Topological defects drive influenza glycoprotein lattice assembly on spherical membranes

Lipid-enveloped viruses, such as influenza virus, assemble by budding from infected cell membranes, packaging internal components including the genome and acquiring an envelope containing surface glycoproteins in the process. Influenza C virus possesses a single surface glycoprotein, the haemagglutinin-esterase-fusion (HEF) protein that forms hexagonal arrays1,2 on the membrane envelope and is sufficient for budding of spherical particles3. However, a two-dimensional hexagonal lattice cannot completely cover a spherical virus membrane without defects. Using electron cryotomography (cryo-ET), we study the structural arrangement of the influenza C virus surface and find the hexagonal HEF lattice contains 5-fold and 7-fold defects organised in grain boundaries. The number of excess dislocations increases with system size while maintaining a net topological charge near 12. Our observations of defects in spherical crystals on influenza C virus particles of varying radius and shape matches theoretical predictions of continuum elastic theory4 for the proliferation of defects on soft lattices and experimental observations5 on colloidal systems. These findings provide new principles for assembly of pleomorphic viruses, extending the description of defects required for viral lattice assembly beyond the Caspar-Klug theory6 developed for isometric viruses. Our study informs a wide range of molecular self-assembly processes in biology and may also have implications for developing lattice materials with curved surfaces.