2.19. One toe-hold binding region is at the 3’ end of G, the second one is in Eout and the third one is inside the sequence F. The computation is initiated after adding input oligonucleotides to the solution containing the gate complex. Gin and Fin are the two inputs which are 36 bases long and complementary sequences G and F respectively within the gate complex. At first, the input Gin binds to its corresponding toehold in G at the 3’ end of the gate complex and displaces G by branch migration. It produces an inert partially double-stranded waste product consists of Eout and F. The waste product contains an exposed toehold in F for the subsequent input sequence Fin. Similarly, Fin binds to the toehold and displaces F and produces Eout as the output sequence which contains a toehold and can be used as the input signal for the downstream gate. Hence, we can say for this two-input AND gate, if and only if both of the input DNA strands are present then only output DNA strand gets generated.
Figure 2.19 Mechanism of two-input AND gate.
The output signal generated from a logic gate has a tendency to interact further with downstream gates before its release which is undesirable. To avoid such interaction, the toehold binding domain of output strands need to be protected. This can be achieved by constructing logic circuit using one AND gate and two translator gates. A translator gate can be defined as single-input AND gate that coverts the input signal to the output signal, all encoded in form of DNA oligonucleotides.
A three-translator gate chemical circuit is constructed for logical OR gate operation. Two of those three gates receive the input strands and releases the same output strands. Then, the remaining strand receives such output strand to release final output strand of the gate. Thus, following this method, the output strand of the OR gate becomes free if and only if at least one input strand is present.
NOT gates, containing single translator gate and single inverter strand, are restricted to the first layer of the proposed circuit. The presence or absence of a single-input strand denotes a Boolean value. The inverter strand should be added with the input simultaneously. If the input strand is absent, the inverter strand activates the translator gate to release an output signal. But the presence of the input strand acts as a competitive inhibitor and preferably anneals with the inverter strand and thus the translator gate cannot be activated.
2.5.2.2 DNA Logic Circuits
After the demonstration of DNA logic gates based on hybridization of the strands and the conformational deviations of the secondary structures, the challenge is to build large, reliable circuits. These circuits can be implemented by the set of Boolean logic functions which uses short oligonucleotides as input as well as output and thus can be cascaded to construct multilayer circuits.
The two drawbacks for which may fail are listed below:
• the gate may be unsuccessful to release enough output signal when it is triggered;
• the spontaneous release of the output signal may lead to gate “leak”.
These disadvantages can be repaired by signal restoration. The first drawback can be fixed by increasing a moderate output amount to the full activation level; the second drawback can be fixed by decreasing a small output amount to a negligible level.
Amplifier gate and threshold gate should be developed to implement signal restoration. The signal restoration module is composed of a threshold gate and amplifier gate. The amalgamation of it confirms the stability of digital representation of the large circuit.
The threshold gate is composed of three-input AND gate where the first input signal and the third input signal are identical. The second input signal, which is the part of threshold unit, is required only for structural reason. Here, the output is unable to surpass half the input signal. For this reason, subsequent amplification is needed for threshold gate. The system can be used as input amplifier and full translator or as fluorescence readout with slight alteration.
Amplifier gate, which is a two-gate feedback circuit, is based on feedback logic. It can linearly amplify the fluorescence output signal with time without releasing it. The two translator gates of the circuit are designed in such a way that the output of the first gate serves as the input of the second one and the output of the second gate serves as the input of the first one.
The researchers [8] have composed a larger circuit combining the predesigned subcircuits consisting of eleven gates to demonstrate modularity and scalability. The inputs to the circuit are DNA analogs of six mouse microRNAs. This experiment discloses that natural RNA sequences can also be used as the input signals logic gates instead of DNA sequences.
2.5.3 DNA Logic Circuits Using DNA Polymerase and Nicking Enzyme
A single logic operation following DNA strand displacement methodology requires approximately 30 minutes time to be executed. Furthermore, the concentration of an output molecule released from a gate cannot exceed that of the gate molecule. These are the major two disadvantages of the model for performing logic operations which has been described in Section 2.5.2. To overcome these drawbacks, Hirose et al. [9] proposed a new model for construction of the combinatorial circuits using DNA polymerase and nicking enzyme. Using this method, the logic gates can be computed quickly and the output molecules can be amplified.
In this model, for each Boolean variable a, two DNA strands A and NA are prepared. The existence of A in the solution implies the evaluation of the Boolean variable a as 1 and the existence of NA in the solution implies the evaluation of the Boolean variable a as 0. Thus, the strands A and NA cannot exist at the same time in the solution. In this model the negation strand NA can be used to implement NOT gate. Now, it is assumed that the nicking enzyme recognizes a double-stranded DNA sequences
The implementations of the above-mentioned reactions using DNA polymerase and nicking enzyme are illustrated in the next subsections. To implement logic circuit the following basic abstract level chemical reactions are required;
2.5.3.1 AND Reaction
Let the input variables of the AND gate be a and b and the output variable be c. The strands A, NA are prepared for the variable a; strands B, NB are prepared for the variable b; strands C, NC are prepared for the variable c. The AND reaction can be represented by A ∧ B → C where the strand C is produced if and only if both of the strands A and B exist in the solution. The OR reaction NA | NB → NC also implements the AND gate. The AND reaction is explained by the following steps (see Figure 2.20) [9].
• Step 1: The reaction solution contains AND complex and sufficient amounts of input DNA strands A and B. The AND complex consists of two DNA strands 5’-C*-R-B*-3’ and 5’-B-R*-A*-3’. Initially, B and R* is hybridized to B* and R, respectively.
• Step 2: The single stranded DNA A, which acts as primer, hybridizes to
