LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Transducers with Programmable Input by DNA
Self-assembly
Nataˇsa Jonoska 1 , Shiping Liao 2 , and Nadrian C. Seeman 2
1 University of South Florida, Department of Mathematics
Tampa, FL 33620, USA
jonoska@math.usf.edu
2 New York University, Department of Chemistry
New York, NY 1003, USA
sl558@nyu.edu, ned.seeman@nyu.edu
Abstract. Notions of Wang tiles, finite state machines and recursive
functions are tied together. We show that there is a natural way to
simulate finite state machines with output (transducers) with Wang tiles
and we show that recursive (computable) functions can be obtained as
composition of transducers through employing Wang tiles. We also show
how a programmable transducer can be self-assembled using TX DNA
molecules simulating Wang tiles and a linear array of DNA PX-JX2
nanodevices.
1 Introduction
In recent years there have been several major developments both experimentally
and theoretically, that use DNA for obtaining three dimensional nanostructures,
computation and as a material for nano-devices.
Nanostructures. The inherently informational character of DNA makes it an
attractive molecule for use in applications that entail targeted assembly. Genetic
engineers have used the specificity of sticky-ended cohesion to direct the
construction of plasmids and other vectors. Naturally-occurring DNA is a linear
molecule in the sense that its helix axis is a line, although that line is typically
not straight. Linear DNA molecules are not well-suited to serve as components
of complex nanomaterials, but it is easy to construct DNA molecules with stable
branch points [20]. Synthetic molecules have been designed and shown to
assemble into branched species [12,23], and more complex species that entail the
lateral fusion of DNA double helices [21], such as DNA double crossover (DX)
molecules [7], triple crossover (TX) molecules [13] or paranemic crossover (PX)
molecules. Double and triple cross-over molecules have been used as tiles and
building blocks for large nanoscale arrays [24,25]. In addition, three dimensional
structures such as a cube [4], a truncated octahedron [29] and arbitrary graphs
[10,19] have been constructed from DNA duplex and junction molecules.
Computation. Theoretically, it has been shown that two dimensional arrays
can simulate the dynamics of a bounded one dimensional cellular automaton
and so are capable of potentially performing computations as a Universal Turing
N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 219–240, 2004.
c○ Springer-Verlag Berlin Heidelberg 2004