Multispecies tilings increase the accuracy in assembly of self-limited structures

The ability to design more complicated subunits for self-assembly, as seen with patchy particles or DNA origami, has opened a large space of complex structures that can be made. One subset of these structures are those with a self-limited length scale, such as spherical shells or cylinders. An interesting consequence of introducing a self-limited length scale larger than the constituent subunits is that the system becomes sensitive to thermal fluctuations, leading to nearby, off-target states in assembly outcomes. We investigate strategies for limiting off-target states from assembly by using multiple types of subunits. To study this assembly strategy we consider tubules composed of triangular monomers. Tube assembly needs at minimum a single type of subunit, where each edge of a triangular monomer has a specific binding angle with another monomer. Tubes with similar widths only differ by slight changes in these binding angles, which are accessible by thermal fluctuations. Using simulations and energetics calculations, we study how multiple species of triangular subunits increases specificity of tubule assembly. We find that the minimum number of subunits needed to achieve full specificity scales with the bending rigidity of the binding sites and the target width of the tube.