Viruses are effective carriers of information. This information is called RNA (sort of like single stranded DNA), which is held in a *vessel* called the capsid. As it is favourable for the virus to be as efficient as possible, the capsid is made up of a repeating structure of proteins, which is coded by the RNA which it holds. Due to this repeating structure, the capsid has **rotational symmetry**.

These constraints on the organisation of the capsid proteins mean that they can only have helical or spherical structures. Thus, there are only a finite number of symmetries that they can have in 3-dimensions, which are embodied by the Platonic Solids.

Most viruses exhibit icosahedral symmetry, meaning they have the same properties as the icosahedron:

- formed of 20 triangles
- 60 rotational symmetries

Source: Wikipedia

Another example is the common cold and HPV (Human papillomavirus), which are both caused by viruses of different sizes, but have the same symmetry: 6-fold rotational symmetry.

HPV | Source: Wikipedia

However, a more interesting group of viruses are those with 5-fold symmetry, as the structure of these is much harder to determine.

**Structure via Symmetry**

Symmetry is the key to finding the structure of a viruses, and as they are too small to see in microscopes, their structure can be determined using a technique called Cryo-electon microscopy, which is a bit like unfolding the shape and laying it out flat.

Cryo-EM of Venezuelan Equine Encephalitis | Source: fromthelabs.bcm.edu

For structures with a 5-fold symmetry axis, this technique is almost impossible to use. An analogy of this is “t*rying to tile a bathroom floor: it is possible with hexagons but not with pentagons.” *This mathematical phenomenon means that it is therefore necessary to know the overall symmetry of structures with 5-fold symmetries before their structure can be determined using cryo-EM.

**But what is the reason for all this symmetry?**

*“Symmetry goes hand in hand with stability. Symmetric configurations are usually more stable, a feature that is important for viruses when transporting their genomic material between hosts.”*

Source

A bit of a different topic today. Let me know if you like it! M x