Simplifying the Role of Signals in Tile Self-assembly

Abstract

Sending signals through DNA-based structures is one of the methods used to enhance the capabilities of DNA self-assembly systems. Signal Tile Assembly Models at temperature one, in supertile-to-supertile attachment mode, have been showed to have universal computational power. We introduce a simplified signal tile assembly model, in one-tile-at-a-time attachment mode, and where signals can only be used to deactivate glues. We prove that such a simplified system at temperature one can still simulate a Turing machine. We also present a simplified signal tile assembly system, in supertile-to-supertile attachment mode, that assembles a thin,N×N!, rectangle and has tile complexity O(log N). This result is an improvement over the tile complexity of existing models for thin rectangle self-assembly .

Example tile

DTAM

The authors define the Detachable Tile Assembly Model (DTAM)model as a variation of STAM. DTAM is a weaker version of STAM, whereby the signals are used only to deactivate glues. Thus all glues will start in the state on, and the state latent is not used. In addition, the signals themselves can only be turned on. Note that, since DTAM does not use the signals to activate glues, no new attachment possibilities(besides those that were present in the initial set-up) will be introduced during the self-assembly process. In Section 4 the authors show that, in spite of these restrictions, the use of DTAM reduces the tile complexity of the construction of a thin rectangle as compared to the results of Complexities for generalized models of self-assembly (Aggerwal, et al.). The authors also introduce the Simplified Detachable Tile Assembly Model(SDTAM),which is a restricted version of SDTAM wherein one starts with a single seed tile and, at each step, only the attachment of a single tile to the current configuration is allowed. In Section 3 the authors prove that SDTAM is Turing universal at temperature 1.