Statistical analysis of sizes and shapes of virus capsids and their resulting elastic properties
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Statistical analysis of sizes and shapes of virus capsids and their resulting elastic properties Anže Lošdorfer Božiˇc · Antonio Šiber · Rudolf Podgornik
Received: 3 December 2012 / Accepted: 20 January 2013 / Published online: 1 March 2013 © Springer Science+Business Media Dordrecht 2013
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. Keywords Capsid · Virus · Geometry · Icosahedron · Faceting · Elasticity
A. Lošdorfer Božiˇc (B) · R. Podgornik Department of Theoretical Physics, Jožef Stefan Institute, 1000 Ljubljana, Slovenia e-mail: [email protected] A. Šiber Institute of Physics, 10001 Zagreb, Croatia R. Podgornik Department of Physics, Faculty of Mathematics and Physics, 1000 Ljubljana, Slovenia
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1 Introduction Viruses are the most abundant source of DNA and proteins in Earth’s oceans, which contain on the order of 1030 virions [1]. Yet their status as living entities is often called into question as they do not conform to the “self-reproduction with variations” standard [2]. It appears that much of their features can be understood in terms of thermodynamic equilibrium physics [3–5], especially when they are “dormant”, i.e. outside the cells which they infect, where they in fact turn into little more than very complicated macromolecules with a “life cycle” [6]. The fact that many features of their life cycle can be understood within the equilibrium fram
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