Convexity Constraints in the HIV-1 Envelope Glycan Shield

This preprint proposes a geometric model for the emergence of broadly neutralizing antibody (bnAb) supersites in the HIV-1 envelope glycan shield. Using principles from polymer brush physics and surface geometry, the framework introduces a curvature-corrected packing parameter describing steric crowding of N-linked glycans on the convex Env trimer surface. The model suggests that dense glycan clusters can transition into correlated canopy structures that produce recurring antigenic patterns targeted by bnAbs. The approach provides a geometric explanation for oligomannose enrichment, supersite convergence at the V1/V2 apex and N332 mannose patch, and patterns of glycan-relocation escape mutations.