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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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Trends of yield vs compactness.(A–B) Scatter plots of the percentages of “A” cubes and octahedra as a function of the number of vertex connections. (C–D): Scatter plots of the percentages of “A” cubes and octahedra as a function of Rg. The trend lines have the following R-squared values. (A) y = 0.1478x−0.0219, R2 = 0.74; (B) y = 0.063x−0.2972, R2 = 0.74; (C) y = −0.0048x+1.7387, R2 = 0.49; (D) y = −0.0052x+1.4345, R2 = 0.77.
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pone-0004451-g007: Trends of yield vs compactness.(A–B) Scatter plots of the percentages of “A” cubes and octahedra as a function of the number of vertex connections. (C–D): Scatter plots of the percentages of “A” cubes and octahedra as a function of Rg. The trend lines have the following R-squared values. (A) y = 0.1478x−0.0219, R2 = 0.74; (B) y = 0.063x−0.2972, R2 = 0.74; (C) y = −0.0048x+1.7387, R2 = 0.49; (D) y = −0.0052x+1.4345, R2 = 0.77.

Mentions: We observed strong correlations between the geometrical compactness of the 2D nets and the yields. Nets with more vertex connections and lower Rg generated the most “A” polyhedra (Fig. 7). We performed statistical analysis under the assumption that the two factors were unrelated. Two-tailed t-tests were completed for statistical significance to verify that the vertex connections and Rg correlated to yields of cubes and octahedra. Our statistical tests compared the percentages of “A” polyhedra to the corresponding values (per net) of vertex connections and Rg for cubes and octahedra independently. The p-values fell within the 0.001% range dictated by the alpha value, which led us to conclude with 99.999% confidence that vertex connections and Rg had statistical significance in average yields of different nets. The statistical significance of the unrelated factors further supports the hypothesis that net success in self-assembly is strongly driven by both of these geometrical factors.


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

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

Trends of yield vs compactness.(A–B) Scatter plots of the percentages of “A” cubes and octahedra as a function of the number of vertex connections. (C–D): Scatter plots of the percentages of “A” cubes and octahedra as a function of Rg. The trend lines have the following R-squared values. (A) y = 0.1478x−0.0219, R2 = 0.74; (B) y = 0.063x−0.2972, R2 = 0.74; (C) y = −0.0048x+1.7387, R2 = 0.49; (D) y = −0.0052x+1.4345, R2 = 0.77.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2636878&req=5

pone-0004451-g007: Trends of yield vs compactness.(A–B) Scatter plots of the percentages of “A” cubes and octahedra as a function of the number of vertex connections. (C–D): Scatter plots of the percentages of “A” cubes and octahedra as a function of Rg. The trend lines have the following R-squared values. (A) y = 0.1478x−0.0219, R2 = 0.74; (B) y = 0.063x−0.2972, R2 = 0.74; (C) y = −0.0048x+1.7387, R2 = 0.49; (D) y = −0.0052x+1.4345, R2 = 0.77.
Mentions: We observed strong correlations between the geometrical compactness of the 2D nets and the yields. Nets with more vertex connections and lower Rg generated the most “A” polyhedra (Fig. 7). We performed statistical analysis under the assumption that the two factors were unrelated. Two-tailed t-tests were completed for statistical significance to verify that the vertex connections and Rg correlated to yields of cubes and octahedra. Our statistical tests compared the percentages of “A” polyhedra to the corresponding values (per net) of vertex connections and Rg for cubes and octahedra independently. The p-values fell within the 0.001% range dictated by the alpha value, which led us to conclude with 99.999% confidence that vertex connections and Rg had statistical significance in average yields of different nets. The statistical significance of the unrelated factors further supports the hypothesis that net success in self-assembly is strongly driven by both of these geometrical factors.

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