Know When to Fold ’Em: Self-assembly of Shapes by Folding in Oritatami - Archive ouverte HAL Access content directly
Conference Papers Year : 2018

Know When to Fold ’Em: Self-assembly of Shapes by Folding in Oritatami


An oritatami system (OS) is a theoretical model of self-assembly via co-transcriptional folding. It consists of a growing chain of beads which can form bonds with each other as they are transcribed. During the transcription process, the δ most recently produced beads dynamically fold so as to maximize the number of bonds formed, self-assemblying into a shape incrementally. The parameter δ is called the delay and is related to the transcription rate in nature. This article initiates the study of shape self-assembly using oritatami. A shape is a connected set of points in the triangular lattice. We first show that oritatami systems differ fundamentally from tile-assembly systems by exhibiting a family of infinite shapes that can be tile-assembled but cannot be folded by any OS. As it is NP-hard in general to determine whether there is an OS that folds into (self-assembles) a given finite shape, we explore the folding of upscaled versions of finite shapes. We show that any shape can be folded from a constant size seed, at any scale n 3, by an OS with delay 1. We also show that any shape can be folded at the smaller scale 2 by an OS with unbounded delay. This leads us to investigate the influence of delay and to prove that, for all δ > 2, there are shapes that can be folded (at scale 1) with delay δ but not with delay δ < δ. These results serve as a foundation for the study of shape-building in this new model of self-assembly, and have the potential to provide better understanding of cotranscriptional folding in biology, as well as improved abilities of experimentalists to design artificial systems that self-assemble via this complex dynamical process. 2
Fichier principal
Vignette du fichier
Oritatami-shapes.pdf (12.56 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01998840 , version 1 (14-12-2019)


  • HAL Id : hal-01998840 , version 1


Erik Demaine, Jacob Hendricks, Meagan Olsen, Matthew Patitz, Trent A. Rogers, et al.. Know When to Fold ’Em: Self-assembly of Shapes by Folding in Oritatami. DNA 2018, Oct 2018, Jinan, China. pp.19-36. ⟨hal-01998840⟩
61 View
11 Download


Gmail Facebook Twitter LinkedIn More