Autonomous Push-down Automaton Built on DNA

In the paper written by Cavaliere, Janoska, Yogev, Piran, Keinan, Seeman [4] the authors propose a theoretical model (i.e. not tested in laboratory) of implementation of the push-down automaton built on DNA. The idea was inspired by two papers: the first one by Rothemund [7] who proposed a simulation of the Turing machine the basic theoretical model of computation and the second one by Benenson, Paz-Elizur, Adar, Keinan, Livneh, Shapiro [1] who proposed a simulation of the finite automaton – the simplest model of computation. The above three implementations represent all the basic theoretical models of computers in the Chomsky hierarchy. But all these simulations have weak points in different places. The Rothemund model is not autonomous. A person must interfere in the process to obtain the required sequences of actions through many restriction enzymes. This is likely a reason why nobody tested it experimentally. Next, Benenson et al. [1] model is autonomous, programmable and was tested in laboratory but it represents the simplest computational model a finite automaton (in fact it was only 2-states 2-symbols finite automata). The next propositions along the same idea (Soreni et al. [10], Unold et al. [11], Krasiński and Sakowski [6]) essentially did not improve the situation. The last model, Cavaliere et al. [4] is more powerful (a push-down automaton), autonomous, programmable (although the action of it was illustrated only on one simple example) but the problem lies in obtaining the right sequence of ligations of transition molecules to the input and to the stack (represented by the same circular DNA). The authors themselves indicate this problem “It is first important to know which side is ligated first, since there is degeneracy in the stack side ... and therefore different transition molecules may be ligated at that end at any stage” and propose two ways to reduce (not eliminate) the problem. Moreover, another problem in their model is that it is not clear biochemically whether the used enzyme PsrI could not accidentally cut transition molecules of the first kind (which add the symbol Z to the stack) before ligating it to the input and to the stack. In this paper we suggest an improvement of the last model of push-down automata to avoid these problems. However, it is a theoretical model not tested yet in laboratory. We propose a new shape of transition molecules and another kind of restriction enzymes, which cut only when the ligation of a transition molecule to the circular molecule of the input will be accomplished on both sides.