The Hidden Geometry of Viral Capsids

In the last installment, we discussed the viral genome, made up of DNA or RNA. DNA and RNA are an extremely efficient means of encoding biological instructions, but they are not robust outside of cells; strings of nucleotides fall apart quickly if they are naked out in the world. For viruses to be successful in transferring between hosts, they must protect their payloads, and a protein capsid is an elegant way to do so. So what exactly is a capsid?

The beauty of the capsid

A capsid is a shell made out of proteins that contains the nucleotide payload of a virus. The viral genome itself contains the instructions for making the proteins that form the capsid, and as the host’s cellular machinery translates those instructions into amino acids and proteins, electrostatic and hydrophobic interactions between the proteins cause them to bind together in a geometric arrangement. Because the viral genome must contain enough information to make all of the proteins that envelop it, these geometries use many copies (thousands, often) of small sets of proteins, rather than a wide array of different proteins, to form a highly symmetrical capsid.

There are two primary geometrical structures that viral proteins form: helical and icosahedral. Helical viruses produce proteins with rotational symmetry such that the proteins naturally tile in a spiralling fashion, creating a cylindrical coil with a hollow center. The center encompasses a copy of the viral genome, and thus the helical structure efficiently protects the payload with as little as a single type of protein.
A helical capsid

In contrast to the cylindrical form of helical viruses, icosahedral viruses appear spherical. In reality, they are icosahedrons-- twenty-sided structures that exhibit rotational symmetry across each edge, each triangular face, and each vertex. (Just like this Ancient Greek die.) The smallest icosahedral viruses form each triangular face of the icosahedron with three protein subunits, requiring a total of 60 proteins per capsid. Larger, more complex viruses can use many more proteins per subunit (into the thousands).

Notably, these structures are actually icosahedrons, and not cubes, pyramids, dodecahedrons, or other geometric assemblies. We suspect that the many-sided symmetry allows relatively few repeated protein components to form a tight, protective shell with stable protein-protein bonds around the nucleotide payload. (What joy to find such mathematical precision in so wild a thing!)
An icosahedral capsid


While most viruses can be categorized as either helical or icosahedral, nature abhors strict categorization, and there are a number of viruses that have unique shapes. Some of these are extensions of the basic helical or icosahedral structures; for example, geminiviruses fuse two icosahedral components to form a single, twinned capsid. Similarly, there are several types of tailed bacteriophages (viruses that infect bacteria) that have an icosahedral head on top of a helical body and a plate-like base.
A bacteriophage with an icosahedral head and helical body
Still other viruses have different shapes altogether-- the poxvirus family of viruses have large oval capsids that require hundreds of distinct proteins. Human immunodeficiency virus (HIV) uses a single, repeated protein to assemble its capsid, but that protein has a flexible arm that allows for asymmetry in the capsid, resulting in an oblong conical shape that is distinctive among viruses.

So, to recap-- a virus is a submicroscopic intracellular parasite that must rely on a host to replicate, and it does so by enclosing a nucleotide payload in a protein capsid. There is another component to many viruses that we haven’t discussed in detail yet: a lipid envelope, which is critical for viruses escaping cells and infecting hosts. We’ll discuss that more in the next installment.



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