Chemical Kinetics is Turing Universal

Interest in chemical computation has followed four different paths. It is one of the natural extensions of discussions about information and thermodynamics, which go back to Maxwell demon arguments and Szilard’s work [1–5]. It is also a rather natural extension to the application of dynamical systems theory to chemical reactions [6–8], in particular logic networks stemming from bistable reaction systems [9]. A lot of effort has been devoted to trying to devise nonstandard computational architectures, and chemical implementations provide a distinct enough backdrop to silicon [10–12]. Finally, in recent years biology has presented us with what looks to be actual chemical computers: the enzymatic cascades of cell signaling [13–15]. One of the first questions that can be asked in this subject is whether universal (Turing) computation can be achieved within some theoretical model of chemistry; the most immediate one is standard chemical kinetics. This question has been recently studied in some detail [16–22], and even subject to experimental tests [23]. In [18–20], Hjelmfelt et al. argued quite convincingly that building blocks for universal computation indeed can be constructed within ideal chemical kinetics, and that they could be interconnected to achieve computation. However, many difficulties still lie in the way. An issue not addressed by Hjelmfelt et al. is structural stability: the tolerance of a system to changes in parameters and functional structure. In particular, “gluing” together two groups of chemical reactions will have appreciable effects on the kinetics of both groups; the basic unit and the couplings used in [18–20] require case-by-case adjustment of individual parameters for proper functioning. The purpose of this Letter is to provide a slightly more formal proof that chemical kinetics can be used to construct universal computers. I will concentrate on the “next” level of difficulty, which is that of the global behavior of a fully coupled system and its structural stability. I will do it through the simplest approach: I will show that classical digital electronics can be implemented through chemical reactions. Since my key problem in this scheme is showing global consistency, and the proof requires arbitrarily large circuits, I will have to show that the output of one gate can be plugged into the input of