Models of topologically-complex self-assembling systems

The design and realization of supramolecular systems with complex topology is an active area of research in physics, chemistry and material science. These systems offers many promising applications, from molecular synthesis to switchable surfaces and nanomachines. Despite this, their realization is still quite challenging in many aspects. In this Thesis, we show how suitably designed theoretical and computational models can help overcome these challenges. First, we present a minimal model for the self-assembly of knotted constructs, where a single building block can be used to assemble more than one knotted geometry, by simply changing the system concentration. The study of this model allows to draw general conclusions which can help the design of self-assemblies with tunable multiple targets. Next, we develop a general strategy for the design, using DNA origami techniques, of mesoscopic building blocks which assemble into topologically-complex structures. In particular, as a first step in this endeavour, we target the realization of a trefoil knot. Finally, we describe a model system which assemble Olympic gels, networks of linked ring polymers whose realization has been so far very challenging. The structural and mechanical properties of the gel are then studied in details, highlighting the role played by mechanical bonding and topological connectivity. We conclude by studying the pore translocation of an exoribonucleases-resistant RNA, to investigate the relations between its three-dimensional structure and its remarkable mechanical features.