HIV Fullerene Cones

The hexagons in this sculpture are 1 1/4 inch hexagon stainless steel tiles from Susan Jablon Mosaics. The pentagons are formed from wood, the substrate is plaster, MDF and steel.

This sculpture is a model of a HIV-1 viron which has the shape of a buckminsterfullerene cone, a stretched out truncated icosahedron. The HIV-1 virons are not identical but all have the common characteristic of having 12 pentagon faces, 7 at one end and 5 at another. This specific fullerene cone is taken directly from the research results of Ganser, et al (1999); it has 1,572 proteins, three at each vertex or point. Each group of three proteins has a bond with three other groups of protein. Geometrically, these bonds are interpreted as edges of polygons, 252 are hexagons and 12 are pentagons as shown below in an interactive graphic.

Usage: Mouse or finger will move the virus. A swipe of mouse or finger off the graphic will leave the virus spinning. A click or touch will stop the spin. A Ctrl+click or two-finger touch will toggle the rendering from wireframe to solid to points.

The next sculptures in the fullerene series were made with 1" white ceramic hexagon tiles along with 12 plastic pentagons created on a 3D printer. There are four sculptures in this set representing each of the HIV-1 structures provided by Ganser et al (1999).

The Science

A virus has many different components. At a basic level a distinction must be made regarding the structure of the viral envelope and the structure of the viral core contained within. The shape of the HIV envelope has been studied for a many years using a variety of techniques. In the 1990s, the envelope was thought to be icosahedral or at least had icosahedral symmetry properties. More more recently, the envelope has been described as being spherical.
Within the envelope is the HIV viron or capsid, the shape of the capsid is an elongated buckminsterfullerene cone, which looks like a stretched version of a truncated icosahedron or soccer ball. [1,2]

Source: [3] Yeager, Mark (2011).

Geometric and computational analysis are among a myriad of techniques used to determine the structure HIV-1 capsid. The distribution of actual and predicted dihedral angles between hexamer faces provides some important insights.[3] With a geometric characterization of the shape providing a reference point the attention can be focused on the atomic level interactions between proteins.[4] Recently, scientists have been able to computational simulate each of 64 million atoms comprising an HIV virus.[5]

The Structure

A polyhedral net for each of the four cones is available to download. These nets are constructed to fit 1 inch hexagons, but can be printed at different scales. Ideally, the net would be printed on a wide printer, otherwise, if printed on 8x11 inch paper it will require about 12 pages which will need to be taped together. The result will look similar to this:

Download a polyhedral net for any of the four fullerene cones:

1. Cone 1-e Net
2. Cone 2 Net
3. Cone 3 Net
4. Cone 4 Net

Each net can be used to create two different viral structures by using both sides of the net; in the first case the printed side is on the outside, in the other case the print is on the inside. The Cone1 above is denoted with an 'e' indicating that it is the enantiomer or mirror image of the viral structure I originally obtained. Enantiomers are non-superposable (not identical), just like as one's left and right hands are the same except different.

Once the fullerene cones are cut, folded and taped together they can be filled with foam (a tricky and sticky endeavor), or painted with clear epoxy. Gorilla Glue has worked well for adhering tiles to the paper cones because it foams up and can fill gaps and small spaces.

To read more about how the first fullerene sculpture was made click here. The next sculpture in the fullerene series will be covered with circuit boards as part of the Computer Virus Sculpture series.

References