Program Size and Temperature in Self-Assembly

  • Ho-Lin Chen
  • David Doty
  • Shinnosuke Seki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

Winfree’s abstract Tile Assembly Model (aTAM) is a model of molecular self-assembly of DNA complexes known as tiles, which float freely in solution and attach one at a time to a growing “seed” assembly based on specific binding sites on their four sides. We show that there is a polynomial-time algorithm that, given an n ×n square, finds the minimal tile system (i.e., the system with the smallest number of distinct tile types) that uniquely self-assembles the square, answering an open question of Adleman, Cheng, Goel, Huang, Kempe, Moisset de Espanés, and Rothemund (Combinatorial Optimization Problems in Self-Assembly, STOC 2002). Our investigation leading to this algorithm reveals other positive and negative results about the relationship between the size of a tile system and its “temperature” (the binding strength threshold required for a tile to attach)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ho-Lin Chen
    • 1
  • David Doty
    • 1
  • Shinnosuke Seki
    • 2
  1. 1.Department of Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of System Sciences for Drug DiscoveryKyoto UniversityKyotoJapan

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