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       • Gel Electrophoresis: Using the strand as probe, the output strands denoting “0” is extracted into the tube . Again, using the strand as probe, the output strands denoting “1” is extracted into the tube , and extract the DNA strands which output value is “1” into the tube . Gel electrophoresis is done with both of the tubes.

      For the tube , DNA strands with length less than a specific threshold ∮ are retained and for the tube , the DNA strands with length greater than ∮ are retained. From this step, a series DNA strands presenting w1, w2, .…, wp are generated.

       • Performing Intersection to generate w: If p is even number, then the set w1, w2, .…, wp is divided into p/2 groups, intersection of each group is solved. If p is odd, then the set divided into (p/2 + 1) groups, and again the interaction for each group is solved. The remainder tube with no match tube directly takes part in the next cyclic grouping, till the last cycle there is one tube remain. If any DNA strand exists, then the intersection of w1, w2, .…, wp can be deduced.

       • The sequence of the strand can be read by performing sequencing.

       • Classification of the unknown input vector: Using the probe 5′ − wij − 3′ the DNA strands are extracted from the weight. The extracted strands are put into a new tube and it is mixed with the solution representing the unknown input vector. The first, second, and third steps are again performed using the solution. Using the strand as probe, the output strands denoting “0” is extracted. Again, using the strand as probe, the output strands denoting “1” is extracted.

      Following these steps, the unknown input vector can be classified.

      So far, we have developed neural model using short DNA sequences and replaced the mathematical aspect of ANN by the elementary operations of the DNA chemistry. In next section, we illustrate the DNA logic gates which are the basic of Boolean algebra. It is essential for the hands-on development of DNA computer.

2.5 DNA Logic Gates

      The activity of the brain resembles the computer as it functions as an input-output device. The basic design of digital computer follows Boolean algebra. McCulloch and Pitts [1] presented their view on the possibility of the brain to use Boolean algebra. As the input and output of the neural model are binary numbers, thus the researcher do proposed that multilayer neural network can implement the basic logic gates, i.e., AND, OR, and NOT. This can be achieved by appropriately choosing the weights. Complex Boolean circuits can be constructed by designing properly connected architecture by neurons.

       • AND Gate: The truth table for AND gate is represented by Table 2.1.Table 2.1 Truth table for AND gate.Input (ix)Input (iy)Output (y)000100010111The function for implementation of AND gate is represented by Equation (2.16).(2.16)where b ≡ bias value and 1 < b < 2;g(.) ≡ step function;ix, iy ≡ input values and ix, iy ∈ {0, 1};y ≡ output value and y ∈ {0, 1}.

       • OR Gate: The truth table for OR gate is represented by Table 2.2.Table 2.2 Truth table for OR gate.Input (ix)Input (iy)Output (y)000011101111The function for implementation of OR gate is represented by Equation (2.17).(2.17)where b ≡ bias value and 0 < b < 1;g(.) ≡ step function;ix, iy ≡ input values and ix, iy ∈ {0, 1};y ≡ output value and y ∈ {0, 1}.

       • NOT Gate: The truth table for NOT gate is represented by Table 2.3.Table 2.3 Truth table for NOT gate.Input (ix)Output (y)0110The function for implementation of NOT gate is represented by Equation (2.18).(2.18)where b ≡ bias value and 0 < b < 1;g(.) ≡ step function;ix ≡ input value and ix ∈ {0, 1};y ≡ output value and y ∈ {0, 1}.

      In this section, we focus on the design strategy of logic gates which has been developed using the secondary structures of DNA molecules. These DNA logic gates are the pillars of logic circuits which are needed to design a competent DNA computer in near future.

      2.5.1 Logic Gates Using Deoxyribozymes

It has been proved that deoxyribozymes, which is the DNA counterparts of ribozymes, can be used to develop logic gates and can solve simple computational problems [6]. Ribozymes, which are specific nucleic acid enzymes, exist in nature. These enzymes are structurally single stranded RNA molecules which have catalytic power and several other biological activities. On the other hand, deoxyribozymes, which are also single stranded structure, have to be synthesized in vitro. These enzymes generally catalyze the reactions of nucleic acid substrates, such as DNA-RNA ligation, RNA cleavage, and many more.

       2.5.1.1 Catalytic Activity of Deoxyribozyme

One of the reactions that deozyribozyme catalyzes is to break the phosphodiester bond which cleaves the DNA or RNA strands. This reaction is commonly performed in the domain of DNA computing. In particular, the enzyme can be phosphodiesterase. By structural modification of this enzyme, the catalytic activity can be altered. For example, if a specific bonding domain is added to deoxyribozyme, then it can specifically bind to a particular complementary nucleic acid strand. These kinds of ligand nucleic acid strands strongly influence the catalytic activity of deoxyribozyme. The catalytic function of the enzyme can be either increased or inhibited by the association of the ligand strands. If the deoxyribozyme actively catalyzes the reactions, then it can cleave oligonucleotide in two shorter products which is shown in Figure 2.12. This reaction is used in the design of DNA logic gate. The generated shorter nucleic acid strands are the output signal of the gate. These signals can further be used as the input of another downstream gate and so on. Thus, using the gate structures and cleaving reactions a large DNA logic circuit can eventually be formed. The output signals of the larger circuit are also represented by short single stranded DNA strands which are tagged with fluorophore to read the signal.

      The mechanism of cleaving nucleic acid strand is shown in Figure 2.12 which is used to perform simple computations and logic operations. In the figure, the substrate strand, i.e., the strand which has to be cleaved is tagged by fluorophore at one end and quencher molecule at the other end. Quenching process decreases the fluorescence intensity of certain molecule. In the process of fluorophore quenching, first the fluorophore enters into excited state by absorbing light [7].

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