Self-Assembly, Self-Folding, and Origami: Comparative Design Principles

Author(s)Jungck, John R.
Author(s)Brittain, Stephen
Author(s)Plante, Donald
Author(s)Flynn, James
Date Accessioned2023-03-08T21:32:38Z
Date Available2023-03-08T21:32:38Z
Publication Date2022-12-27
DescriptionThis article was originally published in Biomimetics. The version of record is available at: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
AbstractSelf-assembly is usually considered a parallel process while self-folding and origami are usually considered to be serial processes. We believe that these distinctions do not hold in actual experiments. Based upon our experience with 4D printing, we have developed three additional hybrid classes: (1) templated-assisted (tethered) self-assembly: e.g., when RNA is bound to viral capsomeres, the subunits are constricted in their interactions to have aspects of self-folding as well; (2) self-folding can depend upon interactions with the environment; for example, a protein synthesized on a ribosome will fold as soon as peptides enter the intracellular environment in a serial process whereas if denatured complete proteins are put into solution, parallel folding can occur simultaneously; and, (3) in turbulent environments, chaotic conditions continuously alternate processes. We have examined the 43,380 Dürer nets of dodecahedra and 43,380 Dürer nets of icosahedra and their corresponding duals: Schlegel diagrams. In order to better understand models of self-assembly of viral capsids, we have used both geometric (radius of gyration, convex hulls, angles) and topological (vertex connections, leaves, spanning trees, cutting trees, and degree distributions) perspectives to develop design principles for 4D printing experiments. Which configurations fold most rapidly? Which configurations lead to complete polyhedra most of the time? By using Hamiltonian circuits of the vertices of Dürer nets and Eulerian paths of cutting trees of polyhedra unto Schlegel diagrams, we have been able to develop a systematic sampling procedure to explore the 86,760 configurations, models of a T1 viral capsid with 60 subunits and to test alternatives with 4D printing experiments, use of MagformsTM, and origami models to demonstrate via movies the five processes described above.
SponsorThis work was supported by the University of Delaware’s GEMS Program (Graduate Education in the Mathematical Sciences) of the Department of Mathematical Sciences, the Summer Undergraduate Research Program (SURP), the Delaware iNBRE Summer Scholars Program funded by the National Institutes of Health—NIGMS, a Sigma Xi (National Scientific Honor Society) outreach grant, and the University of New Hampshire’s Research Experience and Apprenticeship Program (REAP) through the Hamel Center for Undergraduate Research.
CitationJungck, John R., Stephen Brittain, Donald Plante, and James Flynn. 2023. "Self-Assembly, Self-Folding, and Origami: Comparative Design Principles" Biomimetics 8, no. 1: 12.
Keywords4D printing
KeywordsDürer nets
KeywordsSchlegel diagrams
KeywordsHamiltonian circuits
KeywordsEulerian paths
TitleSelf-Assembly, Self-Folding, and Origami: Comparative Design Principles
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