If one applies biochemistry to the world rather than in the classroom, one can learn so much more about the world.
I think that sentence is a bit repetitive; perhaps you should try something like "...one can learn so much more about what's out there," or "...one can learn so much more about what's around us."
Or perhaps instead of the first part you could say "If one applies biochemistry to every-day life rather than just to class..."
Because technically, the classroom is part of the world.
I was amazed at how they are able to couple in a way that would maximize efficiency and productivity in organisms.
Couple sounds a bit weird here, I'd suggest 'function' or 'work together.'
Hey, I might have known you. But I forget names; I took Biochem last summer at Stanford.