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Expanding the range of Protospacer Adjacent Motifs (PAMs) recognized by CRISPR-Cas9 is essential for broadening genome-editing applications. Here, we combine molecular dynamics simulations with graph-theory and centrality analyses to dissect the principles of PAM recognition in three Cas9 variants - VQR, VRER, and EQR - that target non-canonical PAMs. We show that efficient recognition is not dictated solely by direct contacts between PAM-interacting residues and DNA, but also by a distal network that stabilizes the PAM-binding domain and preserves long-range communication with REC3, a hub that relays signals to the HNH nuclease. A key role emerges for the D1135V/E substitution, which enables stable DNA binding by K1107 and preserves key DNA phosphate locking interactions via S1109, securing stable PAM engagement. In contrast, variants carrying only R-to-Q substitutions at PAM-contacting residues, though predicted to enhance adenine recognition, destabilize the PAM-binding cleft, perturb REC3 dynamics, and disrupt allosteric coupling to HNH. Together, these findings establish that PAM recognition requires local stabilization, distal coupling, and entropic tuning, rather than a simple consequence of base-specific contacts. This framework provides guiding principles for engineering Cas9 variants with expanded PAM compatibility and improved editing efficiency.