Punk is an attitude, more than anything--it's transgressive, rejectionist, and all about the unexpected. Which fits perfectly with those writerly goals. There's not much new under the sun in terms of plot, but the way a story is told is incredibly important. If you want your story to stand out, it's got to be a little punk.
I'm almost done with the story I was moved to write, and it's turning out better than I'd imagined. Does it fit into the category of Biopunk? No idea. It's a speculative fiction story, but it's still a story about people, and their motives coming into conflict, and the emotional overdrive that is such a rich product of conflict.
And, it's punk.