Self-Assembled Circuit Patterns

Abstract

Abstract. Self-assembly is a process in which basic units aggregate under attractive forces to form larger compound structures. Recent theoretical work has shown that pseudo-crystalline self-assembly can be algorithmic, in the sense that complex logic can be programmed into the growth process [26]. This theoretical work builds on the theory of twodimensional tilings [8], using rigid square tiles called Wang tiles [24] for the basic units of self-assembly, and leads to Turing-universal models such as the Tile Assembly Model [28]. Using the Tile Assembly Model, we show how algorithmic self-assembly can be exploited for fabrication tasks such as constructing the patterns that define certain digital circuits, including demultiplexers, RAM arrays, pseudowavelet transforms, and Hadamard transforms. Since DNA self-assembly appears to be promising for implementing the arbitrary Wang tiles [30,13] needed for programming in the Tile Assembly Model, algorithmic self-assembly methods such as those presented in this paper may eventually become a viable method of arranging molecular electronic components [18], such as carbon nanotubes [10,1], into molecular-scale circuits.

Two Computational Primitives for Algorithmic Self-Assembly: Copying and Counting

“…Simple examples of algorithmic self-assembly have been demonstrated, first in one-dimension 15,16 and then in two dimensions, 17 using molecular Wang tiles made of DNA. 18,19 Here we show that algorithmic self-assembly can be used to create an extended patternsbinary countingsof technological relevance for molecular electronics as the layout for a demultiplexing circuit [20][21][22][23][24] and of fundamental theoretical interest due to its appearance as a primitive for many other computation and construction tasks. [25][26][27] Additionally, using a subset of these tiles we show that a string of binary information can be propagated along the length of a DNA tube, which is of independent interest to the study of crystal evolution and the origin of life.…”

Reducing Facet Nucleation during Algorithmic Self-Assembly

“…9 In principle, arbitrarily complex objects can be constructed using algorithmic self-assembly, 10 and objects including large finite-sized shapes and some circuit diagrams can be assembled from a small number of components. [11][12][13][14] Aperiodic one- 15,16 and two-dimensional 17,18 structures have been algorithmically self-assembled from programmable crystal monomers constructed from DNA tiles.…”

Complexity of Compact Proofreading for Self-assembled Patterns

“…The output of the self-assembly process is usually considered to be either the shape of the uniquely produced terminal assembly [10,1,2,20] or the pattern produced if we focus on the locations of certain types of tiles [24,4,17,6]. Here we will focus on self-assembling of quarter-plane patterns.…”

“…Tiles do not get used up since it is assumed there is an unbounded supply of tiles of each type. This model has been used to theoretically examine how to use self-assembly for massively parallel DNA computation [21,26,16,13], for creating objects with programmable morphogenesis [10,1,2,20], for patterning of components during nanofabrication of molecular electronic circuits [6], and for studying self-replication and Darwinian evolution of information-bearing crystals [18,19]. Fig.…”