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Let the input variable of the PROP reaction be a and the output variable be b. The strands A, NA are prepared for the variable a; strands B, NB are prepared for the variable b. The PROP reaction can be represented by A → B where the strand B is produced if and only if the strand A exists in the solution. The PROP reactions A → NB and NA → B implement the NOT gate. The PROP reaction is explained by the following steps (see Figure 2.22) [9].

 • Step 1: The reaction solution contains PROP complex and sufficient amount of input DNA strand A. The PROP complex initially consists of a single stranded DNA sequence 5’-B*-R-A*-3’.

 • Step 2: The single stranded DNA A, which acts as primers, hybridizes to A* of the PROP complex. Then, DNA polymerase binds this double-stranded part.

 • Step 3: DNA polymerase elongates the sequence A until it reaches to the 5’-end of the sequence 5’-B*-R-A*-3’.

 • Step 4: A complete double-stranded DNA sequence is formed.

 • Step 5: This sequence is recognized by a nicking enzyme at the site R and R*, and it cleaves the strand R*.

 • Step 6: DNA polymerase, while pushing the strand B away, elongates the strand 5’-A-R*-3’ again until it reaches to the 5’-end of the sequence 5’-B*-R-A*-3’.

 • Step 7: The output strand B is released.

By repeating the steps 5, 6, and 7, the output strand B can be amplified and released.

The researchers experimentally proved that the proposed method is more time-efficient than DNA strand displacement approach. Also, the output of each DNA logic gate can be amplified, and so, the scalability and the feasibility of the proposed system are better than other methods.

Figure 2.22 PROP reaction.

But the method has a problem that the amplification of the output strands continues until DNA polymerase uses up the substrates. So, a bio-lab method for stopping or inhibiting the amplification process is needed in this framework.

In the next subsections, we focus on the applications of DNA logic gate in real life. Researchers have used the DNA logic gates to develop the nano-device with artificial intelligence, which can play tic-tac-toe game. The logic gates also have medical applications which we are going to illustrate.