A precise packing sequence for self-assembled convex structures.

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, and 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 convexity constraints, including an initial spherical convexity constraint for moderate- and large-sized clusters. 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 capsids obtained in vivo. Our findings suggest that this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.