Ken Komiya

State transitions by molecules.

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.

Successive State Transitions with I/O Interface by Molecules

This paper reports three experimental achievements in our computation model based on whiplash reactions. We first show that a single-stranded DNA (ssDNA) can serve as an independent machine by using a solid support technique. Second, we show how to append an arbitrary sequence, e.g. a transition state or a PCR primer, to the 3-end of a molecular machine, thus realizing its I/O interface. Finally we demonstrate the successive state transitions for several steps on solid phase with I/O.

Branching DNA machines based on transitions of hairpin structures

We constructed a DNA machine, the state branches of which depend on input DNA oligomers. The machine is a single DNA oligomer consisting of two hairpin structures connected by a single-stranded section. The input DNA oligomers can invade a hairpins stem via branch migration, opening the hairpin. The branching state is represented by which of the hairpins is opened. This paper describes the design of the DNA machine, an analysis of secondary structure transitions, and experimental results.

Complexity analysis of the SAT engine: DNA algorithms as probabilistic algorithms

Taking advantage of the power of DNA molecules to spontaneously form hairpin structures, Sakamoto et al. designed a molecular algorithm to solve instances of the satisfiability problem on Boolean expressions in clausal form (the SAT problem), and by developing new experimental techniques for molecular biology, they succeeded in solving a 6-variable, 10-clause instance of the 3-SAT problem (Sakamoto et al., Science 288 (2000) 1223). Sakamoto et al. call this computational architecture the SAT Engine. In this paper, we analyze the complexity of the SAT Engine as a probabilistic algorithm. We first estimate the time dependence of the probability of hairpin formation using standard chemical kinetics and the Jacobson-Stockmayer expression. We then estimate the number of DNA molecules required to solve the satisfiability problem with a given error probability. By taking the number of DNA molecules into account, we finally estimate the minimum total time and number of strands, respectively, required to achieve combined error rates of 0.