All Kinds of Behavior are Possible in Chemical Kinetics: A Theorem and its Potential Applications to Chemical Computing

Abstract

Until the late 1950s, it was believed that the processes described by the equations of chemical kinetics are simple: the process of each chemical reaction, concentrations of some chemical substances decrease while concentrations of other substances increases. This belief was shattered when the first periodic reaction -the famous Belousov-Zhabotinsky reactionwas discovered. Since then, it was shown that many other types of unusual behavior is possible for chemical systems. This discovery led to the possibility of finding chemical reactions that emulate non-trivial transformations that occur during computations -and thus, perform computations "in vitro", by actually performing the corresponding chemical reactions. The potential advantages of such chemical computing are numerous, the main advantage is that with 10 23 molecules performing computations in parallel, we have a potential for an unheard-of-parallelization -and thus, of an unheard-of speed-up. The possibility of computing "in vitro" was at first only theoretically conjectured, but then, in 1994, L. Adleman has actually performed successful chemical computations. This started a current boom in chemical computing, with many new ideas and devices appearing all the time.From both practical and theoretical viewpoints, chemical computing has been a clear success story. However, one open problem remained in this area: while many types of behavior have been shown to occur in chemical kinetics, it has been not know whether all types of behavior are possible. In this paper, we prove that every possible behavior can indeed be implemented in an appropriate chemical kinetics system. This result has the following direct implication for chemical computing: no matter what computational device one invents, with whatever weird behavior, it is, in principle, possible to emulate this device by appropriate chemical reactions. In this sense, chemical computing is truly ubiquitous.

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“…What actually happens is that two molecules interact, and then the result of this interaction interacts with the third molecule. This is, for example, what usually happens during catalysis, when an additional molecule (called a catalyst) speeds up the reaction between the two original molecules; see, e.g., [1], [2], [3], [15], [16].…”