Building off Bennett Brown's answer about creating an "alphabet" with DNA...
It is being researched how to efficiently store data in DNA. Here's some thoughts you can cover:
- The efficiency of DNA - a vial around the size of your pinky finger can store a petabyte of DNA (see how much is a petabyte? and this fascinating lecture by one of the eminent researchers in the field)
- The scientific method - multiple papers have been written (I'll try to find a couple of the better ones) continually advancing the field; one of the later ones, about an encoding system called DNA Fountain approaches I think 86% of the theoretical limit for how much information can be stored in a nucleotide.
- The structure of DNA - what a deoxyribonucleotide is (phosphate group, base, etc) and how it is copied and created in the cell. Here also, you can make a foray into the sequencing and synthesis of DNA - a group called Oxford Nanotech is starting to make smaller, handheld synthesizers using nanopores (links will be added) and then there's Illumina's more classic method of fluorescence sequencing. You can talk about why synthesis is so hard - in the cell, a "primer", or strand of already created DNA, is needed to use DNA polymerase, the enzyme that helps "zip" together the nucleotides.
- Information theory, storage, and density. Talk about how Shannon realized that the amount of information in a message depends on how surprising it is - you know more when I say that "the sky is green" versus "the sun rises in the east". You can also talk about how efficiency is measured - how many units of information per unit volume (in DNA storage's case, bits per nucleotide). So, in English, efficiency (actually called information density) would have the unit volume be each letter. Let them explore, and try to create a more efficient alphabet - I'm guessing they'll gravitate towards something like Chinese, where whole concepts, phrases, words, and so on are represented by characters - i.e., a large character set, but each character holds a whole lot of data.
- Error correction, and how scientists are doing that in DNA. Homopolymers (i.e., 'aa', 'gg', etc) are a problem to be avoided in encoding systems. You could explain error correction in normal data, like checksums, and so on.
- Addressing, and how that's used in random access. Why random access is important in DNA storage.
I could keep going (I'm just a bit excited about this field), but it would be well worth the doing to explain the various encoding systems used in research, and let them explore - who knows, they might come up with a great system of their own! I will add links as I have more time.