JOURNAL OF CHEMICAL PHYSICS

VOLUME 118, NUMBER 18

8 MAY 2003
Different operations on a single circuit: Field computation on an excitable chemical system

Takatoshi Ichino

Division of Informatics for Natural Sciences, Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan and Department of Physics, Graduate School of Sciences, Kyoto University & CREST, Kyoto 606-8502, Japan
Yasuhiro Igarashi,a) Ikuko N. Motoike,b) and Kenichi Yoshikawac)
Department of Physics, Graduate School of Sciences, Kyoto University & CREST, Kyoto 606-8502, Japan
Received 21 October 2002; accepted 10 February 2003 Recently, it has been proposed that various kinds of time operations can be performed using an excitable eld, mainly based on computer simulation. In this study, we performed experiments toward the realization of a time operation, such as time-difference detection. We used the photosensitive BelousovZhabotinsky reaction as a spatially distributed excitable eld. We found that a single geometrical circuit can perform different operations with changes in the intensity of light illumination. The experimental results are discussed in relation to the idea of a non-Neumann-type computational device. 2003 American Institute of Physics. DOI: 10.1063/1.1565103

INTRODUCTION

About 50 years ago, von Neumann proposed a computational device that could perform different operations on a single electronic circuit.1 This idea was quite innovative, since with conventional analog computers different circuits must be used to perform different operations. A Neumanntype computer can perform different computations following the instructions in a program and is equipped with a CPU, clock, and memory. Modern human activity relies heavily on this idea, along with those of Turing.2 Although a Neumanntype computer is very powerful, there exists an unavoidable drawback, i.e., all of the operations are processed through the CPU. Higher-order animals perform computations with a complicated network of neurons. Biological neural nets appear to be different from a Neumann computer equipped with a CPU. Recent developments in brain science indicate that the learning process changes the transmissibility of signals through synaptic junctions.35 This is the fundamental idea behind an articial neural net such as back propagation6 and Hopelds neural net.7 After learning, such an articial neural net can provide correct answers in response to different inputs. In addition to such a framework of computations that are accompanied by a change in connectivity between neurons, it is expected that some biological computations are performed even without reconnection of the circuit. Considering the reactions of animals in different situations for example, during the day and night or before and after
Present address: Department of Intelligence Science and Technology, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan. b Present address: Department of Complex Systems, School of Systems Information Science, Future UniversityHakodate, Hakodate 041-8655, Japan. c Author to whom correspondence should be addressed. Electronic mail: yoshikaw@scphys.kyoto-u.ac.jp 0021-9606/2003/118(18)/8185/6/$20.00 8185
eatinganimals most likely perform computations in a different manner using the same neural network. Most probably even under same circuit, animal neural nets can perform different computations on the same input, depending on the context. A strategy of this type is more plausible in living organisms that do not have a complex network of neurons, such as plants and bacteria. In the present study, we examined the possibility of constructing a non-Neumann-type computer based on the characteristics of an oscillatory and/or excitable spatial eld. Showalter and co-workers8,9 have proposed a novel idea based on a logic operation of an excitable eld and have reported clear experimental verication of their idea with an excitable and oscillatory chemical system, the Belousov Zhabotinsky BZ reaction.10,11 Although their idea was interesting, due to their inability to create a diode function, the signal is obliged to propagate through the network of excitable elds in a reversible manner. The direction of signal propagation has no uniqueness, and the signal undergoes backpropagation along the same route between input and output. Recently, we reported that unidirectional signal transmission with an excitable propagating wave could be generated with a spatially asymmetric connection between excitable elds separated by a diffusion eld.12,13 Such a diode function has been seen in an actual experiment with an excitable-chemical system, the BZ reaction,12,14 and also in computer simulations.13,1517 With numerical simulations, we have also proposed various logic gates, such as AND, NOT, 13,16 OR, etc. However, experiments to conrm the results of simulation have not yet been performed, partly because of the technical difculty of cutting a membrane lter to a desired shape in the excitable-chemical system. In this study, we extended our idea to develop diode characteristics and

2003 American Institute of Physics
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J. Chem. Phys., Vol. 118, No. 18, 8 May 2003

Ichino et al.

FIG. 1. Scheme of the experimental setup.
various kinds of logic gates with an excitable eld. As an experimental model, we used a photosensitive version of the BZ reaction, where light illumination results in the production of bromide, which inhibits the oscillatory reaction. In other words, the degree of the excitability can be adjusted by changing the intensity of illumination.14,1720 Thus different kinds of computation can be processed with an excitable eld of a single geometry, with suitable tuning of the light intensity as a eld parameter.

EXPERIMENTAL METHODS

FIG. 2. Chemical diode on photosensitive BZ medium under light illumination. The light intensity in the white part was 3.23104 lx. The black and white areas correspond to excitable and inhibitory elds. a Propagation of a chemical wave from left to right. b Propagation failure. The pictures on the left in a and b are video images and those on the right are quasithree-dimensional representations, where the vertical change indicates the brightness or height of the chemical wave.
The reaction mixture was prepared as described previously from analytical-grade chemicals Wako. The catalyst for the photosensitive reaction, Rubpy3Br2, was synthesized and puried as in Refs. 21 and 22. The solution consisted of NaBrO3 0.15 M, H2SO4 0.3 M, M, KBr0.05 M, and CH2COOH2 0.2 Rubpy3Br2 2.04 mM. Cellulose-nitrate membrane lters Advantec A100A025A with a pore size of 1 m were soaked in BZ solution for 5 min. The membrane was gently wiped with lter paper to remove excess water and placed in a Petri dish. The surface of the membrane was immediately covered with silicon oil Shin-Etsu Chemical Co. to prevent it from drying and to protect it from the inuence of oxygen. The experiments were carried out in an air-conditioned room at 201 C, at which the reaction medium showed no spontaneous excitation and no change in behavior for approximately 1 h. Excitation waves were initiated by gently touching the surface of the membrane with a 1-mm-thick silver wire. The medium was illuminated from below as shown schematically in Fig. 1. The halogen bulb JCD100V-300W of a slide projector Cabin Family II was used as a light source, and the light intensity was varied by an external voltage controller. A black and white picture on a slide in the projector served as an illumination mask to create the appropriate boundary. The experiments were monitored with a digital video camera Panasonic NV-DJ100 from above and recorded on a VTR Panasonic NV-H200G. For image enhancement, a blue optical lter AsahiTechnoGlass V-42 with a maximum transparency at 410 nm was used. The light intensity at the illuminated part was determined by a light intensity meter ASONE LM-332.

EXPERIMENTAL RESULTS

Figure 2 shows the manner of wave propagation around a chemical diode, where the white and black parts are illuminated and masked regions, respectively. In Fig. 2a the chemical wave passes through the gap, whereas in Fig. 2b the signal is not transmitted. A similar diode character has been observed by arranging a membrane lter in essentially the same geometry as in Fig. 2.12 In the present setup, the chemical diode can only be constructed with illumination of the light-sensitive excitable eld at a certain intensity. Figure 3 shows a spatiotemporal diagram on the manner of wave propagation. At low light intensity (I3.07104 lx or at minimum photoinhibition of the excitable eld, the wave propagates in both directions Fig. 3a. At intermediate intensity (I3.24104 lx, the wave propagates only in one direction, from left to right Fig. 3b. At the highest intensity (I3.33104 lx or at the strongest inhibition, the wave is not propagated in either direction Fig. 3c. Thus the result in Fig. 3 clearly indicates that the manner of wave propagation can be switched merely by changing the relative excitability and without changing the spatial geometry of the circuit. Figure 4 shows an experiment on coincidence, under I 2.76104 lx. As shown in Fig. 4a, when a wave propagates from left to right, the signal is not transmitted through the gap into the output channel. Figure 4b shows the AND operation: when two inputs arrive at the center almost simultaneously, a new wave is generated and propagated through the output channel. Figure 5 shows an example of different operations on a single circuit. When the system exhibits low excitability with high light intensity (I3.53104 lx, as shown in Fig.
Different operations on a single circuit
FIG. 5. Different operations with a single input. a At higher light intensity (I3.53104 lx, no output is generated. b At lower light intensity (I 2.48104 lx, an output signal is seen at all three output channels.
FIG. 3. Spatiotemporal representations of the manner of wave propagation, depending on the intensity of illuminated light. The geometry of the chemical diode is shown at the top, and is the same as in Fig. 2. a Bidirectional propagation. b Unidirectional propagation. c Propagation failure.

5a, a single chemical wave moving from left to right does not generate any signal in the output channel. In contrast, when the system is hyperexcited with low light intensity (I 2.48104 lx, as shown in Fig. 5b, a single wave causes
new signals in all three output channels. Thus the system can be made either active or resting by controlling the light intensity. By using a light intensity just above the threshold between the two modes shown in Fig. 5, one can perform an experiment on the coincidence of two opposing waves. Figure 6 shows an experimental time-difference detector, under I2.77104 lx. Similar to the results regarding the detection of coincidence in Fig. 4, when two input waves collide near a detector the edge near the input channel, a new signal is generated in the output channel. Thus output channels I, II, and III detect time differences of t11, 0, and 11 s, respectively. On the other hand, when the time difference deviates or the collision occurs far from the edge detector, no signal is transmitted in the output channels.

COMPUTER SIMULATION

The manner of wave propagation in the BZ reaction can be interpreted by a kinetic mechanism, the so-called Oregonator.23 Numerical studies of these wave propagation phenomena were carried out using TysonFife24 scaling of the Oregonator model, modied to describe the photosensitive BZ reaction:25,26
u 1 D u 2 u qwuwuu 2 , t 1 v D v 2 v u v , t
FIG. 4. Coincidence detection on photosensitive BZ medium at light intensity I2.75104 lx. a A single wave passing from left to right on the bar does not transmit a signal in the output channel. b When two waves collide near the gate, the signal is transmitted toward the output channel.
w 1 D w 2 w qwuw f v , t 2
FIG. 6. Time-difference detection at light intensity I2.77104 lx. a Scheme of the time-difference detector. b Time difference detected at each channel. c Experiments at ve different values of t. The geometry is the same as in Fig. 5.
where u, v , and w correspond to the dimensionless concentrations of NaBrO2, Rubpy3, and Br, respectively. D u , 3 D v , and D w are the diffusion coefcients for u, v , and w, respectively. 2 means / 2 x 2 / 2 y 2. The parameters f 1.0, q0.0015, 1 0.03, and 2 0.0003 are kept constant throughout the calculations. D u and D w are taken to be equal with a good approximation and scaled to be unity: D u D w 1. As Rubpy3 is almost immobilized in the 3 membrane lter27 adopted in the present study, D v is set to be zero. The light intensity is proportional to.25,26 Numerical simulations were carried out on Eqs. 13 using the Euler method with a time step and ADI method28 alternating direction implicit method with a space step. The grid size is 750750 points in a square lattice, and the time interval is t0.0003 and the unit grid size is h0.2. We have numerically examined the effect of the grid size and conrmed that the essential manner of propagation is the same between the conditions, h0.2 and 0.04. In the

present article, we show the numerical results with the grid size of h0.2. The boundary condition at the edge of the frame is taken to be no ux, while that between the excitable and inhibitory elds is free. Figure 7 shows the results for a numerical simulation of a chemical diode. The wave behavior was calculated from Eqs. 13, where corresponds to the light intensity. We used 0.08. This result reproduces well the experimental trends shown in Fig. 2. Figure 8 shows the spatiotemporal plot of wave propagation depending on the light intensity in a numerical simulation. At a low light intensity 0.07, a wave propagates through the gap in both directions. When the light intensity is increased to 0.08, a wave can only pass through the gap from left to right. When 0.09, a wave cannot propagate in either direction. These results in the simulation correspond well to the experimental observations Fig. 3. It may be of value to indicate some difference between
FIG. 7. Computer simulation of wave propagation on a diode, at a time interval of 1.5 using the coupled differential equations 13. a A signal is transmitted from left to right. b Propagation failure. In the pictures on the left in a and b, the value of is indicated by the gray level where white corresponds to the maximum. The pictures on the right in a and b are the quasi-three-dimensional representations. These gures show only the center region grid size 215215 points of the calculated eld grid size 750750 points. Black and gray regions correspond to excitable and inhibitory elds, respectively, and the bright region indicates a propagating wave in quasicolor representation with the variable in Eqs. 13.
FIG. 8. Computer simulation of the manner of wave propagation with the same spatial geometry as in Fig. 7. Space-time plot of traveling waves with the variable in Eqs. 13 along the horizontal centerline of the diode geometry 750 points.
the experiments and numerical simulations; for example, plane waves are generated in Fig. 7, whereas in experiments as in Fig. 2, the wave fronts are curved. According to the standard theoretical consideration29 on the stability of traveling wave, the critical radius on the wave propagation is given as R c D/c, where D and c are correspond to the diffusion coefcient and velocity of wave propagation, respectively. From the experimental observation c is around 102 cm/s. With the plausible order of D as 105 cm2/s, R c is estimated as 103 cm. This means that the effect of curvature may have negligible importance on the manner of wave propagation, at least in our experimental conditions. Curvature effect may become more signicant on the experiments with smaller size in the experimental system.

DISCUSSION

Our results have shown that different operations can be performed depending on the excitability of a system. It is also interesting to note that the time operations can be performed without a clock. In a Neumann computer, a central clock is needed to perform time operations. In the present study, it is shown that this new idea actually works in excitable chemical medium, i.e., the BZ reaction. Thus it is becoming clear that a rich variety of operations can be performed using an excitable eld, without a clock, CPU, or program. The manner of the operation of an excitable eld, or eld computation, can be selected by controlling the eld excitability as a whole. Thus the light intensity in the present
study acts as a kind of hormone to tune the activity of the system. This means that there should be no unavoidable bottleneck as seen in the usual Neumann-type computers. It is also to be mentioned that the adjustment of the excitability with light intensity means a tough reproducibility in the experiments; essentially the same manner of wave propagations is obtained even at different temperature by tuning the light intensity. On the other hand, the BZ reaction is quite fragile: the wet-reaction medium is not suitable for use in a practical computing machine. If a solid-state excitable system can be identied, it may be useful to examine the possibility of eld computation with such a medium. Recently, the generation of an excitable wave has been observed on a solid system.30 Trial on the fabrication of reaction-diffusion chip has also been reported using a semiconductor.31 For the practical application of a eld computer, it will be necessary to construct a circuit on a solid substrate. In addition, it would be interesting to consider a hybrid system with the connection of a eld computer and a Neumann-type computer. That is, the output signals in a eld computer can be transformed into a one-dimensional arrangement of symbols, as in a Turing machine. This indicates that the output from operations with a eld computer can be further processed with a Neumann-type computer. The idea of a hybrid computing system using eld and Neumann computers may be a promising target for the further development of the computational devices. With regard to the spatial geometry of the timedifference detector shown in Fig. 6, it is interesting to note
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