Hairpin formation by single-stranded DNA molecules was exploited in a DNA-based computation in order to explore the feasibility of autonomous molecular computing. An instance of the satisfiability problem, a famous hard combinatorial problem, was solved by using molecular biology techniques. The satisfiability of a given Boolean formula was examined autonomously, on the basis of hairpin formation by the molecules that represent the formula. This computation algorithm can test several clauses in the given formula simultaneously, which could reduce the number of laboratory steps required for computation.

In our previous paper, we described a method by which a state machine is implemented by a single-stranded DNA molecule whose 3%-end sequence encodes the current state of the machine. Successive state transitions are performed in such a way that the current state is annealed onto an appropriate portion of DNA encoding the transition table of the state machine and the next state is copied to the 3%-end by extension with polymerase. In this paper, we first show that combined with parallel overlap assembly, a single series of successive transitions can solve NP-complete problems. This means that the number of necessary laboratory steps is independent from the problem size. We then report the results of two experiments concerning the implementation of our method. One is on isothermal reactions which greatly increase the efficiency of state transitions compared with reactions controlled by thermal cycles. The other is on the use of unnatural bases for avoiding out-of-frame annealing. The latter result can also be applied to many DNA-based computing paradigms.

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