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Everybody Wants to Be a Seed: Arbitrary Single-Tile Seeds in the Abstract Tile Assembly Model

Authors Florent Becker , Marie de Sainte Marie

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Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • DNA origami
  • self-assembly
  • kinetic modeling
  • computational modeling
  • cellular automata

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Abstract

Winfree’s abstract Tile Assembly Model (aTAM) is one of the most popular abstract models for DNA nano-computing. This papers presents a seedless version of the aTAM. Instead of a designated seed assembly, any single isolated tile can initiate the assembly. This paper shows that such system can simulate any aTAM system at constant scale and it presents a tile set to do so. All systems can be simulated at scale at most 10 and most of them can be simulated at scale 5, provided that their seeds are large enough.
Removing the need for seed in self-assembly is a new way of solving the nucleation problem, that is, the problem of controlling the initialisation of any self-assembly process. It also allows for a convergence of the aTAM towards other classical tiling models, such as Wang’s. 
The systems presented are based on independent modules made of tiles. The modules are carefully designed so they act kind of like stem cells. When a module self-assembles from an isolated tile, it grows a pseudo-seed which represents the seed of the simulated system with a Hamiltonian cycle along the borders of the corresponding macrotiles. The other modules, which appear later on during the simulation as components of the "regular" macrotiles, depend on each other to self-assemble. In such cases, the assembly is synchronised in a way so that the growth of any pseudo-seed is blocked. This ensures that a macrotile self-assembles only when interacting either with the pseudo-seed or with previously completed macrotiles.

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Florent Becker and Marie de Sainte Marie. Everybody Wants to Be a Seed: Arbitrary Single-Tile Seeds in the Abstract Tile Assembly Model. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 164:1-164:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.164

Author Details

Florent Becker
  • Laboratoire d’Informatique Fondamentale d’Orléans (UR4022), Université d’Orléans et INSA Centre Val-de-Loire, France
Marie de Sainte Marie
  • Laboratoire d’Informatique Fondamentale d’Orléans (UR4022), Université d’Orléans et INSA Centre Val-de-Loire, France
  • Département d'informatique de l'École Normale supérieure de Lyon, France

Funding

Research funded by CNRS through the projet à risque "CalcADN".

Supplementary Materials

References

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