Magic Sizes Enable Minimal-Complexity High-Fidelity Assembly of Programmable Shells

Area of Science:

• Supramolecular chemistry and materials science
• Computational modeling of self-assembly processes

Background:

• Advances in synthetic methods allow for the design of subunits for self-assembly into precise structures.
• Off-target metastable structures often reduce yields in self-assembly processes.
• Increasing subunit complexity can improve fidelity but slows kinetics and increases costs.

Purpose of the Study:

• To identify design principles for maximizing target yield and minimizing complexity in self-assembling icosahedral shells.
• To explore the relationship between subunit complexity, symmetry, and assembly fidelity.
• To develop a generalizable principle for robust high-fidelity self-assembly.

Main Methods:

• Utilized a symmetry-based construction to create designs of varying complexity, from maximal symmetry to zero symmetry.
• Employed Kinetic Monte Carlo simulations to analyze defect formation and identify causes of off-target assemblies.
• Derived rules based on symmetry to optimize designs for high-fidelity assembly.

Main Results:

• Identified disclinations at rotational symmetry sites as the primary defects leading to off-target assemblies.
• Developed symmetry-based rules for selecting optimal designs that inhibit disclinations, achieving high-fidelity assembly.
• Discovered non-monotonic variation of optimal complexity with target size, with 'magic' sizes for high-symmetry designs.
• Optimal designs at magic sizes require significantly fewer interaction types, reducing assembly time and cost.

Conclusions:

• Symmetry-based design principles can guide the selection of optimal subunit complexity for robust, high-fidelity self-assembly.
• This approach enables the assembly of large, precise finite structures with reduced synthesis complexity and cost.
• The derived principles are generalizable to diverse architectures and topologies beyond icosahedral shells.