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Compactness determines the success of cube and octahedron self-assembly.

Azam A, Leong TG, Zarafshar AM, Gracias DH - PLoS ONE (2009)

Bottom Line: The success of the self-assembly process was determined by measuring the yield and classifying the defects.Our observation of increased self-assembly success with decreased radius of gyration and increased topological connectivity resembles theoretical models that describe the role of compactness in protein folding.Apart from being intellectually intriguing, the findings could enable the assembly of more complicated polyhedral structures (e.g. dodecahedra) by allowing a priori selection of a net that might self-assemble with high yields.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD, USA.

ABSTRACT
Nature utilizes self-assembly to fabricate structures on length scales ranging from the atomic to the macro scale. Self-assembly has emerged as a paradigm in engineering that enables the highly parallel fabrication of complex, and often three-dimensional, structures from basic building blocks. Although there have been several demonstrations of this self-assembly fabrication process, rules that govern a priori design, yield and defect tolerance remain unknown. In this paper, we have designed the first model experimental system for systematically analyzing the influence of geometry on the self-assembly of 200 and 500 microm cubes and octahedra from tethered, multi-component, two-dimensional (2D) nets. We examined the self-assembly of all eleven 2D nets that can fold into cubes and octahedra, and we observed striking correlations between the compactness of the nets and the success of the assembly. Two measures of compactness were used for the nets: the number of vertex or topological connections and the radius of gyration. The success of the self-assembly process was determined by measuring the yield and classifying the defects. Our observation of increased self-assembly success with decreased radius of gyration and increased topological connectivity resembles theoretical models that describe the role of compactness in protein folding. Because of the differences in size and scale between our system and the protein folding system, we postulate that this hypothesis may be more universal to self-assembling systems in general. Apart from being intellectually intriguing, the findings could enable the assembly of more complicated polyhedral structures (e.g. dodecahedra) by allowing a priori selection of a net that might self-assemble with high yields.

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Cube folding dynamics and octahedral conformations.Two distinct folding dynamics during self-assembly were observed for cube nets: (A) net 5 follows pathway 1 and (B) net 3 follows pathway 2. Pathway 1 was characterized by independent folding of two clearly distinguishable sections of the net, which came together when the central hinge folded. Nets following pathway 2 have different folding rates for different sections of the net. Octahedron nets can fold into (C) non-convex boat-shaped or (D) regular octahedra.
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pone-0004451-g004: Cube folding dynamics and octahedral conformations.Two distinct folding dynamics during self-assembly were observed for cube nets: (A) net 5 follows pathway 1 and (B) net 3 follows pathway 2. Pathway 1 was characterized by independent folding of two clearly distinguishable sections of the net, which came together when the central hinge folded. Nets following pathway 2 have different folding rates for different sections of the net. Octahedron nets can fold into (C) non-convex boat-shaped or (D) regular octahedra.

Mentions: For the cubes, we observed that each of the 11 nets folded by one of two distinct pathways (Fig. 4 A–B). The first pathway involved two clearly distinguishable sections of the net folding independently at equal rates and then coming together when a central hinge folded. The second folding pathway was characterized by different folding rates within the sections of the net. Nets 2, 4, 5, 7, 8, and 9 (Fig. 3) followed the first pathway; the remaining nets followed the second pathway. Fig. S1 in the Supporting Information section shows snapshots of all the 11 cube nets during folding. Interestingly, folding of octahedra appeared to follow more complicated pathways, and there were two possible final conformations, either the non-convex boat-shaped octahedron or the convex regular octahedron (Fig. 4 C–D). The formation of non-convex and regular octahedra depended both on the type of net as well as the folding sequence of the individual panels during assembly; some nets formed both types of octahedra.


Compactness determines the success of cube and octahedron self-assembly.

Azam A, Leong TG, Zarafshar AM, Gracias DH - PLoS ONE (2009)

Cube folding dynamics and octahedral conformations.Two distinct folding dynamics during self-assembly were observed for cube nets: (A) net 5 follows pathway 1 and (B) net 3 follows pathway 2. Pathway 1 was characterized by independent folding of two clearly distinguishable sections of the net, which came together when the central hinge folded. Nets following pathway 2 have different folding rates for different sections of the net. Octahedron nets can fold into (C) non-convex boat-shaped or (D) regular octahedra.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2636878&req=5

pone-0004451-g004: Cube folding dynamics and octahedral conformations.Two distinct folding dynamics during self-assembly were observed for cube nets: (A) net 5 follows pathway 1 and (B) net 3 follows pathway 2. Pathway 1 was characterized by independent folding of two clearly distinguishable sections of the net, which came together when the central hinge folded. Nets following pathway 2 have different folding rates for different sections of the net. Octahedron nets can fold into (C) non-convex boat-shaped or (D) regular octahedra.
Mentions: For the cubes, we observed that each of the 11 nets folded by one of two distinct pathways (Fig. 4 A–B). The first pathway involved two clearly distinguishable sections of the net folding independently at equal rates and then coming together when a central hinge folded. The second folding pathway was characterized by different folding rates within the sections of the net. Nets 2, 4, 5, 7, 8, and 9 (Fig. 3) followed the first pathway; the remaining nets followed the second pathway. Fig. S1 in the Supporting Information section shows snapshots of all the 11 cube nets during folding. Interestingly, folding of octahedra appeared to follow more complicated pathways, and there were two possible final conformations, either the non-convex boat-shaped octahedron or the convex regular octahedron (Fig. 4 C–D). The formation of non-convex and regular octahedra depended both on the type of net as well as the folding sequence of the individual panels during assembly; some nets formed both types of octahedra.

Bottom Line: The success of the self-assembly process was determined by measuring the yield and classifying the defects.Our observation of increased self-assembly success with decreased radius of gyration and increased topological connectivity resembles theoretical models that describe the role of compactness in protein folding.Apart from being intellectually intriguing, the findings could enable the assembly of more complicated polyhedral structures (e.g. dodecahedra) by allowing a priori selection of a net that might self-assemble with high yields.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD, USA.

ABSTRACT
Nature utilizes self-assembly to fabricate structures on length scales ranging from the atomic to the macro scale. Self-assembly has emerged as a paradigm in engineering that enables the highly parallel fabrication of complex, and often three-dimensional, structures from basic building blocks. Although there have been several demonstrations of this self-assembly fabrication process, rules that govern a priori design, yield and defect tolerance remain unknown. In this paper, we have designed the first model experimental system for systematically analyzing the influence of geometry on the self-assembly of 200 and 500 microm cubes and octahedra from tethered, multi-component, two-dimensional (2D) nets. We examined the self-assembly of all eleven 2D nets that can fold into cubes and octahedra, and we observed striking correlations between the compactness of the nets and the success of the assembly. Two measures of compactness were used for the nets: the number of vertex or topological connections and the radius of gyration. The success of the self-assembly process was determined by measuring the yield and classifying the defects. Our observation of increased self-assembly success with decreased radius of gyration and increased topological connectivity resembles theoretical models that describe the role of compactness in protein folding. Because of the differences in size and scale between our system and the protein folding system, we postulate that this hypothesis may be more universal to self-assembling systems in general. Apart from being intellectually intriguing, the findings could enable the assembly of more complicated polyhedral structures (e.g. dodecahedra) by allowing a priori selection of a net that might self-assemble with high yields.

Show MeSH