Figure 2.15 Mechanism of NOT gate.
Table 2.5 Truth table for NOT gate.
| Input (iz) | Output |
| 0 | 1 |
| 1 | 0 |
Figure 2.16 Mechanism of AND gate.
2.5.1.6 ANDANDNOT Gates
The AND and NOT gates are called the complete set as any logic function can be represented by specifically connecting certain number of these two gates. Figure 2.17 shows the structure of ANDANDNOT logic gate which is preferable to a cascaded two-enzyme circuit. A single enzyme can implement this logic gate. The ANDANDNOT gate can be formed by combining two activating stem-loop regions to one inhibitory stem-loop region. The gate gets activated by the addition of two input oligonucleotides, ix and iy. But the presence of another input signal ix inhibits the substrate to anneal to its binding region. This logic gate as represented in Figure 2.17 computes xAND yAND NOTz. Table 2.6 represents the truth table for ANDANDNOT gate.
But deoxyribozyme logic gates have certain drawbacks in performing logical operations for large DNA logic circuits. The mechanism explained above takes small sequences as input and produces cleaved or ligated oligonucleotide as the output signal which has different formation than input signal. Thus, the cascading operations become complicated. But, to develop and control nano-scale devices, designing large DNA logic circuit is crucial. This problem has been solved by Seelig and co-workers [8] who have implemented enzymefree logic circuits by nucleic acids.
Figure 2.17 Structure of ANDANDNOT gate.
Table 2.6 Truth table for ANDANDNOT gate.
| Input (ix) | Input (iy) | Input (iz) | Output |
| 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 1 | 1 | 0 |
2.5.2 Enzyme-Free DNA Logic Circuits
Seelig et al. [8] have followed toehold-mediated branch migration and DNA strand displacement procedure to build up molecular logic gate. This method does not require any enzyme. The researchers have also demonstrated Boolean logic gates, cascading, feedback, signal restoration, and amplification by DNA strand displacement in their research work. Following strand displacement methodologies, the input signal and the output signal have identical forms; thus, cascading can be performed to construct multi-layer circuit.
DNA strand displacement can be defined as the enzyme-free exchange of one DNA strand with another DNA strand. It is controlled by the biophysics of DNA molecules. Toehold is the overhanging domain of the original DNA strand which is complementary to the single stranded invading strand. Once toehold domain binds to the invading strand, it extends the hybridization by displacing the prehybridized resident strand of the original DNA strand [7]. Toehold-mediated branch migration and DNA strand displacement is one of the basic operations of several DNA computing models. The pictorial depiction of the above defined process is presented in Figure 2.18.
DNA strand displacement can be quantitatively controlled over a factor of 106 by varying the length and sequence composition of its toehold domain. Now, we focus on enzyme-free formation of DNA logic gate using DNA strand displacement mechanism which is essential for designing logic circuit.
2.5.2.1 Construction of Enzyme-Free DNA Logic Gate
The gate formation methodology proposed in the paper [8] is dependent on DNA strand displacement mediated by toehold domains; thus, hybridization as well as denaturation of the involved strands plays the crucial part. The DNA gate structurally comprises of two parts: one or more gate strands and single-output signal in form of DNA oligonucleotide. The output strand from a gate structure either is used as the input strand to a downstream gate or is tagged with fluorophore for reading out the output signal. Either both the ends and only one end of the output strand can be attached to the proposed gate complex. In the projected experiment, the binary digits “0” and “1” are represented by low and high concentration, respectively.
Figure 2.18 Toehold-mediated DNA branch migration and strand displacement [7].
Figure 2.19 shows the schematic representation of two-input AND gate. Initially, the gate complex is partially double-stranded DNA sequence and inert. The complex consists of three strands, viz., Eout (57 bases long), F (60 bases long) and G (36 bases long). The three toehold binding regions, each of which is 6 bases long, are colored in Figure 2.19. One toe-hold binding region is at the 3’ end