Fig. 1: Geometric frustration in a DNA metastructure.
From: Realizing mechanical frustration at the nanoscale using DNA origami
a Interactions of electronic spins (red arrows) lead to a stable (ferromagnetic) state in a square arrangement, while a triangular design cannot minimize the energy (anti-ferromagnetic). The spins in the Kagome lattice exhibit complex magnetic frustration behaviors. b Electronic spin can be replaced by mechanical strain in two distinct deformation modes. Interactions between neighboring building blocks lead to adaptability (cooperative deformation) or inadaptability (frustration due to conflicting deformation). Both modes differ geometrically only in the orientation of a unit cell. c Schematic of theoretical DNA origami design combining both modes into a single lattice, with edges made of 84-nt-long 2HB DNA. The edges highlighted in red, blue, and green can serve as actuators (DNA jacks). d, e Activating the red edge in conjunction with green steers the structure into the adaptable state (d), while blue and red together lead to the inadaptable state (e). f, g MD simulated conformations of adaptable and inadaptable DNA. The structures are colored based on internal forces, with blue indicating compression and red indicating extension. h Free energy profiles of adaptable and inadaptable modes using umbrella sampling. The x-axis is the distance of the edges indicated by green and blue arrows in (f and g).
