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uc2006 - Turing Complete Catalytic Particle Computers...

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Turing Complete Catalytic Particle Computers Anthony M. L. Liekens 1 and Chrisantha T. Fernando 2 1 Dept. of Biomedical Engineering, Technische Universiteit Eindhoven, Netherlands 2 Dept. of Computer Science, University of Birmingham, United Kingdom Abstract. The Bare Bones language is a programming language with a minimal set of operations that exhibits universal computation. We present a conceptual framework, Chemical Bare Bones, to construct Bare Bones programs by programming the state transitions of a multi- functional catalytic particle. Molecular counts represent program vari- ables, and are altered by the action of the catalytic particle. Chemical Bare Bones programs have unique properties with respect to correctness and time complexity. The Chemical Bare Bones implementation is natu- rally suited to parallel computation. Chemical Bare Bones programs are constructed and stochastically modeled to undertake computations such as multiplication. 1 Introduction 1.1 Chemical computing An approach for programming a chemical computer is to design a complex ‘par- ticle’ capable of a controlled transition between configurations, where each con- figuration is capable of catalyzing a specific set of reactions. Ribozymes can be artificially selected that catalyse specific reactions [1]. Multi-enzyme complexes are common in cells, e.g. PDGF and Tar Complexes [2]. Just as we require, they possess multiple catalytic activities and exist in many states. Programmability arises because the state of a complex subunit is dependent on the states of other subunits on the complex. The topology of the complex can be designed, e.g. clusters, chains, rings, to allow appropriate ‘conformational spread’ [3]. Approx- imately digital solid-state circuitry can be produced in proteins [4]. Our approach differs from other work in chemical computing with reaction networks in the following ways. Chemical Bare Bones (CBB) does not make explicit the implementation details of the catalytic reactions; the substrates may be proteins, RNAs or metabolites. Although DNA hybridization catalyst circuits have been proposed by Seelig et al, they model at the algorithm level, circuits of logic gates, not serially executable programs [5]. CBB describes computations carried out by only one particle complex with multiple states, and not networks of catalytic particles computing in a distributed manner. Such neural network metaphors utilize coupled cascade cycles, where the weights are the extent of allosteric and covalent modification of the equilibrium position between binary protein configurations that represent activities [6–8]. Although it is possible to
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produce logic gates with an enzyme cascade cycle it will be a formidable task to assemble many of these gates together into a network [9]. The demonstration that CBB is Turing universal lies in the isomorphism between chemical reactions and the Bare Bones language. This overlays the underlying Turing universality of chemical kinetics on which our system depends [10]. Other approaches to
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