From my reading of the primary and secondary literature, this is my understanding of H2S production and its relation to N deficiency. Proteins are made of amino acids, and two important amino acids contain sulfur. The yeast has to provide the sulfur to form these compounds to the proper organelle during protein synthesis. It does so in the form of H2S, which it extracts from more complex sulfur-containing compounds. One organelle passes the H2S off to the organelle responsible for protein synthesis.
However, nitrogen is a major component of amino acids (hence the root amine, from ammonia.) If there is a dearth of N, the organelle responsible for synthesizing the sulfur-containing amino acid cannot do its job; this results in a surfeit of H2S, which the yeast then excretes.
As John points out, we are extraordinarily sensitive to H2S and thiols (larger SH-containing molecules). That is why they add a tiny (ppm) amount of methane thiol to your natural gas supply, so that you can smell when you have a gas leak. This is good for gas-leak detection, but the unfortunate result for winemaking is that we cannot tolerate very much H2S excretion by our pet yeasts.
Hope this helps!
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