Design principles for rapid folding of knotted DNA nanostructures

Vid Kočar,Nino Bašić,Slavko Čeru,Helena Gradišar,Roman Jerala,Tomaž Pisanski,John S Schreck,Jonathan P K Doye

doi:10.1038/ncomms10803

Abstract

Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the ‘free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins.

Highlights

Knots are some of the most remarkable topological features in nature
Folding of DNA square pyramids composed of the same modules and encoding the same topology revealed that only the design with the folding pathway designed according to the ‘free-end’ rule folds efficiently into the target structure
The successful folding of designed single-chain DNA into a highly knotted target implies that the predicted folding pathways make a dominant contribution to the actual ensemble of folding pathways, and that differences in the sequential arrangements of modules with respect to stability can be used to guide the folding pathway

Summary

Introduction

Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the ‘free-end’ rule folds efficiently into the target structure. Besides the need for the target structure to possess favourable thermodynamic properties, kinetic features of the energy landscape, which affect the rate of folding and the ability to attain complex folds, should be considered[3] One such example is the formation of knots, which are intricate topological features with important natural and technological implications. Folding of DNA square pyramids composed of the same modules and encoding the same topology revealed that only the design with the folding pathway designed according to the ‘free-end’ rule folds efficiently into the target structure. Besides high folding yields on slow annealing, this design folds rapidly on temperature quenching and dilution from chemical denaturant

Methods

Results

Conclusion