Limits of economy and fidelity for programmable assembly of size-controlled triply-periodic polyhedra

TL;DR

This paper extends symmetry principles for viral capsid assembly to programmable, size-controlled triply-periodic polyhedra, revealing a fundamental tradeoff between design economy and assembly fidelity due to topological defects.

Contribution

It introduces a symmetry-based framework for designing size-controlled crystalline assemblies and analyzes the tradeoffs between design simplicity and assembly accuracy.

Findings

Assembly efficiency is comparable to viral shells.

Optimal assembly requires intermediate flexibility in local geometry.

Topological defects arise from symmetry principles, affecting fidelity.

Abstract

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply-periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies -- in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g. periodicity) -- is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.