start, but it's valuable to create visual images for yourself as well. Here's an image adapted from Phil Nelson's text, Biological Physics.**

Here's a nice figure to give you a visual sense of the scale of the structure in a eukaryotic cell. Can you identify the numbered elements?

A nice exercise to help you build your sense of scale visually is given as a follow-on problem.

Joe Redish 8/16/20

*If you have already had a number of biology classes, you may know about these structures and even seen them in microscopes or photos in your biology textbooks. As of this writing, however, many biology texts and classes focus on qualitative structures and don't even put a scale on photos of cells or sub-cellular structures.  Hopefully, this is beginning to change!

**This is an excellent text to support your learning of how physics applies to biology if you are comfortable with calculus. Highly recommended!

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