Mediates the side-chain deamidation of N-terminal glutamine residues to glutamate, an important step in N-end rule pathway of protein degradation. Conversion of the resulting N-terminal glutamine to glutamate renders the protein susceptible to arginylation, polyubiquitination and degradation as specified by the N-end rule. Does not act on substrates with internal or C-terminal glutamine and does not act on non-glutamine residues in any position. H2O + N-terminal L-glutaminyl-[protein] = N-terminal L-glutamyl-[protein] + NH4(+) Monomer. Belongs to the NTAQ1 family.