Protein that can both mediate the addition of adenosine 5'-monophosphate (AMP) to specific residues of target proteins (AMPylation), and the removal of the same modification from target proteins (de-AMPylation), depending on the context (By similarity). The side chain of Glu-250 determines which of the two opposing activities (AMPylase or de-AMPylase) will take place (By similarity). Acts as a key regulator of the unfolded protein response (UPR) by mediating AMPylation or de-AMPylation of Hsc70-3/BiP. In unstressed cells, acts as an adenylyltransferase by mediating AMPylation of Hsc70-3/BiP at 'Thr-518', thereby inactivating it. In response to endoplasmic reticulum stress, acts as a phosphodiesterase by mediating removal of ATP (de-AMPylation) from Hsc70-3/BiP at 'Thr-518', leading to restore HSPA5/BiP activity (By similarity). ATP + L-tyrosyl-[protein] = diphosphate + O-(5'-adenylyl)-L-tyrosyl-[protein] ATP + L-threonyl-[protein] = 3-O-(5'-adenylyl)-L-threonyl-[protein] + diphosphate 3-O-(5'-adenylyl)-L-threonyl-[protein] + H2O = AMP + H(+) + L-threonyl-[protein] The side chain of Glu-250 determines which of the two opposing activities (AMPylase or de-AMPylase) will take place. In response to endoplasmic reticulum stress, mediates de-AMPylase activity (By similarity). Adenylyltransferase activity is inhibited by the inhibitory helix present at the N-terminus: Glu-250 binds ATP and competes with ATP-binding at Arg-389, thereby preventing adenylyltransferase activity (By similarity). In unstressed cells, disengagement of Glu-250 promotes adenylyltransferase activity (By similarity). Activation dissociates ATP-binding from Glu-250, 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 (By similarity). Homodimer. The fido domain mediates the adenylyltransferase activity. Belongs to the fic family.