Involved in sulfur transfer in the conversion of molybdopterin precursor Z to molybdopterin. Cofactor biosynthesis; molybdopterin biosynthesis. Heterotetramer of 2 MoaD subunits and 2 MoaE subunits. Forms a stable heterotetrameric complex of 2 MoaD and 2 MoeB during adenylation of MoaD by MoeB. During catalysis MoaD shuttles between the two heterotetrameric complexes (By similarity). Belongs to the MoaD family.