Capillary physics links HIV capsid geometry to nuclear pore translocation

The protective capsid encasing the genetic material of HIV can traverse the nuclear pore complex (NPC) intact, despite being far larger than conventional passive cargo. This is attributed to the properties of the capsid surface, which promote partitioning into cohesive assemblies of the disordered proteins that form the NPC's permeability barrier: phenylalanine-glycine nucleoporins (FG-Nups). The implication, at the mesoscale, is that capsid-NPC interactions are characterized by the interfacial physics of wetting and capillarity. To capture this, we develop a minimal theory that reduces to an interplay between capsid geometry, effective cytoplasmic and nucleoplasmic contact angles, and a ratio of interfacial tensions. By combining analytical calculations, sharp- and diffuse-interface numerics, we make several predictions: A geometry-dependent trade-off between penetration depth and the wetting transition; asymmetric capillary forces that generate torques and lead to metastable "stalled" states that are tilted; a topological classification of the possible mechanisms underlying the largest energetic barrier; and spontaneous symmetry breaking of displaced FG-Nups. These behaviors connect capsid shape and orientation to the topology and symmetry of FG-Nup displacement, and to the molecular compositions on each side of the pore. They are consistent with published cryoelectron tomography orientations, which provide an initial estimate of the cytoplasmic contact angle. Crucially, our results identify a capillary advantage for the HIV capsid's characteristic broken-symmetry geometry.