The hkcage command creates a cage of hexagons and pentagons to represent the arrangement of proteins in an icosahedral virus capsid. See also: marker, Cage Builder
The arrangement of subunits in an icosahedral capsid can be described as a sheet of hexagons in which curvature is introduced by replacing certain hexagons with pentagons, as in a geodesic dome. The pentagons occupy the points of the icosahedron, while the indices h and k refer to the number and arrangement of hexagons in each face. A virus T number (T = h2 + hk + k2) is proportional to the number of subunits in the capsid. VIPERdb includes viruses with T = 1, 3, 4, 7, 13, and in a few cases, even higher. For more details, see the VIPERdb description and the following reference:
Quasi-equivalent viruses: a paradigm for protein assemblies. Johnson JE, Speir JA. J Mol Biol. 1997 Jun 27;269(5):665-75.The arguments h and k are required; each can be a positive integer or zero, but not both zero at the same time.
The basic T number equation describes lattices built from repeats of the same asymmetric unit. However, expanded versions of the lattices are possible for capsids with vertices occupied by different proteins or different domains. For a given T number, the number of hexagons and pentagons remains the same, but the total surface area increases by a factor α due to additional polygons (triangles and squares). Such expanded lattices can be constructed with the alpha option.
The cage is centered at (0,0,0). It is created as a marker model unless mesh true is used to specify a surface model instead. Hexagons are bent where they cross from one triangular face of the icosahedron to another, so that certain “hexagon” edges are formed by two straight segments rather than one.
Set cage size, where cage-radius is the distance from the center of the icosahedron to a 5-fold vertex (default 100.0 in physical distance units).
Set marker model stick-radius (default 1% of the cage-radius). See also: size
The type of icosahedral orientation can be:
- 222 (default) – with two-fold symmetry axes along the X, Y, and Z axes
- 2n5 – with two-fold symmetry along X and 5-fold along Z
- n25 – with two-fold symmetry along Y and 5-fold along Z
- 2n3 – with two-fold symmetry along X and 3-fold along Z
- 222r – same as 222 except rotated 90° about Z
- 2n5r – same as 2n5 except rotated 180° about Y
- n25r – same as n25 except rotated 180° about X
- 2n3r – same as 2n3 except rotated 180° about Y
Specify the the weight of the sphere component in an interpolation between an icosahedron and a sphere of equal radius. The sphere factor f ranges from 0.0 (default, icosahedron) to 1.0 (sphere). The interpolation only involves vertex positions and will not generate curved mesh lines.
Capsids in which the vertices are occupied by different proteins or domains (rather than identical asymmetric units) may form expanded versions of the lattices, as described in:The missing tailed phages: Prediction of small capsid candidates. Luque A, Benler S, Lee DY, Brown C, White S. Microorganisms. 2020 Dec 8;8(12):1944.
Structural puzzles in virology solved with an overarching icosahedral design principle. Twarock R, Luque A. Nat Commun. 2019 Sep 27;10(1):4414.
The alpha option allows creating such expanded lattices, with choices for alphatype (see Fig. 2 in the paper):
Thanks to the Luque Lab at San Diego State University for developing the code for this option, with funding from the NSF.
- hexagonal (default)
Specify a color for the cage model (default white).
mesh true | false
Whether to create a wire-mesh surface model instead of a marker model. If a surface model is created, a marker model can be generated from it later with the command marker fromMesh.
replace true | false
Whether to replace an existing hkcage model with the new one rather than opening an additional model.