Specifically catalyzes the deamidation of the C-terminal glutamine of the prokaryotic ubiquitin-like protein Pup to glutamate, thereby rendering Pup competent for conjugation. Also displays depupylase (DPUP) activity, removing conjugated Pup from target proteins; is thus involved in the recycling of Pup and may function similarly to deubiquitinases (DUBs) in eukaryotes to prevent or promote proteasomal degradation of certain proteins. [prokaryotic ubiquitin-like protein]-C-terminal-L-glutamine + H2O = [prokaryotic ubiquitin-like protein]-C-terminal-L-glutamate + NH4(+) ATP is required for the deamidation and depupylation reactions but is not hydrolyzed during the reactions. Protein degradation; proteasomal Pup-dependent pathway. Interacts with the prokaryotic ubiquitin-like protein Pup. Disruption of dop abolishes pupylation. Cells lacking this gene also become hypersensitive to reactive nitrogen intermediates (RNI) and are severely attenuated for survival and growth in mice. They also cannot depupylate proteasome substrates. Belongs to the Pup ligase/Pup deamidase family. Pup deamidase subfamily. Extended N-terminus.