Physical synthesis of DNA circuits with spatially localized gates

With the current DNA nanotechnology, we are now able to arrange DNA molecules on a DNA origami to compose a logic gate. This in turn realizes a spatially localized DNA circuit, on which the logic gates are placed on the specific locations as in electronic circuits. In this paper, we address three key problems in designing large-scale spatially localized DNA circuits. An AND gate, made of four hairpins, functions in stochastic manner and sometimes outputs a wrong result. Given tolerable error probability at each circuit output, we address how the probability that each AND gate functions correctly can be determined, which in turn determines the location of constituent hairpins. In the second problem, we study how hairpins are arranged on a DNA origami to minimize the area of a whole circuit, which determines the area of the origami board. The third problem regards the DNA domain assignment so that connected gates can communicate without interference.