Landau Theory and the Emergence of Chirality in Viral Capsids

TL;DR

This paper develops a generalized Landau theory to explain how chiral and achiral icosahedral structures emerge and transition in viral capsids on spherical surfaces, aligning with recent simulations.

Contribution

It introduces a Landau-Brazovskii framework for modeling symmetry transitions in viral capsids, highlighting the conditions for chiral and achiral icosahedral structures.

Findings

Achiral density modulations with icosahedral symmetry occur via first-order transitions.

Stable chiral icosahedral structures emerge through continuous or weakly first-order transitions.

Theoretical predictions align with recent numerical simulation results.

Abstract

We present a generalized Landau-Brazovskii theory for the solidification of chiral molecules on a spherical surface. With increasing sphere radius one encounters first intervals where robust achiral density modulations appear with icosahedral symmetry via first-order transitions. Next, one en- counters intervals where fragile but stable icosahedral structures still can be constructed but only by superposition of multiple irreducible representations. Chiral icoshedral structures appear via continuous or very weakly first-order transitions. Outside these parameter intervals, icosahedral symmetry is broken along a three-fold axis or a five-fold axis. The predictions of the theory are compared with recent numerical simulations.