Fig 1.
Sketch of a budding HIV-1 virion just prior to pinch-off.
The lipid bilayer covering the capsid is connected to the plasma membrane by a highly curved neck. The large hole surrounding the pinch-off site is also a feature of the completed virion.
Fig 2.
Brownian Dynamics simulation of the budding of an enveloped virus using a coarse-grained model of the lipid molecules and capsid proteins of the alpha virus (square inset).
The strength ϵgg of the interaction between the capsid proteins was 2kB T. A) Snapshot of the simulation at an early stage of the bud. B) Snapshot of the bud during pausing.
Fig 3.
Shape of a bud that minimizes the Helfrich bending energy.
The blue line, which represents the bare lipid bilayer membrane, has the shape of catenoid of revolution. The heavy red line, which represents the lipid bilayer attached to a curved layer of capsid proteins, has the shape of spherical cap. The interface is a circle. The boundary between the two bilayers and the center of the sphere spans a cone with aperture angle 2α. For purposes of illustration, RNA genome molecules associated with the bud are indicated by a black line. Two capsid proteins diffusing along the lipid bilayer are indicated as two red bars associated both with the membrane and an RNA genome molecule. A curvilinear coordinate system (s, φ) is indicated where s measures the shortest arc distance between a point and the cross-section with minimum diameter (s = 0). The value of s ranges from sM > 0 to sm < 0. Finally, φ is the azimuthal angle of the circle on the surface perpendicular to the central axis on which the point is located.
Fig 4.
Comparison between the shape of the bud obtained from the simulations (open circles) and the one that minimizes the Helfrich bending energy.
The latter is composed of a spherical cap (black line) joined to a catenoid of revolution (red line). Vertical axis: height Z in arbitrary units. Horizontal axis: radial distance r in arbitrary units. The aperture angle α is treated as a fitting parameter.
Fig 5.
Example of the dependence of the aperture angle α* that minimizes the free energy on the growth parameter ρ for the case of a fluyid shell.
The partial shell in the shape of a spherical cap with α* > 0 is locally stable along the black line and unstable along the red dashed line. The completed capsid with α* = 0 is stable along the blue line. The black dashed lines mark limits of local stability. Parameter values: κC = 0.5, σ = 0, , and τ = 0.5.
Fig 6.
Example of the dependence of the free energy minimum on the growth parameter ρ for the case of a solid shell.
The parameters were the same as for Fig 5 while the cohesion energy parameter σ was set to zero. The dot indicates the point where the neck diameter has shrunk to zero. Note that there is an activation barrier for low values of the growth parameter but not at the point of pinch-off.
Fig 7.
Solid red line: Diffusion current I from the exterior to the growing bud versus relative size ρ/ρM of the bud computed from Eq 17.
γ = 0.9 was the sole fitting parameter. The current and the growth parameter were normalized with respect to their maximum values. Black dots: assembly current obtained from the Brownian Dynamics simulation of Fig 2. Error bars were obtained by averaging over three runs. The strength ϵgg of the interaction between the capsid proteins was 6kBT. The black arrow indicates the location of the maximum of the current profile predicted by conventional diffusive transport theory (i.e. γ = 0 in Eq 11).
Fig 8.
(A) (left) Image of a trimer subunit, with attractors (‘A2’-‘A5’) in green and excluders (‘B1’ and ‘B6’) in red. (right) Schematic of the subunit geometry, with views from directly above the plane of the membrane and within the plane of the membrane. Membrane excluders are not shown in these schematics to aid visual clarity. (B) Image of a subunit trimer, showing attractors (green, type ‘A’), excluders (red, type ‘B’), and membrane excluders (magenta, type ‘VX’).