Self-Assembly of Triply-Periodic Minimal Surfaces, An “Inverted” Caspar-Klug Approach

The seminal work of Caspar and Klug paved the way to deepen our understanding of the formation of viral shells. Since then, many efforts have been put into understanding the structural properties of a wide variety of viruses. Recently, with the development of DNA nanotechnology, it has been possible to program DNA nanoparticles to self-assemble into intricate shapes by carefully designing some elemental building blocks. In this work, we are interested in studying an “inverted” Caspar-Klug problem, focussed primarily on structures with negative Gaussian curvature. More specifically, we study a family of surfaces called triply periodic minimal surfaces (TPMS). During this talk I’ll describe our efforts to discretize these surfaces using a Caspar-Klug approach. Furthermore, I’ll discuss how we can encode some simple rules on the programable matter in order to self-assemble into the desired structures. We perform Monte Carlo simulations to test the validity of the matching rules and finally touch upon the robustness of the assembled structures with the introduction of imperfections in the assembly process.