Yellow Fluorescent Proteins are a great example of this. Very loosely speaking, there is this open ended barrel structure that 'hides' the fluorescent part in the center. The fluorescent part in the center will glow yellow when you hit it with blue-shifted light (Stoke's Shift). You send light in, and you get less energetic light out. What makes the florescent part glow yellow in color is an interaction between neighboring molecules. How do those parts interact, like the real guts of the interaction? Quantum Mechanics. Resonance energy transfer and all that jazz, oh you know, elementary graduate level quantum classes (/sarcasm).
So when we say that the process is non-deterministic, maybe that is not quite right. Some of the processes are deterministic, in the sense that quantum mechanics is deterministic in the sense of probability density functions. Which is to say, who knows.
Yeah, molecular biology is right on the edge of being total random noise and actually making things happen. Where any one part of a spaghetti mess of interactions falls on that edge in a given temperature, ph, or salinity level, well, we could use more funding.