Molecular tiling and DNA self-assembly

We examine hypotheses coming from the physical world and address new mathematical issues on tiling. We hope to bring to the attention of mathematicians the way that chemists use tiling in nanotechnology, where the aim is to propose building blocks and experimental protocols suitable for the construction of 1D, 2D and 3D macromolecular assembly. We shall especially concentrate on DNA nanotechnology, which has been demonstrated in recent years to be the most effective programmable self-assembly system. Here, the controlled construction of supramolecular assemblies containing components of fixed sizes and shapes is the principal objective. We shall spell out the algorithmic properties and combinatorial constraints of "physical protocols", to bring the working hypotheses of chemists closer to a mathematical formulation.