Physical models of properties and structure of viral capsids

Abstract

Los virus son los sistemas bi´ologicos m´as simples de la naturaleza, y por ello fueron los primeros en ser tratados matem´aticamente. Es fundamental obtener la mayor cantidad de informaci´on posible a trav´es de todas las ramas de la ciencia para obtener una imagen completa de sus caracter´ısticas, dadas las propiedades emergentes del conocimiento. Es por ello que las propiedades f´ısicas son tan importantes como las biol´ogicas o las qu´ımicas. En este trabajo se introducen los principales modelos f´ısicos (de autoensamblaje, cin´etica, elasticidad, etc.), con especial ´enfasis en las c´apsides icosa´edricas debido a sus propiedades de simetr´ıa. A continuaci´on, se desarrolla la base de un modelo coarse-grained de 60 unidades asim´etricas que junto a las propiedades del grupo de simetr´ıa del icosaedro nos permite calcular el n´umero de modos normal de un virus icosa´edrico sin hacer c´alculos expl´ıcitos. Tambi´en se obtiene informaci´on cualitativa del comportamiento de estos modos. Estos resultados son despu´es comparados con c´alculos reales de los modos normales del virus del Zika llevados a cabo por un grupo surcoreano [1] con buenos resultados.

Viruses are the simplest biological systems in nature, and because of that they were the first to be treated mathematically. It is fundamental to obtain as much information about them through all branches of science as possible to be able to get a full picture of their characteristics, due to the emergent properties of knowledge. Therefore, their physical properties are as important as their biological or chemical ones. We introduce some of the main physical models (self-assembly, kinetics, elasticity, etc.), with special emphasis on icosahedral capsids because of their symmetry properties. We then develop the basis of a 60 asymmetric units coarse-grained model that in conjunction with the symmetries of the icosahedral point group, allow us to calculate the number of normal modes of an icosahedral virus without making explicit calculations. We also gain some qualitative information about the behaviour of the normal modes. These results are then compared with the actual calculations of the normal modes of the Zika virus made by a South Corean reasearch group [1], with good agreement.