Th. Plesser

Two-dimensional spectrophotometry of spiral wave propagation in the Belousov—Zhabotinskii reaction. I. experiments and digital data representation

Abstract The spiral-shaped wave of chemical activity propagating in a 1 mm layer of an excitable solution of the Belousov-Zhabotinskii reaction is analysed quantitatively for a 5 min time interval in a 4.5 × 4.5 mm area. The spatial distribution of the reaction catalyst and indicator ferroin is measured by light absorption at 490 nm with a video- and computer-based two-dimensional spectrophotometer. Digital images with 10 μm spatial and 256 digital units intensity resolution are acquired at a frequency of 20 per minute. Initially, the spiral has a pitch of 1.18 mm, a revolution time of 17.2 s, and the wavefronts propagate outwards with a velocity of 69 μm/s. After 5 min these quantities have changed by up to 5%. Three-dimensional graphic procedures and image analysis reveal that the wave profiles are symmetric close to the spiral center and become highly asymmetric during their outward displacement. The core of the spiral has a radius of 0.35 mm. Its center is a singular site (diameter

Two-dimensional spectrophotometry of spiral wave propagation in the belousov—Zhabotinskii reaction. II. Geometric and kinematic parameters

Abstract Spectrophotometric data of the two-dimensional concentration distribution of the reaction catalyst ferroin/ferriin are analyzed for the spiral wave of chemical activity propagating in the Belousov-Zhabotinskii reaction. The Archimedian spiral and the involute of a circle fit equally well the iso-intensity levels corresponding to the highest and lowest values of terriin concentration. Initially, the spiral pitch is 1.19 mm and the revolution time is 17.0 s. From these data a wave propagation velocity of 70 μm/s is calculated. During 5 min the pitch and the period increase slightly, whereas the velocity remains approximately constant. The time course of these parameters is described by second order polynomials. The time evolution of parameters agrees with results that were previously obtained by local evaluation methods. Ferriin concentration profiles are fitted by splines. From their derivatives concentration gradients are estimated to reach 5 mM/mm. The transition from a quasi-stationary state at the spiral center to the full wave amplitude outside the core is quantified.

The onset of convection in a finite container due to surface tension and buoyancy

Abstract A method for predicting instabilities which combines recent techniques from bifurcation theory with the finite-element method is described. It is applied to the prediction of the onset of convection driven by both surface tension and buoyancy in rectangular containers. For zero buoyancy, the critical values of the Marangoni number for the first two bifurcations from the trivial solution are found for a two-dimensional cavity of aspect ratio 2. The variation of these critical values with aspect ratio is obtained by continuation methods and this reveals an interlacing of modes as the container size increases. It is established that the bifurcation to an even number of cells is transcritical rather than pitchfork and the turning point on the subcritical branch is located as a function of aspect ratio. The hysteresis associated with the transcritical bifurcation is small. As the surface tension forces decrease to zero, so that the convection is driven by buoyancy alone, the amount of hysteresis associated with the transcritical bifurcation becomes vanishingly small. The reason for this is not fully understood.

Hydrodynamic instabilities and pattern formation in a cytoplasmic medium from yeast

1. Matile, P.: The Lytic Compartment of Plant Cells. New York: Springer 1975 2. Matile, P.: Ann. Rev. Plant Physiol. 29, 193 (1978) 3. Matile, P.: Naturwissenschaften 71, 18 (1984) 4. Marty, F., et al., in: The Biochemistry of Plants, Vol. 1, p. 625 (Stumpf, P.K., Conn, E.E., eds.). London-New York: Academic Press 1980 5. Constabel, F.: Naturwissenschaften 47, 1 (1960); Planta 59, 330 (1963) 6. Sticher, L., et al.: J. Cell Sci. 48, 345 (1981); Sticher L., et al., in: Plant Tissue Culture 1982, p. 223 (A. Fujiwara, ed.), Tokyo ; Kevers C., et al. : Plant Growth Regul. 1, 61 (1982) 7. Oleson, A.E., Fahrlander, P.D., in: Plant Tissue Culture 1982, p. 219 (Fujiwara, A., ed.), Tokyo 8. Boiler, T., Kende, H. : Plant Physiol. 63, 1123 (1979) 9. Nishimura, M., Beevers, H. : ibid. 62, 44 (1978) 10. Alberts, B., et al. : Molecular Biology of the Cell. New York-London: Garland 1983 11. Gaspar, T., etal.: Phytochemistry 22, 2657 (1983) 12. Matile, P.: Z. Pflanzenphysiol. 99, 475 (1980) 13. Barz, W., in: Plant Tissue Culture and its Biotechnological Application, p. 153 (Barz, W., et al., eds.). Berlin: Springer 1977 14. Barz, W., K6ster, J., in: Biochemistry of Plants, Vol. 7, p. 35 (Stumpf, P.K., Conn, E.E., eds.). London-New York: Academic Press 1981 15. B6hm, H., in: Frontiers of Plant Tissue Culture 1978, p. 201 (Thorpe, T.A., ed.). Calgary: IAPTC 1978; Olson, A.C., et al. : Plant Physiol. Lancaster 44, 1594 (1969); Berlin, J., et al. : Phytochemistry 23, 1277 (1984) 16. Wink, M., Hartmann, T.: Z. Naturforsch. 37, 369 (1982) 17. Wink, M., et al.: Planta Med. 38, 238 (1980) 18. Zenk, M.H.: Verh. Ges. Dt. Naturf. )~rzte, p. 145 (1982) 19. Bergmeyer, H.U.: Methods of Enzymatic Analysis. Weinheim: Verlag Chemie 1983 20. Wink, M. : submitted for publication 21. McNeil, M., et al. : Ann. Rev. Biochem. 53, 625 (1984)

Deconvolution of periodic heat signals by fast fourier transform

Abstract The simultaneous measurement of the rate of heat production and of at least one other physical signal generated by an oscillating chemical or biochemical reaction is a promising tool for the elucidation of the underlying reaction steps and their correlation in time. An essential prerequisite for the interpretation of the experiments is the deconvolution or “desmearing” of the recorded signals. The usefulness of Fast Fourier Transform (FFT) algorithms for the deconvolution is shown by numerical simulations. Various systematic errors superimposed on the “true” signal by the time resolution of the apparatus in use are analyzed as well as statistical noise and serially correlated errors in the measured data. A short description of a robust and easy to use software package of the deconvolution algorithm is given. The package is written in FORTRAN 77 and executable on personal computers and mainframes.

Oscillatory phenomena in biological systems

Recently, under the auspices of the European Molecular Biology Organization (EMBO) and supported by the Max-Planck-Gesellschaft and the Deutsche Forschungsgemeinschaft, a workshop on oscillatory phenomena was held, 3-6 October 1976, covering the thermodynamic and kinetic requirements for the generation of periodic phenomena, mathematical methods as well as specific chemical, biochemical and biological systems.

Calorimetric measurements of an intermittency phenomenon in oscillating glycolysis in cell-free extracts from yeast

Abstract Intermittencies, i.e. quiet non-oscillating periods between oscillating regimes, are described for the first time in glycolytic oscillations and discussed in energy terms. The different regimes in the power-time-curves are of approximately equal energy content and independent of the initial sugar concentration while the total heat produced is a linear function of the sugar concentration. It renders an enthalpy change of -(134±10) kJ per mole glucosyi units in good agreement with data from the literature. A device for the calorimetric vessel is presented which combines effective stirring of the vessel content with simultaneous measurement of optical absorbance and heat flux.

Chemical Turnover and the Rate of Heat Production in Complex Reaction Systems

Chemical turnover, the formation and modification of chemical compounds, constitutes the basis for many processes going on in a broad spectrum of organized objects covering the cellular level in living matter as well as the production facilities in the chemical industry. The complexity of the processes depends on the available input and the required output; it may just consist of one simple first order reaction or a long sequence of intermediate steps with branching points and reaction loops.

Wave propagation in the Belousov-Zhabotinskii reaction depends on the nature of the catalyst

Propagation of waves of chemical activity has been described in excitable media of the ferroin-catalyzed Belousov-Zhabotinskii (BZ) oscillator, readily detectable in the visible range [1-4] . Target patterns have also been reported for oscillatory media of the Ru(bipy)~+-catalyzed BZ reaction [5]. For homogeneous stirred conditions, however, the mechanism and the detailed properties of the BZ reaction have been described for the ceriumcatalyzed system [6-7] , while no spatial pattern formation in thin layers of this system has been directly observed yet because the color changes of the Ce(IV)/Ce(III) redox couple from yellow to colorless are invisible at low concentrations and/or in thin layers of the reagent. Addition of ferroin as an indicator to visualize the cerium waves in the BZ reaction changes the properties of the cerium-catalyzed system [8] because ferroin is itself a catalyst of the BZ reaction. This means that BZ solutions containing both cerium and ferroin can be considered as mixed catalyst systems. This is valid for the manganese catalyst as well. The four catalysts also differ from each other regarding their redox properties and the respective rate constants of the composite reactions of the oscillation containing the catalyst [7]. This should lead to differences in the properties of the chemical waves because they represent a coupling between diffusion and chemical reactions. In this paper we re-

Extended batch calorimetry on periodic chemical reactions

Abstract Three small setups for a batch microcalorimeter are described which allow for simultaneous determinations of the rate of heat production and of light absorbance, electrode potential or gas production. The setups are tested with fast chemical reactions and the time constants of the calorimetric signal have been determined thereby. Finally, examples are presented showing the usefulness of the device for investigations of periodic chemical reactions.