Adenylation and deadenylation of glutamate--ammonia ligase. Involved in the regulation of glutamine synthetase GlnA, a key enzyme in the process to assimilate ammonia. When cellular nitrogen levels are high, the C-terminal adenylyl transferase (AT) inactivates GlnA by covalent transfer of an adenylyl group from ATP to specific tyrosine residue of GlnA, thus reducing its activity. Conversely, when nitrogen levels are low, the N-terminal adenylyl removase (AR) activates GlnA by removing the adenylyl group by phosphorolysis, increasing its activity. The regulatory region of GlnE binds the signal transduction protein PII (GlnB) which indicates the nitrogen status of the cell. [glutamine synthetase]-O(4)-(5'-adenylyl)-L-tyrosine + phosphate = [glutamine synthetase]-L-tyrosine + ADP [glutamine synthetase]-L-tyrosine + ATP = [glutamine synthetase]-O(4)-(5'-adenylyl)-L-tyrosine + diphosphate Belongs to the GlnE family.