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Design principles for rapid folding of knotted DNA nanostructures.

Kočar V, Schreck JS, Čeru S, Gradišar H, Bašić N, Pisanski T, Doye JP, Jerala R - Nat Commun (2016)

Bottom Line: 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.This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins.

View Article: PubMed Central - PubMed

Affiliation: Department of Biotechnology, National Institute of Chemistry, Hajdrihova 19, Ljubljana 1000, Slovenia.

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.

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FFS simulations of a designed P1 folding pathway using the oxDNA model.For each connection-forming step, we report three measured quantities, a representative simulation structure and its schematic representation.  is the relative rate of formation of the first base pair in the sampled ith connection. The term  denotes the probability that the formation of the first base pair leads to the successful completion of the ith edge relative to that of the first edge. Multiplication of these two quantities yields the relative rate of forming the ith connection . Domains that require the threading of longer tails through a loop are marked with an asterisk (*), whereas the domains that require the threading of shorter tails are marked with a hashtag (#). Black arrows indicate properly formed connections. Coloured arrows indicate the upcoming connection-forming step in the designed folding pathway. It is noteworthy that although a single pathway is considered, owing to the similar thermodynamic stabilities of the Aa and Bb, and Gg and Hh module pairs, pathways where their order of formation is reversed are also likely to play a significant role. Importantly, these alternative pathways also comply with the free-end rules.
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f2: FFS simulations of a designed P1 folding pathway using the oxDNA model.For each connection-forming step, we report three measured quantities, a representative simulation structure and its schematic representation. is the relative rate of formation of the first base pair in the sampled ith connection. The term denotes the probability that the formation of the first base pair leads to the successful completion of the ith edge relative to that of the first edge. Multiplication of these two quantities yields the relative rate of forming the ith connection . Domains that require the threading of longer tails through a loop are marked with an asterisk (*), whereas the domains that require the threading of shorter tails are marked with a hashtag (#). Black arrows indicate properly formed connections. Coloured arrows indicate the upcoming connection-forming step in the designed folding pathway. It is noteworthy that although a single pathway is considered, owing to the similar thermodynamic stabilities of the Aa and Bb, and Gg and Hh module pairs, pathways where their order of formation is reversed are also likely to play a significant role. Importantly, these alternative pathways also comply with the free-end rules.

Mentions: Initially, we designed the folding to proceed from the centre of the chain towards the 3′-terminus (Aa→Dd), followed by the threading of the remaining unbound 5′-terminus through the partially folded pyramid (P0; Supplementary Fig. 3a). However, simulations revealed a kinetic bottleneck (observe the small relative rate of forming the 5th connection in Supplementary Fig. 4) caused by the difficulty of threading a long tail through a small loop, which we believe was the most probable cause for experimentally observed lower efficiencies of folding P0 (Supplementary Fig. 3b,c). The subsequently optimized P1 design (Fig. 2) implemented an ‘inside-out' folding strategy in which the longer tails were threaded earlier in the folding process. In addition, the lengths of the free 3′- and 5′-termini were minimized by designing the folding pathway symmetrically around the middle of the chain (refer to P1 in Fig. 3a). The corresponding FFS simulations demonstrated that generally increased as the folding progressed, demonstrating cooperativity as a result of the progressively preorganized structure37.


Design principles for rapid folding of knotted DNA nanostructures.

Kočar V, Schreck JS, Čeru S, Gradišar H, Bašić N, Pisanski T, Doye JP, Jerala R - Nat Commun (2016)

FFS simulations of a designed P1 folding pathway using the oxDNA model.For each connection-forming step, we report three measured quantities, a representative simulation structure and its schematic representation.  is the relative rate of formation of the first base pair in the sampled ith connection. The term  denotes the probability that the formation of the first base pair leads to the successful completion of the ith edge relative to that of the first edge. Multiplication of these two quantities yields the relative rate of forming the ith connection . Domains that require the threading of longer tails through a loop are marked with an asterisk (*), whereas the domains that require the threading of shorter tails are marked with a hashtag (#). Black arrows indicate properly formed connections. Coloured arrows indicate the upcoming connection-forming step in the designed folding pathway. It is noteworthy that although a single pathway is considered, owing to the similar thermodynamic stabilities of the Aa and Bb, and Gg and Hh module pairs, pathways where their order of formation is reversed are also likely to play a significant role. Importantly, these alternative pathways also comply with the free-end rules.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759626&req=5

f2: FFS simulations of a designed P1 folding pathway using the oxDNA model.For each connection-forming step, we report three measured quantities, a representative simulation structure and its schematic representation. is the relative rate of formation of the first base pair in the sampled ith connection. The term denotes the probability that the formation of the first base pair leads to the successful completion of the ith edge relative to that of the first edge. Multiplication of these two quantities yields the relative rate of forming the ith connection . Domains that require the threading of longer tails through a loop are marked with an asterisk (*), whereas the domains that require the threading of shorter tails are marked with a hashtag (#). Black arrows indicate properly formed connections. Coloured arrows indicate the upcoming connection-forming step in the designed folding pathway. It is noteworthy that although a single pathway is considered, owing to the similar thermodynamic stabilities of the Aa and Bb, and Gg and Hh module pairs, pathways where their order of formation is reversed are also likely to play a significant role. Importantly, these alternative pathways also comply with the free-end rules.
Mentions: Initially, we designed the folding to proceed from the centre of the chain towards the 3′-terminus (Aa→Dd), followed by the threading of the remaining unbound 5′-terminus through the partially folded pyramid (P0; Supplementary Fig. 3a). However, simulations revealed a kinetic bottleneck (observe the small relative rate of forming the 5th connection in Supplementary Fig. 4) caused by the difficulty of threading a long tail through a small loop, which we believe was the most probable cause for experimentally observed lower efficiencies of folding P0 (Supplementary Fig. 3b,c). The subsequently optimized P1 design (Fig. 2) implemented an ‘inside-out' folding strategy in which the longer tails were threaded earlier in the folding process. In addition, the lengths of the free 3′- and 5′-termini were minimized by designing the folding pathway symmetrically around the middle of the chain (refer to P1 in Fig. 3a). The corresponding FFS simulations demonstrated that generally increased as the folding progressed, demonstrating cooperativity as a result of the progressively preorganized structure37.

Bottom Line: 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.This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins.

View Article: PubMed Central - PubMed

Affiliation: Department of Biotechnology, National Institute of Chemistry, Hajdrihova 19, Ljubljana 1000, Slovenia.

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.

Show MeSH
Related in: MedlinePlus