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Figure 4.3 Design of strand displacement (seesaw) DNA logic gates [53]. (a) Strand displacement‐based sensor for nucleic acid detection. (b) Two‐input AND logic gate, which consist of the complex ī_A and ī_B with OUT1, releases OUT1 as an output upon binding to inputs ī_A and ī_B. Red dashed line indicates unique sequence independent on the sequence of ī_A and ī_B strands. (c) Dual‐rail logic. YES gate made with rail logic. X0 and X1 represent negative or positive input, respectively. Y0 and Y1 represent negative or positive output signal, respectively.

      The advantages of this system for DNA logic gate design are the following:

Seelig et al. designed a series of logic gates including AND, NOT, OR, thresholder, and amplifier [53]. A general idea for the design of a 2iAND gate is illustrated by Figure 4.3b. Strand ī_B forms a complex with strands ī_A and OUT1. Strand OUT1 is released free in solution only in the presence of the two oligonucleotide inputs I_A and I_B, which bind strands ī_A and ī_B, respectively, forming the “waste” duplex products. Strand OUT1 can then serve as a unique input for the downstream gates due to the presence of a unique sequence (shown as a red fragment in Figure 4.3b). Using this strategy, Seelig et al. demonstrated a five‐layer DNA gate integration, which consisted of 11 gates and accepted six inputs [53]. A systematic construction of strand displacement gates can lead to up to 78 gates performing simultaneously [54]. The gates can be used for solving as complex tasks as mimicking natural neural networks [55]. The disadvantages of strand displacement gates include the following: (i) The intensity of signal is proportional to strand concentration, unlike that of RCDZ, in which signal is enhanced by the catalytic action of RCDZ. (ii) DNA interactions are thermodynamically driven, which leads to irreversibility of the circuits or continuous accumulation of the DNA waste products in each operational round. (iii) Strand displacement is slower than hybridization of two single‐stranded oligonucleotides.

Instead of interpreting presence of a particular strand as a positive signal and absence of the strand as a negative signal, one can use two sequences as positive and negative signals, respectively. Such method is called dual‐rail logic (Figure 4.3c) [56]. Using this method, any gate that consists of AND/OR/NOT gates can be redesigned by using AND and NOT gates [56]. This approach was used for making logic gates suitable for both cascading and multiple operations [56,57]. Specific sequence complementary to one of the signal strands can be introduced in the solution, bind the input sequence, decompose the gate–input complex, and reactivate the gates. It leads to reassociation of the gate with its outputs. After that, a new input can be introduced into the computational system, with the ability to generate the proper output being saved.

The response rate of a DNA computational unit is limited by the time required for an input sequence and a gate to encounter each other in solution (Figure 4.4). To mitigate this limitation, the logic gates can be localized at a short distance from each other, which allows for faster inter‐gate communication [27]. A scaffold/substrate, suitable for gate immobilization, can be a DNA tile [27]. Chatterjee et al. localized strand displacement DNA logic gates on a DNA origami tile (Figure 4.4) [58]. Up to eight hairpins could communicate with each other [58], suggesting a possibility to integrate eight layers of DNA logic gates. Co‐localization of the circuit elements decreased the computation time from hours to minutes, as compared with solution‐based seesaw circuits.

Figure 4.4 DNA strand displacement logic gates attached to a DNA origami tile. Input strand I_A binds to hairpin I*_A and unwinds it. The unwound end interacts with a closely placed hairpin I_B, which consequently becomes unwound and encounters a fluorophore‐labeled strand I*_B, with fluorescence being attenuated by the quencher‐carrying strand Out. I_B reassociates with I*_B, which leads to increase in fluorescence.

      The decrease in signal intensity associated with the increase in the number of integrated gates was observed for the propagation of information through the chain of the conjugated gates. This is an expected limitation of the approach, since the presence of only one oligonucleotide input provides only limited contribution to the stabilization energy for the DNA strand association (e.g. shown in Figure 4.4): additional energy input is needed to ensure robust communication of the conjugated gates. A combination of both strand displacement and deoxyribozyme logic gates [59,60] can address this issue, since an active RCDZ can be produced and used for fueling the cascades by cleaving RNA phosphodiester bonds.

4.4 Logic Gates Connected Via DNA Four‐Way Junction (4WJ)

Arguably, any DNA‐based sensor can be converted into a set of DNA logic gates. One of the most elegant nucleic acid sensors is the molecular beacon (MB) probe [61,62], a fluorophore‐ and a quencher‐conjugated DNA hairpin (Figure 4.5a). MB probes have been used in DNA analysis in biomedical practice [62,65]. We designed a series of logic gates using an MB probe as a convenient fluorescent reporter [27,63,64,66,67]. Figure 4.5b,c demonstrates two designs for DNA YES gates. In both designs, DNA strands associate to form a structure stabilized through the formation of 4WJ, which gave the name to the DNA gates: “4WJ‐1” and “4WJ‐2.” 4WJ‐1 YES gate consists of two oligoethylene glycol‐modified DNA strands A and B and an MB probe. These three oligonucleotides coexist in solution in a dissociated state when a nucleic acid analyte is absent; MB is in the stem‐loop conformation, and the fluorescent signal is low. Addition of a DNA input leads to the cooperative hybridization of strands A and B both to the analyte and to the MB probe, which results in the formation of a 4WJ‐containing complex (Figure 4.5b, bottom). The fluorophore and the quencher are remote from each other in this complex, which results in high fluorescence. Addition of oligoethylene glycol linkers to strands A and B was required to ensure the elongated conformation of the MB probe in the 4WJ complex [63]. YES gate in 4WJ‐2 design responds to the input presence according to a similar scheme. However, strands O and C constituting the gate do not require oligoethylene glycol modifications, since the two MB‐binding arms of strand C ensured the required elongated MB conformation in the input‐bound complex [64].

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