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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 A* of the AND 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: The double-stranded part, i.e., gets detached from the AND complex. Now, the solution contains another single stranded DNA sequence 5’-C*-R-B*-3’.

 • Step 5: The strand B, which acts as primer, hybridizes to B* of the sequence 5’-C*-R-B*-3’ and DNA polymerase binds this double-stranded part.

 • Step 6: DNA polymerase elongates the sequence B until it reaches to the 5’-end of the sequence 5’-C*-R-B*-3’.

 • Step 7: A complete double-stranded DNA sequence is formed.

 • Step 8: This sequence is recognized by a nicking enzyme at the site R and R*, and it cleaves the strand R*.

 • Step 9: DNA polymerase, while pushing the strand C away, elongates the strand 5’-B-R*-3’ again until it reaches to the 5’-end of the sequence 5’-C*-R-B*-3’.

 • Step 10: The output strand C is released.

Figure 2.20 AND reaction.

By repeating the steps 8, 9, and 10, the output strand C can be amplified and released.