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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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(A–C) Cubes and octahedra were classified according to the following criteria. (Ai–iii) “A” cubes have no defects. (Bi, Biii) “B” cubes may have one misaligned face, or display slight underfolding or overfolding. (Ci–iii) “C” cubes are (Ci) severely twisted, (Cii) have a missing or unfolded face, or (Ciii) have a severely misfolded/misaligned face. (D) All 11 cube nets were capable of folding into “A” cubes. (E) All 11 octahedron nets were also capable of all self-assembling into “A” octahedra. There are two conformations of the folding of the octahedron nets: the regular octahedron and the non-convex octahedron (boat shape). A common defect observed in the folding of octahedron nets was (F) a tetrahedron. All of these are 200-micron scale structures.
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pone-0004451-g005: (A–C) Cubes and octahedra were classified according to the following criteria. (Ai–iii) “A” cubes have no defects. (Bi, Biii) “B” cubes may have one misaligned face, or display slight underfolding or overfolding. (Ci–iii) “C” cubes are (Ci) severely twisted, (Cii) have a missing or unfolded face, or (Ciii) have a severely misfolded/misaligned face. (D) All 11 cube nets were capable of folding into “A” cubes. (E) All 11 octahedron nets were also capable of all self-assembling into “A” octahedra. There are two conformations of the folding of the octahedron nets: the regular octahedron and the non-convex octahedron (boat shape). A common defect observed in the folding of octahedron nets was (F) a tetrahedron. All of these are 200-micron scale structures.

Mentions: The data gathered from the assembly of 200 µm and 500 µm polyhedra indicated that all of the nets, with varying levels of defects (Fig. 5A–C), were capable of forming perfectly-folded polyhedra (Fig. 5 D–E). We organized the self-assembled cubes and octahedra into four categories (labeled A through D) according to their defects. We could not discern any defects in “A” polyhedra using optical microscopy. They had well-aligned faces and hinges that folded for form dihedral angles of 90° for cubes (Fig. 5A) and 109.4° for octahedra. “B” polyhedra were observed to have either one misaligned face (Fig. 4Bi, 4Biii) or slightly (deviation<15°) under/overfolded faces. Underfolding occurred when excess solder was present at a hinge between two faces, and overfolding occurred when an inadequate amount of solder was present in the hinge. “C” polyhedra were missing one face, or were severely (deviation>15°) over/underfolded (Fig. 5Cii, 5Ciii). In some cases with cubes, we observed a twist deformation and also classified those as “C” cubes (Fig. 5Ci). “D” polyhedra had two or more of the defects described for “C” polyhedra. Various other defects were observed in octahedra but not in cubes, which were a result of the comparatively more complicated folding mechanics; one common defect that occurred with the folding of octahedron nets was the overfolding of several sides, resulting in a tetrahedron (Fig. 5F) instead. Yields for cubes and octahedra are plotted in Figure 6 and listed in Tables S1, S2, with average ranges of “A” polyhedra plotted in Figure S2.


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

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

(A–C) Cubes and octahedra were classified according to the following criteria. (Ai–iii) “A” cubes have no defects. (Bi, Biii) “B” cubes may have one misaligned face, or display slight underfolding or overfolding. (Ci–iii) “C” cubes are (Ci) severely twisted, (Cii) have a missing or unfolded face, or (Ciii) have a severely misfolded/misaligned face. (D) All 11 cube nets were capable of folding into “A” cubes. (E) All 11 octahedron nets were also capable of all self-assembling into “A” octahedra. There are two conformations of the folding of the octahedron nets: the regular octahedron and the non-convex octahedron (boat shape). A common defect observed in the folding of octahedron nets was (F) a tetrahedron. All of these are 200-micron scale structures.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2636878&req=5

pone-0004451-g005: (A–C) Cubes and octahedra were classified according to the following criteria. (Ai–iii) “A” cubes have no defects. (Bi, Biii) “B” cubes may have one misaligned face, or display slight underfolding or overfolding. (Ci–iii) “C” cubes are (Ci) severely twisted, (Cii) have a missing or unfolded face, or (Ciii) have a severely misfolded/misaligned face. (D) All 11 cube nets were capable of folding into “A” cubes. (E) All 11 octahedron nets were also capable of all self-assembling into “A” octahedra. There are two conformations of the folding of the octahedron nets: the regular octahedron and the non-convex octahedron (boat shape). A common defect observed in the folding of octahedron nets was (F) a tetrahedron. All of these are 200-micron scale structures.
Mentions: The data gathered from the assembly of 200 µm and 500 µm polyhedra indicated that all of the nets, with varying levels of defects (Fig. 5A–C), were capable of forming perfectly-folded polyhedra (Fig. 5 D–E). We organized the self-assembled cubes and octahedra into four categories (labeled A through D) according to their defects. We could not discern any defects in “A” polyhedra using optical microscopy. They had well-aligned faces and hinges that folded for form dihedral angles of 90° for cubes (Fig. 5A) and 109.4° for octahedra. “B” polyhedra were observed to have either one misaligned face (Fig. 4Bi, 4Biii) or slightly (deviation<15°) under/overfolded faces. Underfolding occurred when excess solder was present at a hinge between two faces, and overfolding occurred when an inadequate amount of solder was present in the hinge. “C” polyhedra were missing one face, or were severely (deviation>15°) over/underfolded (Fig. 5Cii, 5Ciii). In some cases with cubes, we observed a twist deformation and also classified those as “C” cubes (Fig. 5Ci). “D” polyhedra had two or more of the defects described for “C” polyhedra. Various other defects were observed in octahedra but not in cubes, which were a result of the comparatively more complicated folding mechanics; one common defect that occurred with the folding of octahedron nets was the overfolding of several sides, resulting in a tetrahedron (Fig. 5F) instead. Yields for cubes and octahedra are plotted in Figure 6 and listed in Tables S1, S2, with average ranges of “A” polyhedra plotted in Figure S2.

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