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Chemical Wave Logic Gates




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Chemical Wave Logic Gates Oliver Steinbock,† Petteri Kettunen,‡ and Kenneth Showalter* Department of Chemistry, West Virginia UniVersity, Morgantown, West Virginia 26506-6045 ReceiVed: April 29, 1996; In Final Form: August 6, 1996X Logic gates based on chemical wave propagation in geometrically constrained excitable media are demonstrated in a Belousov-Zhabotinsky membrane system. The catalyst of the reaction is printed in specific predetermined patterns with geometries designed to provide various logic operations. Computational studies of the serial coupling of elements to form multicomponent gates and general chemical wave circuitry are presented. Introduction Propagating wave behavior is pervasive in living organisms, from waves of electrical activity in heart tissue1 to action potentials in neuronal systems.2,3 Waves in excitable media serve to transform information in the temporal domain, for example, the rhythm of pacemaker cells or the firing of a neuron, into signals in the spatial domain, which are transmitted from one location to another. In addition to signal transmission, propagating waves can provide information on optimal pathways through spatial networks and mazes,4,5 thus offering a mecha- nism for self-optimization in biological processes, such as the aggregation of amoebae in the slime mold Dictyostelium discoideum.6,7 Propagating waves can also provide the basis for information processing, such as image manipulation8 and simple computational tasks.9,10 Image edge enhancement, for example, relies on the transition of phase waves to autowaves, converting shallow gradients of an image into sharp bound- aries.11,12 Logic gates that rely on wave initiation as a threshold switch have been based on waves propagating through narrow channels.9 Constant velocity wave propagation has even been used to measure the value of pi, x2, and the golden mean.10 In this report, we describe a new scheme for carrying out logic operations with propagating chemical waves that is based on determining optimal pathways through specific geometrical configurations of excitable media. A conceptual framework for chemical based computations has been advanced in a series of papers by Ross and co- workers.13-16 They proposed operational models for the experimental implementation of various logic gates and simple circuits based on coupled reactors with nonlinear chemical reactions. Hjelmfelt, Schneider, and Ross17 proposed a chemical neural network for pattern recognition, and Laplante et al.18 have implemented such a network in an experimental system consist- ing of bistable iodate-arsenite reactions in eight coupled CSTRs. Other studies of logic gates using bistable reactions have been carried out by Schneider et al.,19,20 and enzymatic reactions as switches in reaction networks have been considered by Okamoto and co-workers.21 A recent study by Adleman22 has shown how the manipulation of DNA sequences can be used to solve directed Hamiltonian path problems. Perhaps the earliest suggestion of chemical-based computation was by Ro¨ssler,23 who, some 20 years ago, proposed using bistability as a switch in logic devices. Following Ross and co-workers,13-16 a scheme for logic gates based on the propagation of chemical waves through narrow channels with no-flux boundaries has been developed.9 Excit- able Belousov-Zhabotinsky24 (BZ) reaction mixtures were connected by precision-bore capillary tubes through which waves could propagate from ...





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