A transducer consists of an input/output alphabet, a finite set of states, and a transition function. From an input symbol applied to a given state, the transition function determines the next state, and an output symbol. Using DNA, we have constructed a transducer that divides a number by 3. The input consists of a series of individually addressable 2-state DNA nanomechanical devices that control the orientations of a group of flat 6-helix DNA motifs; these motifs have edge domains tailed in sticky ends corresponding to the numbers 0 and 1. Three-domain DNA molecules (TX tiles) act as computational tiles that correspond to the transitions that the transducer can undergo. The output domain of these TX tiles contains sticky ends that also correspond to 0 or 1. Two different DNA tiles can chelate these output domains: a 5 nm gold nanoparticle is attached to the chelating tile that binds to 0-domains and a 10 nm gold nanoparticle is attached to the chelating tile that binds to 1-domains. The answer to the division is represented by the series of gold nanoparticles, which can be interpreted as a binary number. The answers of the computation are read out by examination of the transducer complexes under a transmission electron microscope. The start or end points of the output sequence can be indicated by the presence of a 15 nm gold nanoparticle. This work demonstrates two previously unreported features integrated in a single framework: a system that combines DNA algorithmic self-assembly with DNA nanomechanical devices that control that input, and the arrangement of non-DNA species, here metallic nanoparticles, through DNA algorithmic self-assembly. The nanomechanical devices are controlled by single-stranded DNA strands, allowing multiple input sequences to be applied to the rest of the system, thus guiding the algorithmic self-assembly to a variety of outputs.
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