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What Everyone Should Know About the Belousov-Zhabotinsky Reaction

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Frontiers in Mathematical Biology

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 100))

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.

    Article  Google Scholar 

  • Chance, B., Ghosh, A.K., Pye, E.K. & Hess, B. (1973). Biological and Biochemical Oscillators, Academic Press, New York & London.

    Google Scholar 

  • de Kepper, P., Rossi, A. & Pacault, A. (1976). Étude expĂ©rimentale d’une rĂ©action chimique pĂ©riodique. Diagramme d’etat de la rĂ©action de Belousov-Zhabotinskii. C.R. Acad. Sci. Paris 283 C., 371–375.

    Google Scholar 

  • Field, R.J. (1972). A reaction periodic in time and space. J. Chem. Educ. 49, 308–311.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Geiseler, W. & Foellner, H.H. (1977). Three steady state situation in an open chemical reaction system. I. Biophys. Chem. 6, 107–115.

    Article  Google Scholar 

  • Györgyi, L. & Field, R.J. (1991). Simple modles of deterministic chaos in the Belousov-Zhabotinsky reaction. J. Phys. Chem. 95, 6594–6602.

    Article  Google Scholar 

  • Györgyi, L. & Field, R.J. (1992). A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction. Nature (Lond.) 355, 808–810.

    Article  Google Scholar 

  • Keener, J.P. (1986). A geometrical theory for spiral waves in excitable media. SIAM J. Appl. Math. 46, 1039–1056.

    Article  MathSciNet  MATH  Google Scholar 

  • Keener, J.P. (1988). The dynamics of three-dimensional scroll waves in excitable media. Physica D 31, 269–276.

    Article  MathSciNet  MATH  Google Scholar 

  • Keener, J.P. & Tyson, J.J. (1986). Spiral waves in the Belousov-Zhabotinskii reaction. Physica D 21, 307–324.

    Article  MathSciNet  MATH  Google Scholar 

  • Keener, J.P. & Tyson, J.J. (1992). The dynamics of scroll waves in excitable media. SIAM Rev. 34, 1–39.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Luther, R. (1906). Raumliche Fortpflanzung chemischer Reaktionen. Z. Elektrochemie 12, 596–600.

    Article  Google Scholar 

  • Martiel, J.L. & Goldbeter, A. (1987). A model based on receptor desensitization for cyclic AMP signaling in Dictyostelium cells. Biophys. J. 52, 807–828.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Roux, J.C., Simoyi, R.H. & Swinney, H.L. (1983). Observation of a strange attractor. Physica D 8, 257–266.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Scott, S.K. (1991). Chemical Chaos, Oxford Univ. Press, Oxford UK.

    Google Scholar 

  • Simoyi, R.H., Wolf, A. & Swinney, H.L. (1982). One-dimensional dynamics in a multicomponent chemical reaction. Phys. Rev. Lett. 49, 245–248.

    Article  MathSciNet  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Tyson, J.J. (1979). Oscillations, bistability and echo waves in models of the Belousov-Zhabotinskii reaction. Ann. N.Y. Acad. Sci. 316, 279–295.

    Article  MathSciNet  Google Scholar 

  • 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.

    Google Scholar 

  • Tyson, J.J. (1991). Modeling the cell division cycle: cdc2 and cyclin interactions. Proc. Natl. Acad. Sci. USA 88, 7328–7332.

    Article  Google Scholar 

  • Tyson, J.J. & Fife, P.C. (1980). Target patterns in a realistic model of the Belousov-Zhabotinskii reaction. J. Chem. Phys. 73, 2224–2237.

    Article  MathSciNet  Google Scholar 

  • Tyson, J.J. & Keener, J.P. (1988). Singular perturbation theory of traveling waves in excitable media (a review). Physica D 32, 327–361.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Tyson, J.J. & Murray, J.D. (1989). Cyclic-AMP waves during aggregation of Dictyostelium amoebae. Development 106, 421–426.

    Google Scholar 

  • Tyson, J.J. & Strogatz, S.H. (1991). The differential geometry of scroll waves. Inter. J. Bifur. Chaos 1, 723–744.

    Article  MathSciNet  MATH  Google Scholar 

  • Welsh, B.J. (1984). Pattern Formation in the Belousov-Zhabotinsky Reaction, Thesis, Glasgow College of Technology, p. 35.

    Google Scholar 

  • Winfree, A.T. (1972). Spiral waves of chemical activity. Science 175, 634–636.

    Article  Google Scholar 

  • Winfree, A.T. (1973). Scroll-shaped waves of chemical activity in three dimensions. Science 181, 937–939.

    Article  Google Scholar 

  • Winfree, A.T. (1974). Rotating chemical reactions. Sci. Amer. 230 (6), 82–95.

    Article  Google Scholar 

  • Winfree, A.T. (1984). The prehistory of the Belousov-Zhabotinsky oscillator. J. Chem. Educ. 61, 661–663.

    Article  Google Scholar 

  • Winfree, A.T. (1987). When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, Princeton Univ. Press, Princeton NJ.

    Google Scholar 

  • Winfree, A.T. (1990). Stable particle-like solutions to the nonlinear wave equations of three-dimensional excitable media. SIAM Rev. 32, 1–53.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Zaikin, A.N. & Zhabotinsky, A.M. (1970). Concentration wave propagation in two-dimensional liquid-phase self-oscillating system. Nature (Lond.) 225, 535–537.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Zhabotinsky, A.M. & Zaikin, A.N. (1973). Autowave processes in a distributed chemical system. J. Theor. Biol. 40, 45–61.

    Article  Google Scholar 

  • Zykov, V.S. (1980). Kinematics of the steady circulation in an excitable medium. Biophysics 25, 329–333.

    Google Scholar 

  • Zykov, V.S. (1987). Simulation of Wave Processes in Excitable Media, Manchester Univ. Press, Manchester UK.

    MATH  Google Scholar 

  • Zykov, V.S. & Morozova, O.L. (1979). Speed of spread of excitation in a two-dimensional excitable medium. Biophysics 24, 739–744.

    Google Scholar 

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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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  • DOI: https://doi.org/10.1007/978-3-642-50124-1_33

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