Adenylylation, more commonly known as AMPylation, is a process in which an adenosine monophosphate (AMP) molecule is covalently attached to the amino acid side chain of a protein. This covalent addition of AMP to a hydroxyl side chain of the protein is a post-translational modification. Adenylylation involves a phosphodiester bond between a hydroxyl group of the molecule undergoing adenylylation, and the phosphate group of the adenosine monophosphate nucleotide (i.e. adenylic acid). Enzymes that are capable of catalyzing this process are called AMPylators.

Reference
Wiki: Ampylation