A Ginzburg-Landau model for the expansion of a dodecahedral viral capsid

TL;DR

This paper introduces a Ginzburg-Landau model to describe the expansion of dodecahedral viral capsids, focusing on symmetry-breaking transitions and their implications for viral maturation.

Contribution

It develops a symmetry-based energy expansion for capsid deformation, classifies minima, and predicts that expansion generally preserves icosahedral symmetry.

Findings

Expansion typically results in icosahedral symmetry breaking.

The model predicts a unique transition from closed to expanded form.

The approach highlights the role of symmetry in capsid conformational changes.

Abstract

We propose a Ginzburg-Landau model for the expansion of a dodecahedral viral capsid during infection or maturation. The capsid is described as a dodecahedron whose faces, meant to model rigid capsomers, are free to move independent of each other, and has therefore twelve degrees of freedom. We assume that the energy of the system is a function of the twelve variables with icosahedral symmetry. Using techniques of the theory of invariants, we expand the energy as the sum of invariant polynomials up to fourth order, and classify its minima in dependence of the coefficients of the Ginzburg-Landau expansion. Possible conformational changes of the capsid correspond to symmetry breaking of the equilibrium closed form. The results suggest that the only generic transition from the closed state leads to icosahedral expanded form. Our approach does not allow to study the expansion pathway, which is likely to be non-icosahedral.