ATP-dependent ligase that catalyzes 2 steps in the biosynthesis of the side chain of the aminoglycoside antibiotics in the biosynthetic pathway of butirosin. Mediates the addition of one molecule of L-glutamate to a dedicated acyl-carrier protein. Following decarboxylation of the product by BtrK, adds a second L-glutamate molecule. ATP + holo-[BtrI ACP] + L-glutamate = ADP + gamma-L-glutamyl-[BtrI ACP] + phosphate 4-aminobutanoyl-[BtrI ACP] + ATP + L-glutamate = 4-(gamma-L-glutamylamino)butanoy-[BtrI ACP] + ADP + H(+) + phosphate Binds 2 magnesium or manganese ions per subunit. Antibiotic biosynthesis; butirosin biosynthesis. Monomer.