Abstract
In the early 1950s a Soviet biochemist, Boris P. Belousov, was trying to develop a simple chemical model of the oxidation of organic molecules in living cells. Central to these pathways is the Krebs cycle, whereby organic acids are oxidized to CO2 and H2O. In aerobic organisms, oxygen is the oxidizing agent, and the reactions are catalyzed by enzymes and electron-transport proteins, many of which rely on iron ions (Fe2+/Fe3+) to move electrons around. In his testtube version of metabolism, Belousov used citric acid (one of the intermediates of the Krebs cycle) as an organic substrate, bromate ions (BrO3-) as oxidizing agent, and cerium ions as catalyst. Any chemist would expect the reaction to proceed monotonically to equilibrium, perhaps showing one visible sign of progress by changing from a colorless solution (cerium in the reduced state, Ce3+) to pale yellow (the oxidized state, Ce4+). So we can imagine Belousov’s surprise when his reaction mixture turned yellow then colorless, then yellow again and colorless, oscillating dozens of times between oxidized and reduced states (Fig. 1).
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References
Agladze, K.I., Kocharyan, R.A. & Krinsky, V.l. (1991). Direct observation of vortex ring collapse in a chemically active medium. Physica D 49, 1–4.
Chance, B., Ghosh, A.K., Pye, E.K. & Hess, B. (1973). Biological and Biochemical Oscillators, Academic Press, New York & London.
de Kepper, P., Rossi, A. & Pacault, A. (1976). Étude expérimentale d’une réaction chimique périodique. Diagramme d’etat de la réaction de Belousov-Zhabotinskii. C.R. Acad. Sci. Paris 283 C., 371–375.
Field, R.J. (1972). A reaction periodic in time and space. J. Chem. Educ. 49, 308–311.
Field, R.J. & Burger, M.(1985). Oscillations and Traveling Waves in Chemical Systems, Wiley-Interscience, New York. Belousov’s article appears on pp. 605–613.
Field, R.J. & Försterling, H.D. (1986). On the oxybromine chemistry rate constants with cerium ions in the Field-Körös-Noyes mechanism of the Belousov-Zhabotinskii reaction: The equilibrium HBrO2 + BrO3 - + H+ = 2BrO2 + H2O. J. Phys. Chem. 90, 5400–5407.
Field, R.J., Körös, E. & Noyes, R.M. (1972). Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system. J. Am. Chem. Soc. 94, 8649–8664.
Field, R.J. & Noyes, R.M. (1974). Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys. 60, 1877–1884.
Field, R.J. & Noyes, R.M. (1974). Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction. J. Am. Chem. Soc. 96, 2001–2006.
Foerster, P., Mueller, S.C. & Hess, B. (1989). Critical size and curvature of wave formation in an excitable chemical medium. Proc. Natl. Acad. Sci. USA 86, 6831–6834.
Geiseler, W. & Bar-Eli, K. (1981). Bistability of the oxidation of cerous ions by bromate in a stirred flow reactor. J. Phys. Chem. 85, 908–914.
Geiseler, W. & Foellner, H.H. (1977). Three steady state situation in an open chemical reaction system. I. Biophys. Chem. 6, 107–115.
Györgyi, L. & Field, R.J. (1991). Simple modles of deterministic chaos in the Belousov-Zhabotinsky reaction. J. Phys. Chem. 95, 6594–6602.
Györgyi, L. & Field, R.J. (1992). A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction. Nature (Lond.) 355, 808–810.
Keener, J.P. (1986). A geometrical theory for spiral waves in excitable media. SIAM J. Appl. Math. 46, 1039–1056.
Keener, J.P. (1988). The dynamics of three-dimensional scroll waves in excitable media. Physica D 31, 269–276.
Keener, J.P. & Tyson, J.J. (1986). Spiral waves in the Belousov-Zhabotinskii reaction. Physica D 21, 307–324.
Keener, J.P. & Tyson, J.J. (1992). The dynamics of scroll waves in excitable media. SIAM Rev. 34, 1–39.
Körös, E., Ladanyi, L., Friedrich, V., Nagy, Z. & Kis, A. (1974). The Ru(dipy)32+-bromate-malonic acid oscillating system. Reac. Kin. Catal. Lett. 1, 455–460.
Luther, R. (1906). Raumliche Fortpflanzung chemischer Reaktionen. Z. Elektrochemie 12, 596–600.
Martiel, J.L. & Goldbeter, A. (1987). A model based on receptor desensitization for cyclic AMP signaling in Dictyostelium cells. Biophys. J. 52, 807–828.
Panfilov, A.V. & Pertsov, A.M. (1984). Vortex ring in a three-dimensional active medium described by reaction-diffusion equations. Dokl. Biophys. 274, 58–60.
Panfilov, A.V., Rudenko, A.N. & Krinskii, V.I. (1986). Vortical rings in three-dimensional active media with diffusion over two components. Biophysics 31, 926–931.
Rinzel, J. (1980). Impulse propagation in excitable systems. In Dynamics and Modelling of Reactive Systems (Stewart, W.E., Ray, W.H. & Conley, C.C.), pp. 259–291, Academic Press, New York.
Roux, J.C., Simoyi, R.H. & Swinney, H.L. (1983). Observation of a strange attractor. Physica D 8, 257–266.
Schmitz, R.A., Graziani, K.R. & Hudson, J.L. (1977). Experimental evidence of chaotic states in the Belousov-Zhabotinskii reaction. J. Chem. Phys. 67, 3040–3044.
Scott, S.K. (1991). Chemical Chaos, Oxford Univ. Press, Oxford UK.
Simoyi, R.H., Wolf, A. & Swinney, H.L. (1982). One-dimensional dynamics in a multicomponent chemical reaction. Phys. Rev. Lett. 49, 245–248.
Smoes, M.L. (1980). Chemical waves in the oscillatory Zhabotinskii system. A transition from temporal to spatio-temporal organization. In Dynamics of Synergetic Systems (Haken, H.), pp. 80–96, Springer-Verlag, Berlin-Heidelberg.
Tyson, J.J. (1979). Oscillations, bistability and echo waves in models of the Belousov-Zhabotinskii reaction. Ann. N.Y. Acad. Sci. 316, 279–295.
Tyson, J.J. (1985). A quantitative account of oscillations, bistability, and traveling waves in the Belousov-Zhabotinskii reaction. In Oscillations and Traveling Waves in Chemical Systems (Field, RJ. & Burger, M.), pp. 93–144, Wiley-Interscience, New York.
Tyson, J.J. (1991). Modeling the cell division cycle: cdc2 and cyclin interactions. Proc. Natl. Acad. Sci. USA 88, 7328–7332.
Tyson, J.J. & Fife, P.C. (1980). Target patterns in a realistic model of the Belousov-Zhabotinskii reaction. J. Chem. Phys. 73, 2224–2237.
Tyson, J.J. & Keener, J.P. (1988). Singular perturbation theory of traveling waves in excitable media (a review). Physica D 32, 327–361.
Tyson, J.J. & Manoranjan, V.S. (1984). The speed of propagation of oxidizing and reducing wave fronts in the Belousov-Zhabotinskii reaction. In Non-Equilibrium Dynamics in Chemical Systems (Vidal, C. & Pacault, A.), pp. 89–93, Springer-Verlag, Berlin-Heidelberg.
Tyson, J.J. & Murray, J.D. (1989). Cyclic-AMP waves during aggregation of Dictyostelium amoebae. Development 106, 421–426.
Tyson, J.J. & Strogatz, S.H. (1991). The differential geometry of scroll waves. Inter. J. Bifur. Chaos 1, 723–744.
Welsh, B.J. (1984). Pattern Formation in the Belousov-Zhabotinsky Reaction, Thesis, Glasgow College of Technology, p. 35.
Winfree, A.T. (1972). Spiral waves of chemical activity. Science 175, 634–636.
Winfree, A.T. (1973). Scroll-shaped waves of chemical activity in three dimensions. Science 181, 937–939.
Winfree, A.T. (1974). Rotating chemical reactions. Sci. Amer. 230 (6), 82–95.
Winfree, A.T. (1984). The prehistory of the Belousov-Zhabotinsky oscillator. J. Chem. Educ. 61, 661–663.
Winfree, A.T. (1987). When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, Princeton Univ. Press, Princeton NJ.
Winfree, A.T. (1990). Stable particle-like solutions to the nonlinear wave equations of three-dimensional excitable media. SIAM Rev. 32, 1–53.
Winfree, A.T. & Jahnke, W. (1989). Three-dimensional scroll ring dynamics in the Belousov-Zhabotinsky reagent and in the two-variable Oregonator model. J. Phys. Chem. 93, 2823–2832.
Zaikin, A.N. & Zhabotinsky, A.M. (1970). Concentration wave propagation in two-dimensional liquid-phase self-oscillating system. Nature (Lond.) 225, 535–537.
Zhabotinskii, A.M. (1964). Periodic course of oxidation of malonic acid in solution (investigation of the kinetics of the reaction of Belousov). Biophysics 9, 329–335.
Zhabotinsky, A.M. & Zaikin, A.N. (1973). Autowave processes in a distributed chemical system. J. Theor. Biol. 40, 45–61.
Zykov, V.S. (1980). Kinematics of the steady circulation in an excitable medium. Biophysics 25, 329–333.
Zykov, V.S. (1987). Simulation of Wave Processes in Excitable Media, Manchester Univ. Press, Manchester UK.
Zykov, V.S. & Morozova, O.L. (1979). Speed of spread of excitation in a two-dimensional excitable medium. Biophysics 24, 739–744.
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Tyson, J.J. (1994). What Everyone Should Know About the Belousov-Zhabotinsky Reaction. In: Levin, S.A. (eds) Frontiers in Mathematical Biology. Lecture Notes in Biomathematics, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50124-1_33
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