Construction of Stable Mesh Using Self-Assembly Chains

We study the problem of unique and stable self-assembling mesh nanostructure from short chains of molecules. Although the motivation comes from coiled-coil protein molecules, our results are applicable also to other molecules like DNA. We abstract the problem to a more general problem of periodic stable and non-ambiguous embedding of n k-link chains into a mesh. The interaction between the individual chain links is defined by an interaction matrix M. In the paper we first bound the number of different interaction matrices and then design an algorithm to check whether the set of chains defined by the matrix M uniquely and stably self-assemble into a mesh structure. Our experimental results show that for k = 2 and n = 4 there is no such embedding.