A periodic table of molecular knots

Consider a short piece of rope—could you guess which knots are more likely to form if you crumple and shake it? Synthetic chemists have long been working on a molecular version of this problem, and so far, have succeeded at synthesizing a half-dozen knot types using molecular self-assembling techniques. But which other knot types could be realized in the future? This is the challenging question that SISSA scientists, in association with the University of Padua, have tackled using computer simulations in this new work published in Nature Communications.

The scientists identified a shortlist, a kind of “periodic table” of the most designable knot types, i.e. those knots that could easily self-assemble under appropriate physical and chemical conditions. The findings, obtained with computational predictive models, are supported by the latest experimental results and ought to aid the synthesis of as yet undiscovered topologies. This study and the increasingly predictive capability of molecular modeling techniques can create novel possibilities for future advanced applications, like the construction of sophisticated molecular machines for loading and delivering nanoscale cargo.

Not just an intellectual challenge

“There is a growing scientific interest in complex molecules. In this context, the possibility to design and synthesize novel types of molecular knots is particularly appealing,” says Mattia Marenda, first author of this research.

“Until recently, only a few types of molecular knots had been synthesized. These were the simplest knots in mathematic tables, i.e. those having at most 5 essential crossings.” One could have thus predicted that the next knot type to be synthesized would have had six crossings. However, in a computational study of 2015, co-author Cristian Micheletti and collaborators argued that the simplest and most designable undiscovered knot type was significantly more complex and featured as many as eight essential crossings. This prediction was experimentally confirmed in 2017 and motivated the current study, which employed a more systematic exploration of the shapes or configurations that can be formed from identical building blocks stitched together in a string-like fashion.

“With these models, we aimed at discovering which new molecular knots types, if any, would be easiest to obtain with current synthetic chemistry techniques, particularly self-assembly. We found that these privileged knot types do exist, but are very rare. Only a dozen different topologies are realizable among millions of simple knot types. The results of our models had an inherent simplicity,” says Marenda. “The molecular weaving of these knot types is modular and highly symmetric. We used these features as selection criteria to sift the huge combinatorial space of molecular weaving patterns and obtained a shortlist of knot types expected to be easily assembled from few identical building blocks.”

Read more: A periodic table of molecular knots

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