The peptidoglycan cell wall is a branched polymer made of alternating NAG [β-D-N-acetylglycosamine] and NAM [β-D-N-acetylmuramic acid] residues.  Polypeptide chains are attached to the NAM residues and these vary depending on the strain of bacteria.  The mechanism for cross-linkage is shown below.  It is the terminal D-alanyl-D-alanine residues of the polypeptide chain off of the NAM residues that binds to the transpeptidase which cross-links that chain with the adjacent peptidoglycan strand.4