Optimal design of frustrated self assembly building blocks

Nature's ability to organize building blocks into large structures of finite size has inspired many researchers to attempt similar constructs with synthetic subunits. DNA origami triangles are such synthetically built subunits capable to self assemble to shells of various shapes.

Subunits and their interactions are typically designed so that they match the target shell geometry as much as possible. Such designs, however, require an increasing number of subunit types as the target shell complexity increases.

Instead, we propose a computational scheme aimed to reduce the required subunit specificity in such assemblies, by relaxing the exact geometrical constraints on the target surface and exploiting subunit deformability.

Two example structures will be considered, in both of which subunits are triangular and the assembly is stress mediated. The first one is an icosahedral structure of either of two sizes, both in a mechanically stressed state.

Our aim is to find the appropriate subunit design which assembles both sizes with prescribed yields, from a single type of subunits, by adjusting the subunit's mechanical properties. The second structure is an ellipsoidal shell, which, again, we aim to assemble from a single species of subunits.

Finite compliance allows subunits to adapt to the local geometry and coordination, however, the associated frustration raises the problem of controling long range elastic interactions and rules out naive subunit designs.

As a solution, we propose an optimization approach to efficiently adjust the subunits' mechanical properties until a target free energy minimum is reached at the required sizes and shapes.

We use a coarse grained triangle model with a grand canonical Monte Carlo scheme for equilibrium and dynamical simulations.

Progressing from the fastest towards the most accurate estimates of the free energy we intend to provide a full stack methodology for finding the most optimal subunit parameters given a target structure.