Step 1: The question asks for the FALSE statement about penicillin binding proteins (PBPs).
Step 2: PBPs are enzymes that sit on the cytoplasmic membrane, not on the outer face of the cell wall. They face the periplasmic side and build the peptidoglycan layer from inside out. So option A is the wrong (false) statement, and that is the answer.
Step 3: Option B is true. PBPs catalyse the final cross-linking steps of peptidoglycan, so they are essential for cell wall synthesis. Blocking them stops the wall from forming and the cell lyses.
Step 4: Option C is true. PBPs work as transpeptidases (they cross-link the peptide chains) and as carboxypeptidases (they trim terminal D-alanine residues). Beta-lactams mimic the D-Ala-D-Ala terminus and bind the active site.
Step 5: Option D is true. MRSA carries the mecA gene that codes for PBP2a, a low-affinity PBP. Beta-lactams cannot bind it, so altered PBP is the main resistance mechanism in MRSA.
Conclusion: The false statement is that PBPs are localized on the outer face of the cell wall. Answer: option A.