Capillarity Reveals the Role of Capsid Geometry in HIV Nuclear Translocation

TL;DR

This work frames HIV nuclear entry as a capillarity problem, showing that capsid geometry and interfacial energetics with FG-Nup condensates govern NPC translocation. By combining sharp-interface (Surface Evolver) and diffuse-interface (phase-field) methods, the authors derive how two contact angles, an interfacial-energy ratio $\alpha$, and cone-like capsid geometry control penetration depth, reorientation torques, and energy-barrier topologies during translocation. They classify translocation into topological (snap-through, detachment, contact) and angle-dependent regimes, revealing that mismatches in $\theta_{Cy}$ and $\theta_{Nuc}$ can dramatically lower barriers and, in some cases, render translocation thermally accessible. The results suggest that HIV capsid shape is tuned for NPC passage and offer a framework for predicting how capsid geometry and NPC physics mediate large cargo transport, with potential implications for antiviral understanding and biotechnological cargo delivery across the NPC.

Abstract

The protective capsid encasing the genetic material of Human Immunodeficiency Virus (HIV) has been shown to traverse the nuclear pore complex (NPC) intact, despite exceeding the passive diffusion threshold by over three orders of magnitude. This remarkable feat is attributed to the properties of the capsid surface, which confer solubility within the NPC's phase-separated, condensate-like barrier. In this context, we apply the classical framework of wetting and capillarity -- integrating analytical methods with sharp- and diffuse-interface numerical simulations -- to elucidate the physical underpinnings of HIV nuclear entry. Our analysis captures several key phenomena: the reorientation of incoming capsids due to torques arising from asymmetric capillary forces; the role of confinement in limiting capsid penetration depths; the classification of translocation mechanics according to changes in topology and interfacial area; and the influence of (spontaneous) rotational symmetry-breaking on energetics. These effects are all shown to depend critically on capsid geometry, arguing for a physical basis for HIV's characteristic capsid shape.

Figures (13)

• Figure 1: Casting HIV's transit through the NPC in terms of wetting and capillary forces. The protective capsid that carries the viral genome of HIV has been shown to cross the NPC intact (panel a, zila_cone-shaped_2021). This is remarkable, since the HIV capsid is over one thousand times larger than the limit for passive diffuse transport, which arises due to a barrier at the centre of the NPC. The diffusion barrier comprises hundreds of proteins (the FG-Nups) that are anchored in the walls of the central transport channel and whose disordered regions are interspersed with repeated weakly-interacting hydrophobic “FG” motifs, causing them to form a condensate-like milieu with ‘good solvent’ properties (panel a, yu_visualizing_2023). The surface of the HIV capsid has been shown to be decorated by binding motifs dickson_hiv_2024 and other surface chemistry fu_governed_2025 that are complementary to the FG repeats, rendering it soluble in the diffusion barrier (panel a). Characterising these molecular interactions by per-unit-area free energy differences, the essential physics of HIV’s nuclear access is then captured by wetting and capillarity. The key variables are the ratio, $\alpha$, of FG-Nup:nucleoplasm and FG-Nup:cytosol interfacial energies, wetting angles at the cytoplasmic and nucleoplasmic interfaces---$\theta_\mathrm{Cy}$ and $\theta_\mathrm{Nuc}$, respectively---and the capsid geometry (panel b).
• Figure 1: (a) Level the gel raises to, $z^\star$, as a function of tip coordinate, $z_0$. (b) Height of the cone embedded, $z^\star - z_0$ as a function of tip coordinate, $z_0$.
• Figure 2: Confinement, wetting and penetration. Due to the confinement of the NPC's central channel, FG-Nups must be displaced for capsids to enter. The interplay between such confinement and the characteristic conelike geometry of capsids is captured by analysing cones with different angles, $\phi$, subtended at their tip (panel a). For a given $\phi$ and (acute) $\theta_\text{Cy}$, the energy (\ref{['eq:E']}) has a non-trivial minimum as a function of penetration depth (panel b). This is because the energetic benefits of exchanging FG-Nup:cytosol and FG-Nup:capsid interfacial areas---and the resultant capillary forces---are eventually counterbalanced by increases in the total FG-Nup interfacial area due to increased FG-Nup displacement as the cone penetrates more deeply (panel b). Since the amount of displaced FG-Nup increases less rapidly with penetration depth for cones with a smaller $\phi$, those capsids have a deeper energy-minimising penetration, $d^\star$ (panel b). However, for similar reasons, the onset of the wetting transition occurs at smaller $\theta_\mathrm{Cy}$ for cones with smaller $\phi$, implying wetting over a smaller range of contact angles [panel c, solid lines represent numerics and dashed lines analytical approximation (Supplementary Material)]. The effects of confinement and displacement are modulated by $\alpha$: smaller values of $\alpha$ permit displaced FG-Nup to be accommodated by the nucleoplasmic interface, and hence reduce the effects of $\phi$ (panel d). Unless otherwise specified, data was produced using sharp-interface numerics with $\alpha = 1$.
• Figure 2: (a) Free energy of the system as a function of capsid depth for a variety of cone angles, $\phi$, (b) Free energy as a function of depth for a variety of dimensionless surface tension differences, $\Delta\gamma$. (c) Insertion depth of the capsid in the minimum energy state as a function of contact angle, $\theta_\text{c}$ in degrees. This is plotted for three values of cone angle $\phi$.
• Figure 3: Capillary-force driven reorientation. Torques arising from asymmetric capillary forces can reorientate capsids arriving at the cytosolic side of the NPC. To capture this, we compute the initial energy minima of capsids penetrating the NPC that are fixed at different angles of rotation. Torque-free configurations are then given by the extrema of these landscapes. Such points (indicated by dots), their basins of attraction (indicated by overbars), the heights of the barriers that separate them, and the penetration depths to which they correspond, all depend on the shape of the capsid and the cytoplasmic contact angle, $\theta_\text{Cy}$ (see main text). Whilst increasing $\theta_\text{Cy}$ broadly reduces the heights of the barriers separating a given pair of minima, there are two notable differences between ellipsoidal and conelike shapes. First, conelike capsids have greater penetration depths, permitting contact with the nucleoplasmic interface at low $\theta_\text{Cy}$ (panels a & d). Second, the local minimum of conelike capsids---with the tip pointing into the cytosol at an intermediate angle---not only has a much larger basin of attraction than their ellipsoidal counterpart, but becomes globally stable with increasing $\theta_\text{Cy}$ (panels d, e & f). Data was produced using sharp-interface numerics with $\alpha = 1$ and capsid shapes codified by (\ref{['eq:3-parameter']}) (Materials & Methods).