Edit: I hope this post isn't wildly inappropriate, you just got the chemist in me really exited, and the artist in me really inspired!
This is such a awesome idea! But why stop at the DNA molecule?
A lot of molecules are visualized as lines and bubbles, which can be really inspiring (this is the part were i started to explain why they usually visualize it like that, and what the meaning is, but then i realized that doesn't matter. It looks pretty, that's all that matters! )
For example, you can use tiny beads for the lines parts, and bigger beads for the bubbles. or strait beads for the lines and round beads for the bubbles.
Here is a picture of Theobromine; the stimulant in chocolate.
Now wouldn't this make a pretty piece?And for some other occasions:
CaffeinenicotineEthyl Alcohol (looks like a balloon-dog

)