A Precise Packing Sequence for Self-Assembled Convex Structures

TL;DR

This paper reveals a precise packing sequence in self-assembled convex structures, showing how cone-shaped particles form specific clusters with robust, unique arrangements, which relate to virus capsid structures and are driven by free energy minimization.

Contribution

It demonstrates a universal packing sequence in self-assembly of convex structures, linking it to virus capsid formations and extending models to simple sphere systems.

Findings

Clusters of specific sizes have unique, robust structures.

The packing sequence matches virus capsid structures.

Sequence is driven by free energy minimization under convexity constraints.

Abstract

Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters comprised of particular numbers of cones (e.g. 4 - 17, 20, 27, 32, 42) have a unique and precisely packed structure that is robust over a range of cone angles. These precise clusters form a sequence of structures at specific cluster sizes- a precise packing sequence - that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres. We further show that this sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to certain convexity constraints. This sequence contains six of the most common virus capsid structures obtained in vivo including large chiral clusters, and a cluster that may correspond to several non-icosahedral, spherical virus capsid structures obtained in vivo. Our findings suggest this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.