Size control and escape mechanisms in geometrically frustrated assemblies

The self-limited assembly (SLA) of building blocks into structures with large, but well-defined finite sizes, is an essential capability of biological systems. Developing human-engineered building blocks with a similar ability to undergo SLA is of great interest in nanotechnology. Recently, it has been theoretically proposed that SLA can be achieved through ‘geometric frustration’, in which the preferred local packing of subunits is incompatible with their preferred large-scale assembly structure.

In this talk we describe simulations of geometrically frustrated assembly motivated by ongoing experiments on DNA origami building blocks. We consider triangular subunits that self-assemble into a hexagonal array, but have interaction geometries that favor formation of catenoid structures. The resulting negative Gaussian curvature is incompatible with hexagonal order, leading to geometric frustration. We use dynamic MC simulations and free energy calculations to demonstrate that this incompatibility leads to equilibrium SLA in some parameter regimes, and identify mechanisms by which the system escapes self-limitation in other regimes.