Self-assembly of knots and links

E Orlandini and G Polles and D Marenduzzo and C Micheletti, JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 034003 (2017).

DOI: 10.1088/1742-5468/aa5bb5

Guiding the self-assembly of identical building blocks towards complex three-dimensional structures with a set of desired properties is a major goal in material science, chemistry and physics. A particularly challenging problem, especially explored in synthetic chemistry, is that of self-assembling closed structures with a target topology starting by simple geometrical templates. Here we overview and revisit recent advancements, based on stochastic simulations, where the geometry of rigid helical templates with functionalised sticky ends has been designed for self-assembling efficiently and reproducibly into a wide range of three-dimensional closed structures. Notably, these include non trivial topologies of links and knots, including the 819 knot that we had predicted to be highly encodable and that has only recently been obtained experimentally. By appropriately tuning the parameters that define the template shape, we show that, for fixed concentration of templates, the assembly process can be directed towards the formation of specific knotted and linked structures such as the trefoils, pentafoil knots, Hopf and Solomon links. More exotic and unexpected knots and links are also found. Our results should be relevant to the design of new protocols that can both increase and broaden the population of synthetise molecular knots and catenanes.

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