各種病毒的串珠模型

去年(2019 Spring semester)一組學生製作了四種不同型態的病毒模型：一般常見的二十面體病毒結構（Icosahedral virus）、菸草花葉病毒（Tobacco Mosaic virus）、HIV病毒、噬菌體（bateriaphage）。



還有另一組製作了另一種設計的噬菌體。



當時新冠病毒尚未流行，沒人想到要做一個模型。（Molecular Aesthetics 2019）

Bead model of coronavirus (SARS-CoV-2)

A group of students in my class, "Molecular Aesthetics", is working on a bead model of coronavirus(SARS-CoV-2). They adopt (8,0)-Goldberg polyhedron for the envelop with 60 spikes distributed on the surface. I hope they can complete it next week.

Dendritic structures

Mr. Horibe made a number of dendritic fullerenes which are similar to the Kepler's stellated polyhedrons. By using the Euler theorem, it is quite straightforward to show that, in a cage-like fullerene without hole, N₅-N₇=12, where N₅ and N₇ are the number of pentagons and heptagons, respectively. In the typical fullerenes where the local Gaussian curvature is positive everywhere, we should have N₇=0. The total number of pentagons is 12. Another way to put it is to introduce the so-called topological charge, 1 for a pentagon and -1 for a heptagon. So the topological charge of a cage-like fullerene is 12.

Heptagons always generate a negative Gaussian curvature. For a cage-like fullerene, whenever we introduce an extra heptagon, we have to include a pentagon in order to satisfy the identity N₅-N₇=12.

One can replace a pentagon in a Goldberg icosahedron (icosahedral fullerene) by 6 pentagons (a hemisphere of C20) and 5 heptagons to get a spike. So the topological for this area is still 1 after replacement. Similarly, we can do the same replacement for all other 11 pentagons to get a dendritic structure.



Of course, we can use the same kind of trick to "grow" a spike (a carbon nanotube endcapped with the hemisphere of a C₂₀) along the normal direction of any pentagon on any kind of graphitic structure.

Incidentally, this structure without the C20 caps is just the inner part of the high-genus fullerenes we have done before.

Yet another beaded virus

Beaded Virus

In all of the high-genus fullerenes, the structures of inner parts are covered by an outer sheet. It is difficult to see the organization of beads inside. In the following few photos, I gave the inner-layer structures of a high-genus fullerene at several different stages of construction. The first figure shows the HG-fullerene with only inner part. It is astonishing that this molecule has such a resemblance to a virus.

With a careful examination, one can see the inner part consists essentially of twelve necks arranged on the surface of a dodecahedron. More importantly, these necks are nothing but the inner-rim of a toroidal carbon nanotube with 120 carbon atoms (T120), which is my favorite molecule. So a simple counting indicates that this structure should have 12*10=120 heptagons in all necks. To weave this structure, I have used about 3 fishing threads with a length about 3.5 m. Of course, by a carefully designed weaving sequence, one can in principle use only one fishing thread to make the whole structure.

From Beaded Virus

From Beaded Virus

From Beaded Virus

From Beaded Virus

From Beaded Virus

From Beaded Virus