Discovering privileged topologies of molecular knots with self-assembling models

Abstract

Despite the several available strategies to build complex supramolecular constructs, only a handful of different molecular knots have been synthesised so far. Here, in response to the quest for further designable topologies, we use Monte Carlo sampling and molecular dynamics simulations, informed by general principles of supramolecular assembly, as a discovery tool for thermodynamically and kinetically accessible knot types made of helical templates. By combining this approach with the exhaustive enumeration of molecular braiding patterns applicable to more general template geometries, we find that only few selected shapes have the closed, symmetric and quasi-planar character typical of synthetic knots. The corresponding collection of admissible topologies is extremely restricted. It covers all known molecular knots but it especially includes a limited set of novel complex ones that have not yet been obtained experimentally, such as 10124 and 15n41185, making them privileged targets for future self-assembling experiments.

Tying different knots in a molecular strand

“…whether the stereochemistry of some strand crossings could determine the crossing orientation of others? This could allow access to molecular knots of low symmetry; a contemporary challenge for knot synthesis as the topologies prepared to date have generally relied on high symmetry self-assembly 20 of multiple building blocks [6][7][8][11][12][13][14][21][22][23][24] . Nature folds peptide chains to reach discrete 3D structures, including knots, 2,25,26 often through the assistance of chaperones that guide folding to a particular conformation through the myriad of possible pathways.…”

Piecewise-linear embeddings of knots and links with rotoinversion symmetry

“…The formation of molecular knots is currently a very active area of synthetic chemistry. We refer to recent papers for references (Marenda et al, 2018;Dang et al, 2019Dang et al, , 2020Leigh et al, 2020Leigh et al, , 2021O'Keeffe & Treacy, 2020a,b;Zhang et al, 2018). In our approach we treat the structures as being piecewise linear with straight, non-intersecting segments (edges or 'sticks'), meeting at 2-coordinated vertices (corners) (Liu et al, 2018).…”

Isogonal weavings on the sphere: knots, links, polycatenanes

“…Weavings, knots, links and related geometrical structures are currently of considerable interest in materials chemistry and biochemistry, as testified in recent reviews (Lim & Jackson, 2015;Flapan, 2015;Bruns & Stoddart, 2016;Pieters et al, 2016;Horner et al, 2016;Fielden et al, 2017) and in other recent reports (Danon et al, 2017;Wu et al, 2017;Kim et al, 2018;Zhang et al, 2018;Leigh et al, 2019;Sawada, Saito et al, 2019;Sawada, Inomata et al, 2019;Inomata et al, 2020). Suggested knots most suitable for self-assembly have recently been identified (Marenda et al, 2018). We are particularly interested in such structures from the perspective of reticular chemistry, which is concerned with the directed assembly of symmetrical frameworks from molecular components (Yaghi et al, 2003).…”

“…Reith et al, 2012). They also feature prominently in the knots most amenable to construction by molecular self-assembly (Marenda et al, 2018). Notable recently achieved molecular examples are (4,3) (Danon et al, 2017), (8,3) (Kim et al, 2018), and (7,2) and (8,2) (Inomata et al, 2020).…”