Physical models of properties and structure of viral capsids
Date
2020Abstract
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.