Convexity Constraints in the HIV-1 Envelope Glycan Shield

This work introduces a curvature-corrected glycan packing parameter (Φ_curv) to explain the emergence of broadly neutralizing antibody (bnAb) supersites on the HIV-1 envelope glycoprotein (Env). While the glycan shield is traditionally understood as a uniform barrier to immune recognition, bnAbs frequently target glycan-dense regions such as the V1/V2 apex and the N332-centered high-mannose patch. This paper proposes that these regions arise from geometric constraints imposed by glycan crowding on convex surfaces, producing cooperative “canopy” regimes with reduced configurational freedom and increased structural legibility. Φ_curv integrates local glycan density, surface curvature, and glycan occupancy into a single operational metric computable from structural data. The framework predicts that curvature-corrected density outperforms density alone in identifying bnAb supersites, reframing glycan-mediated vulnerability as an emergent property of constraint rather than failure of shielding. This model provides a testable structural hypothesis with implications for immunogen design and glycoengineering.