Involved in the biosynthesis of the thiazole moiety of thiamine. Catalyzes the conversion of NAD and glycine to adenosine diphosphate 5-(2-hydroxyethyl)-4-methylthiazole-2-carboxylate (ADT), an adenylated thiazole intermediate, using free sulfide as a source of sulfur. glycine + hydrogen sulfide + NAD(+) = ADP-5-ethyl-4-methylthiazole-2-carboxylate + H(+) + 3 H2O + nicotinamide Cofactor biosynthesis; thiamine diphosphate biosynthesis. Homooctamer; tetramer of dimers. Belongs to the THI4 family.