Catalyzes the first step of diphthamide biosynthesis, i.e. the transfer of the 3-amino-3-carboxypropyl group from S-adenosyl-L-methionine (SAM) to the C2 position of the imidazole ring of the target histidine residue in translation elongation factor 2 (EF-2). L-histidyl-[translation elongation factor 2] + S-adenosyl-L-methionine = 2-[(3S)-amino-3-carboxypropyl]-L-histidyl-[translation elongation factor 2] + H(+) + S-methyl-5'-thioadenosine Binds 1 [4Fe-4S] cluster per subunit. The cluster is coordinated with 3 cysteines and an exchangeable S-adenosyl-L-methionine. Protein modification; peptidyl-diphthamide biosynthesis. Homodimer. Unlike the enzymes in the radical SAM superfamily, Dph2 does not form the canonical 5'-deoxyadenosyl radical. Instead, it breaks the C(gamma)-S bond of SAM and generates a 3-amino-3-carboxypropyl radical intermediate. Thus, the P.horikoshii Dph2 represents a previously unknown, SAM-dependent, [4Fe-4S]-containing enzyme that catalyzes unprecedented chemistry. Moreover, the chemistry requires only one [4Fe-4S] cluster to be present in the Dph2 dimer, although each monomer can bind a [4Fe-4S] cluster. In contrast to eukaryotes that require four gene products (DPH1, DPH2, DPH3 and DPH4) to catalyze the first step of diphthamide biosynthesis, no other protein than Dph2 is required in P.horikoshii. Belongs to the DPH1/DPH2 family.