Statistical analysis of sizes and shapes of virus capsids and their resulting elastic properties

TL;DR

This study statistically analyzes virus capsid sizes and shapes, revealing common structural features and elastic properties, and introduces a shape fitting method to compare capsid geometries for insights into their relatedness.

Contribution

It presents a novel quantitative shape fitting procedure to analyze and compare virus capsid elastic properties and shapes, linking structural features to functional similarities.

Findings

Capsid proteins have a mean diameter of 5 nm and thickness of 3 nm.

Capsid shapes can be classified by their similarity to sphere and icosahedron.

Different viruses show similar elastic properties despite structural differences.

Abstract

From the analysis of sizes of approximately 130 small icosahedral viruses we find that there is a typical structural capsid protein, having a mean diameter of 5 nm and a mean thickness of 3 nm, with more than two thirds of the analyzed capsid proteins having thicknesses between 2 nm and 4 nm. To investigate whether, in addition to the fairly conserved geometry, capsid proteins show similarities in the way they interact with one another, we examined the shapes of the capsids in detail. We classified them numerically according to their similarity to sphere and icosahedron and an interpolating set of shapes in between, all of them obtained from the theory of elasticity of shells. In order to make a unique and straightforward connection between an idealized, numerically calculated shape of an elastic shell and a capsid, we devised a special shape fitting procedure, the outcome of which is the idealized elastic shape fitting the capsid best. Using such a procedure we performed statistical analysis of a series of virus shapes and we found similarities between the capsid elastic properties of even very different viruses. As we explain in the paper, there are both structural and functional reasons for the convergence of protein sizes and capsid elastic properties. Our work presents a specific quantitative scheme to estimate relatedness between different proteins based on the details of the (quaternary) shape they form (capsid). As such, it may provide an information complementary to the one obtained from the studies of other types of protein similarity, such as the overall composition of structural elements, topology of the folded protein backbone, and sequence similarity.