Figure 2. Design of a rule 110–124 circuit using the Seesaw Compiler.

(a) Gate diagram and truth table of a digital logic circuit that computes the transition rules 110 and 124 of elementary cellular automata. (b) Seesaw gate diagram of the equivalent DNA strand displacement circuit. Each seesaw node connected to a dual-rail input implements input fan-out. Each pair of seesaw nodes labelled and implements a dual-rail AND and OR gate, respectively. Each pair of dual-rail AND and OR gates implements an AND, OR or NAND gate in the original logic circuit. Each dual-rail output is converted to a fluorescence signal through a reporter, indicated as a half node with a zigzag arrow. Each circle and dot inside a seesaw node indicates a double-stranded threshold and gate molecule, respectively. Each dot on a wire indicates a single-stranded fuel molecule. (c) Simulations of the DNA strand displacement circuit using the previously developed model for purified seesaw circuits. Trajectories and their corresponding outputs have matching colours. Overlapping trajectories were shifted to be visible. Dotted and solid lines indicate dual-rail outputs that represent logic OFF and ON, respectively. For example, when input LCR=001, meaning L⁰, C⁰ and R¹ were introduced at a high concentration and L¹, C¹ and R⁰ at a low concentration, two output trajectories R124⁰ and R110¹ reached an ON state and the other two output trajectories R124¹ and R110⁰ remained in an OFF state, indicating that the output was computed to be 0 and 1 for rule 124 and 110, respectively. Simulations were performed at 1 × =50 nM—the compiler recommended standard concentration for large-scale purified seesaw circuits.