Self-limited filaments via programmable geometrically-frustrated assembly

Geometrically frustrated assembly occurs when local subunit interactions are naturally misfitting, causing subunits to deform in order to bind and leading to an accumulation of intra-assembly strain. This assembly archetype has been invoked to explain the formation of structures in various soft materials, including the formation of fibrin filaments, the crystallization of colloidal particles on curved membranes, and the packing of non-space-filling shapes (e.g., tetrahedra). However, to date, geometrical frustration has rarely been used to intentionally design assemblies. In this talk, I will describe the deliberate design of curved subunits that are geometrically frustrated, creating finite-sized, self-limiting stacks. We use DNA origami to create small arcs, called curvamers, that can bind to themselves to create one-dimensional assemblies. Because all curvamers share the same radius of curvature, their binding forces the subunits to adopt a new curvature within the assemblies. By tuning the preferred curvature of the curvamers, as well as their inter-subunit binding strength, we investigate the conditions under which stacks become self-limited or assemblies escape frustration to form unbounded structures.