A train is made up of individual cars (monomers). For our train there is an engine, a caboose, and cars that can carry either pillows, milk or lead.
Now imagine a train made with exactly 6 cars (a polymer). There would have to be an engine at the front and a caboose in the back. But we can put whatever we want in the middle four positions.
If you were the engineer of this train you would definitely want to know what those four cars were carrying. For example, a train with three cars carrying pillows and one carrying milk will be very different to control than a train with three cars carrying milk and one carrying lead. The maximum speed, stability, time to stop, etc. will be determined by those four cars. The fundamental idea here is that the properties of the polymer are determined by the monomers that make it up.
This drawing can also be used to help students understand that, even with a small number of monomers, many distinct polymers can be made. You need to know two things:
n = number of monomers to choose from
r = number of choices to make (i.e. how long the polymer is)
To find the number of possible combinations use:
This assumes that repetition is allowed (i.e. you can have a train that is lead-lead-lead-lead) and order matters (i.e. lead-lead-lead-milk is considered to be different than lead-lead-milk-lead).
For our train we only need to worry about those middle four positions. We have three choices (pillows, milk, lead) so n=3. There are four spots to fill so r=4. Therefore,
the number of possible trains = 34 = 81 different trains. Each of those 81 trains will have slightly different properties because of the make-up and order of the cars.
We can extend this thinking to one biologically important class of polymers, proteins (or polypeptides). Almost all proteins are made out of the same set of 20 amino acid monomers. For proteins n=20.
"Molecular structures of the 21 proteinogenic amino acids" by Dan Cojocari ✉·✍· - Own work This vector graphics image was created with Adobe Illustrator.. Licensed under CC BY-SA 3.0 via Wikimedia Commons.
Proteins have tremendous variation in length. The human genome encodes around 30,000 proteins with an average length of 450 amino acids (the largest, the muscle protein titin, is about 33,000 amino acids long). For the average human protein r=450.
This is the number of possible different proteins that are 450 amino acids long. This is a big number...a very big number. In fact, physicists tell us that this number is greater than the number of atoms in the universe! So with just 20 amino acids (monomers) a huge number of distinct polymers could theoretically be made.
(I used the same formula in my recent post about PCR primers.)