what pairs a coenzyme with the group transfered by that coenzyme?

Answer 1

There are two answers to your question, depending on exactly what interpretation we put on it.

We might ask, how does an enzyme come into contact with the molecules they are intended to react with? The answer to this is not entirely intuitive. At the molecular scale in which enzymes operate, entirely different forces are dominant. Brownian motion from heat moves everything constantly around.

In our experience, it takes work to put a basketball through a hoop. If you put a hoop in a bingo ball spinner, though, balls would go through it all the time. FINDING things aren't a problem on the molecular scale, just HOLDING them once they're found!

And thus we come to what would be the second interpretation of your question - how do enzymes interact with their target reactants and nothing else? Pretty much all enzymes achieve specificity by their shape. Most have niches into which most molecules simply can't fit. Some can change shape so when the right thing smacks into them they wrap around and can also apply different kinds of pressure to the reactants. Electostatic attraction also plays a VERY big role in holding and moving the right thing in the right way, much like you might use a magnet to push iron filings around.

You'll note I don't mention coenzymes specifically - there's no need, really. They're just sub-sections of a larger enzyme complex, and thus are just gears in a more complicated machine.

Hope that helps!