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of more powerful microprocessors depends on continued progress in miniaturizing their components. However, if current trends continue, conventional silicon chips will soon reach their physical limits [4]. Several research groups have created molecular ensembles that perform logic operations [2,3,5–9]. Even though small‐scale integration of logic elements has been achieved, there is still a lack of examples of universal large‐scale integration. Therefore, the challenges of component integration must be further addressed to advance the molecular computation field, as well as for its practical implementations [2,3].

DNA has been considered as an excellent candidate both for in vitro computation [10] and as a convenient building block for molecular switches and other devices [11–13]. Pioneered by Stojanovic [14], a great number of nucleic acid‐based logic gates of various designs have been proposed in the last 17 years [15–26]. Despite significant progress in the design of individual molecular logic gates, there is still a great challenge in solving the following technical problems: achieving high scale integration of molecular logic units, precise localization of the molecular gates in nano‐environment for efficient inter‐gate communication, and achieving reusability of DNA hardware [27–30]. Moreover, connecting the gates to an appropriate interface for convenient communication with human users is needed [31,32].

      This chapter describes approaches for connecting DNA logic gates in circuits with the emphasis on (i) deoxyribozyme (Dz) logic gates, (ii) strand displacement (seesaw) logic gates, and (iii) DNA logic gates connected via four‐way junctions (4WJs). Most common problems on the way toward creating long chains of communicating DNA logic gates are discussed.

4.2 Connecting Deoxyribozyme Logic Gates

The logic gate designed by Stojanovic et al. [14] took advantage of deoxyribozymes – nonnaturally occurring DNA sequences that catalyze chemical reactions [33,34]. One of most commonly used deoxyribozyme classes in DNA‐based molecular computation is a class of RNA‐cleaving deoxyribozymes (RCDZ). The design principles for RCDZ‐based two‐input AND gate (2iAND) are shown in Figure 4.1. A DNA strand containing an RCDZ catalytic core and two substrate‐binding arms is rendered inactive by the two inactivating stems. Binding the two oligonucleotide inputs I1 and I2 to the input‐recognition loop modules unwind the inactivating stems, thus enabling binding of a fluorogenic F substrate (F sub). The cleavage of F sub results in fluorescent increase due to the separation of the fluorophore from quencher. Importantly, when added separately, I1 and I2 are unable to restore the catalytic activity of RCDZ, which ensures the appropriate logic behaviours of the 2iAND construct. NOT, OR, ANDNOT, and even three‐input ANDNOTANDNOT gates can be designed by following similar principles of RCDZ core activation and inactivation [35,36]. Splitting the RCDZ core in two halves enables designing the gates that can process up to five inputs (e.g. 5iAND gate shown in Figure 4.1b) [37]. RCDZ logic gates have been used to build complex systems including automatons that can play Tic‐Tac‐Toe game with human, which utilize over hundreds of logic gates [38,39] (reviewed in [11]).

Figure 4.1 Examples of deoxyribozyme‐based logic gates. (a) One of the first DNA logic gates: deoxyribozyme (Dz)‐based two‐input AND gate (2iAND)[14]. Input‐recognition modules are in green and blue. Upon hybridization of inputs I_A and I_B, the substrate‐binding arms are unblocked, which restores RCDZ activity to cleave a fluorophore‐ and quencher‐labeled reporter substrate (F sub). FAM is fluorescein; Q is a dark quencher of fluorescence. (b) Dz‐based five‐input AND gate (5iAND). Dz catalytic core regains activity only when all five oligonucleotide inputs (I1–I5) are present. I1, I2, I3, and I4 open the inactivating stems, while I5 bridges strands Dz_a and Dz_b together to form a catalytic core [37].

      Source: Based on Stojanovic et al. [14].

The RCDZ logic gates can be connected via cascades of deoxyribozyme‐catalyzed reactions. For example, Stojanovic et al. connected YES, NOT, AND, and ANDNOT logic gates to downstream YES RCDZ gate [40]. An example of 2iAND gate is shown in Figure 4.2. Deoxyribozyme ligase‐based 2iAND gate, when activated by the two DNA inputs I_A and I_B, can bind the two short strands OUTa and OUTb and covalently link them into a longer oligonucleotide OUT (Figure 4.2c). The latter can be recognized by a downstream RCDZ gate, as shown in Figure 4.2d. Such cascade resulted in a two‐layer logic gate integration. Incubation period for up to 60 minutes was required for this system to achieve fluorescent response above the background. The disadvantage of the system is slow release of the output oligonucleotide from the complex with the ligase gate, since the product of ligation has higher affinity to the DNA ligase than the substrates (OUTa and OUTb).

Figure 4.2 AND deoxyribozyme ligase gate connected to YES RCDZ gates. (a) DNA ligase‐based two‐input AND gate: the ligase Dz is inhibited by two stem‐loop structures. Inputs I_A and I_B unwind the inactivating stem‐loops and enable the DNA ligase to ligate strands OUTa and OUTb to produce the OUT strand. The OUT strand activates RCDZ for cleavage of F sub followed by fluorescence increase. (b) Beads 1 and 2 contain immobilized RCDZ constructs and their corresponding substrates. They act as YES logic gates: in the presence of the oligonucleotide inputs I1 and I2, they activate RCDZ and release OUT1 and OUT2 oligonucleotides. The released OUT1 and OUT2 can activate AND2,3 gate on the third bead, which can be monitored via fluorescence.

Yashin et al. immobilized RCDZ constructs on microsphere beads together with their substrates (Figure 4.2b) [41]. The substrates were inactivated by complementary strands, which could be removed by inputs I1 and I2, respectively (not shown in Figure 4.2b). The YES beads, activated by certain input combination, could release their oligonucleotide outputs in solution (OUT1 and OUT2), which then could be recognized by downstream logic gates (AND2,3 gate in Figure 4.2b). Three-layer integration was achieved. The advantage of the approach is in the ability to monitor the fluorescent signal from individual beads by flow cytometry. However, hybridization of the bead‐immobilized oligonucleotides might be significantly slower than that in solution [42]. Indeed, time needed to observe a strong signal on the last bead in this case was 16 hours [41].

      Bone et al. used split cascades based on the most catalytically active 10–23 Dz that enable realizing inactivated RCDZ [43]. This approach can reduce the amount of input required for cascade activation from 20–1000 nM to 20–100 pM [43,37,44].

4.3 Connecting Gates Based on DNA Strand Displacement

The design of seesaw gates [53] takes advantage of DNA strand displacement, e.g. the ability of a partial DNA duplex to release one strand upon hybridization of the second strand with an interfering strand that can form more Watson–Crick base pairs than presented in the original duplex (Figure

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