Biologists: how is it cellular functions often happen at nearly the speed of light, but don't use energy?

A lot of stuff (protein and RNA/DNA synthesis) is moved along by getting the molecules (amino acids, mostly) jostled around by simple Brownian motion - and when they get to a proper receptor site, they drop in. Of course, the Brownian motion needs an energy source, usually thermal). So you burn ATP, releasing heat energy, and that moves everything along....