Heh... here are two EXCELLENT ideas to integrate polymers & their chemistry with real world biochemical applications:
(1) The production of resins for solid phase peptide synthesis. High yield chemical synthesis of polypeptides is not possible without a solid support resin to build the molecule on. Bruce Merrifield won the Nobel prize in the 80s for his pioneering work in chemical synthesis of polypeptides. A large part of this was the conceptualization and development of the resin.
The first generation of resins (Merrifield resins) were made through a polymerization reaction with vinyl benzene and divinyl benzene to create a large solid polymer with unique swelling properties in certain solvents. Check out the Merrifield Nobel lecture in Chemistry (available for free online at the Nobel site) for some nice figures and a fuller explanation of this process. There are other resins available now with better properties than the originals, but this chemistry is the easiest to grasp.
But at the end you can link it to how SPPS now allows creation of thousands of peptides each year in many, many labs and is leading the development of new peptide-based medicines to treat many diseases.
(2) Peptide and protein PEGylation. Polyethylene glycol polymers represent a new and very attractive method of chemical modifcation to proteins and peptides for their use as therapeutic entities.
Thus far the most successful PEGylated proteins to be on the market are the interferons, however MANY more are coming and many of us will likely use one at some point of our lives.
PEG is a simple ethylene glycol repeat ranging in size. They have many properties which make them attractive entities to attach to a protein/peptide for administration in the clinical setting. Check the wiki PEG page for examples, I've already given you enough information. =)
http://en.wikipedia.org/wiki/Polyethylene_glycol
You could take the microtubule/actin route, however then you would need to describe the chemistry required to make these materials and I'm not sure you want to divulge into that realm in a "polymer chemistry" course.
I'd go with Merrifield's work. Guaranteed A. ;-P
Oh yea and you're going to have a hard time linking enzymes and receptors to polymer chemistry, especially in 15 minutes. About the only thing you could possibly do is to explain how the ribosome creates proteins, which is essentially a continuous polymerization reaction it catalyzes with various amino acids to create the final product. I don't think you could do this in 15 minutes, nor does it sound like you have the background to do so...