Adenylyltransferase that mediates the addition of adenosine 5'-monophosphate (AMP) to specific residues of target proteins. ATP + L-tyrosyl-[protein] = diphosphate + O-(5'-adenylyl)-L-tyrosyl-[protein] ATP + L-threonyl-[protein] = 3-O-(5'-adenylyl)-L-threonyl-[protein] + diphosphate Adenylyltransferase activity is inhibited by the inhibitory helix present at the C-terminus: Glu-186 binds ATP and competes with ATP-binding at Arg-118, thereby preventing adenylyltransferase activity. Activation dissociates ATP-binding from Glu-186, allowing ordered binding of the entire ATP moiety with the alpha-phosphate in an orientation that is productive for accepting an incoming target hydroxyl side chain. Homodimer. Auto-AMPylation at Tyr-183 in vitro. Defined as class III fido-domain containing proteins, in which the inhibitory helix is present at the C-terminus of the Fido domain.