Müller, Stefan C.

Plesser, Theo

Siegert, Florian

Weijer, Cornelis J.

English

Open Access LMU

Spatio-Temporal Organization in Nonequilibrium Systems Contributions to the Dortmunder Dynamische Woche June 1992 Edited by Stefan C. Müller and Theo Plesser Projekt verlag Table of Contents BZ-waves propagation along a line of diffusion-jump 1-7 Agladze, KI. and De Kepper, P. Models of cytoplasmic motion 8-10 Alt, W. Pattern formation and topological defects in nonlinear optics 11-12 Arecchi, F.T. Wave phenomena in an excitable surface reaction 13-15 Bär, Μ., Eiswirth, Μ , Rotermund, H.H. and Eni, G. Dynamic instabilities in a coupled electrochemical and 16-18 biochemical reaction system Baier, G. and Urban, P. Bifurcations and symmetries of spiral waves 19-20 Barkley, D. Experiments on interacting electrochemical oscillators 21-24 Bell, J.C, Wang, Y., Jaeger, N.I. and Hudson, J.L. Convection in gasses at elevated pressures 25 Bodenschatz, Ε, Morris, S.W., deBruyn, J.R., Cannell, D.S. and Ahlers, G. Evolutionary consequences of spatial pattern formation 26-28 Boerlijst, M.C. and HogewegP. Spatial structures in reaction-diffusion systems 29-31 Borckmans, P., De Wit, A. and Dewel, G. Localized solutions of envelope and phase equations 32-33 Brand, HR andDeissler, RJ. Spiral drift in a light-sensitive active medium with spatial 34-36 gradient of excitability Braune, Μ. and Engel, Η. Mathematical modeling of oscillations and waves of oxidation 37-39 and reduction in the cerium and ferroin-catalyzed BZ-reaction Buchholtz, F. Pattern formation in populations of chemotactic bacteria 40 Budrene, E.O. Transitions to tertiary and quaternary states of fluid flows Busse, H.-G. and Clever, R.M. 41-43 I I Stochastic effects in nonlinear chemical systems 44-45 Careta, A. and Sagues, F. Pattern formation in oscillators submitted to a parametric 46-58 forcing close to the frequency cut-off Coullet, P., Frisch, Τ. and Sonn'mo, G. Spiral waves of excitation in isolated cardiac muscle 59-62 Davidenko, J.M., Pertsov, A.M., Salomonsz, R. Baxter, W.T. and Jalife, J. Spiral waves in a small disk and on a small sphere 63-64 Davydov, V.A. and Zykov, V.S. Cellular automaton modeling of pattern formation by 65-67 filamentous fungi Deutsch, Α., Dress, A. and Rensing, L . Oscillations and waves of cytosolic calcium: properties of a 68-70 model based on calcium-induced calcium release Dupont, G. and Goldbeter, A. Symmetry breaking instability in a model of chemical reaction 71-74 and molecular diffusion Dutt, A.K. Chemical pattern formation: An overview 75-77 Epstein, LR. Pattern formation in the oscillatory regime of the CO-oxidation 78-81 on Pt(110) Falcke, M. and Engel, Η. Period doublings, period three, chaos, and quasiperiodicity in 82-84 the peroxidase - oxidase reaction: Experimental and theoretical studies Geest, Τ., Larter, R, Steinmetz, C. and Oben, L.F. A cellular automaton model of excitable media 85-88 Gerhardt, Μ. Developmental complexity and evolutionary order 89 Goodwin, B. Theorist's view of a beautiful experiment: how many states of 90-92 Rayleigh-Benard turbulence? Grossmann, S. and Lohse, D. I I I Dependence of the spatial and temporal dynamics on the 93-95 acidity in the ferroin-catalyzed Belousov-Zhabotinsky reaction Guria, G.T., Zhabotinsky, A.M., Plesser, Tlx., Kiyatkin, A.B. and Epstein, LR Pattern formation in the early Drosophila embryo 96-99 Hoch, M. and Jackie, H. Instabilities in propagating reaction-diffusion fronts 100-101 Honrath, D., Petrov, V., Scott, S.K and Showalter, Κ The role of "excess work" in nonequilibrium thermodynamic 102-104 systems Hunt, K.L.C., Hunt, P.M., Peng, B., Chu, X. and Ross, J. Ginzburg-Landau parameters for reaction-diffusion systems 105-107 Hynne, F., S0rensen, P.G., Ipsen, M., Kristiansen, K.R. and Florian, Μ. Transition from order to spatiotemporal turbulence in 108-110 catalytic NO reduction Imbihl, R. Nonlinear forecasting as a tool to diagnose heart disease 111-112 J0rgensen, B.L., Junker, Α., Mickley, H, Mobiler, Μ., Christiansen, Ε. and Olsen L.F. Transient bimodality in turbulence 1-turbulence 2 transition in 113-116 electrohydrodynamic convection in nematic liquid crystals Kai, S., Andoh, M. and Yamaguchi, S. Reactive dynamics in a multi-species lattice-gas automaton 117-118 Kapral, R, Lawniczak, A. and Masiar, P. Scroll waves in myocardium 119-121 Keener, J.P. and Panfilov, Α. V. Excitation wave propagation through narrow pathways 122-127 Kogan, B.Y., Karplus, W.J. and Billett, B.S. Coupled excitable cells 128-131 Kosek, Κ and Marek, Μ. Hyperchaos in a surface reaction 132-134 Kruel, Tfu-M., Eiswirth, M., Schneider, F.W. andErtl, G. Intracellular calcium waves: propagation, annihilation and 135-137 excitability Lechleiter, J.D. and Clapham, D. IV Scaling relations in thermal turbulence: global measurements 138-140 and boundary layers estimate Libchaber, A. Patterns of temperature waves on electrically heated catalytic 141-143 ribbons Luss, D. Reaction-diffusion patterns in heterogeneous media 144-145 Malchow, Η. and Sattler, C. Microtubules: Structure, dynamics, oscillations, and spatial 146-150 patterns Mandelkow, K, Marx, Α., Trinczek, B. and Mankelkow, E.-M. Pattern formation in neural activator-inhibitor networks 151-153 Markus, Μ. and Schepers, H.E. Spatial long-range coherence in squid giant axons 154-155 Matsumoto, G. Molecular evolution iin traveling waves 156-157 McCaskill, IS. Complex biological pattern formation by linking several 158-161 pattern forming reactions Meinhardt, Η. A big chemical-wave: accelerating propagation and surface 162-165 deformation induced by a spontaneous convection Miike, H., Yamamoto, H. and Kai, S. Diffusive coupling of spatio-temporal patterns in 166-170 nonequilibrium systems Mimura, M. Spiral waves in the Oregonator model: A study of time-space 171-175 correlations Müller, KH. and Plesser, Th. Growth patterns in two-phase systems 176 Müller-Krumbhaar, H. Formation of temporal patterns in the swimming behaviour of 177-179 Halobacteria: Possible dynamical mechanisms Naber, H. Dynamics of spiral waves in the Belousov-Zhabotinsky reaction 180-181 Nagy-Ungyarai, Zs. ν Unstable wave propagation in the Belousov-Zhabotinsky reaction Nagy-Ungvarai, Zs., Ungvarai, J., Hess, B., Pertsov, A.M. and Müller, S.C. 182-183 Reaction diffusion patterns in the catalytic CO oxidation on Pt(llO) - Front propagation and spiral waves -Nettesheim, S., v. Oertzen, Α., Rotermund, H.H. and Eni, G. 184-186 Measuring an accelerating propagation of a big wave by sequential image processing Nomura, Α., Miike, H. and Hashimoto, H. 187-189 Experiments at the boundary of two worlds: Reaction, diffusion, electric conduction and multicomponent convection in gel and fluid reactors Noszticzius, Z., Farkas, H, Schubert, Α., SwiftJ., McCormic, W.D. and Swinney, H.L. 190-193 Turing instability in the CI MA reaction Ouyang, Q. and Swinney, H.L. 194-196 Self-organized criticality in a semiconducting charge density wave compound Parisi, J., Peinke, J., Dumas, J. and Kittel, A. 197-199 Asymptotics of spiral waves 200-204 Pelci, P. and Sun, J. Turing-Hopf localized structures 205-210 Perraud, J.-l, Dulos, E., De Kepper, P., De Wit, Α., Dewel, G. and Borckmans, P. Electrohydrodynamic convection in nematics: The homeotropic case Pesch, W., Hertrich, A. and Kramer, L . 211-213 Interaction of chemical waves with convective flows induced by density gradients: A comparison between experiments and computer simulations Plesser, Th., Wilke, H. and Winters, KH. 214-216 Scaling exponents, wrinkled graphs, and the high Reynolds number geometry of turbulence Procaccia, I. 2Y7-21Q Spatio-temporal patterns in gas discharge systems Purwins, H.-G. and Willebrand, Η 221 Self-trapping of travelling-wave pulses Riecke, H. 222-223 VI Spiral turbulence in Taylor-Couette-flow Roesner, KG. Chemical implementation of computers Ross, J. Induction of temporal patterns in the locomotor behavior of Halobacterium - an indication of nonlinear dynamics Schimz, A. and Hildebrand, Ε. Pattern formation in molecular evolution - A physicist's look at biology Schuster, P. Observation of defect dynamics in small system Sepulchre, JA. and Babloyantz, A. Spatio-temporal patterns of on-going and evoked activity in cat visual cortex Shoham, D., Oilman, S. and Grinvald, A. Three-dimensional autowaves control cell motion in Dictyostelium slugs Siegert, F., Steinbock, Ο., Weijer, C.J. and Müller, S.C. Wave propagation and cell movement control morphogenesis of the cellular slime mould Dictyostelium discoideum Siegert, F. and Weijer, C.J. Spatio-temporal patterns in ionic diffusion chemical system Snita, D., Dvorak, L . and Marek, Μ. Pairs of pacemakers Spoerel, U., Peuker, A. and Busse, H.-G. Rotating vortex initiation in excitable media: pulse chemistry control Starm.er, C.F., Krinsky, V.l., Romashko, D.N., Aliev, R.R. and Stepanov, M.R Light-controlled spiral waves Steinbock, Ο. and Müller, S.C. Second control loop in the Belousov-Zhabotinsky reaction investigated at different acidities Varga, M. and Försterling, H.-D. Waves in a liquid, locally heated along a wire Vince, J.M., Dubois, M. and Berge, P. V I I Spontaneous nucleation in a reactive lattice gas automaton 266-269 Weimar, J.R. Numerical experiments on filament motion 270-273 Winfree,A.T. Hydrodynamic fluctuations in nematics 274-276 Winkler, B.L., Hörner, F., Richter, Η. and Rehberg, I. Artificial retina - photo image processing in the Belousov- 277-280 Zhabotinsky reaction in gels Yamaguchi, T., Ohmori, T. and Matumura-Inoue, T. Dynamic mode of entrainment in coupled chemical oscillators 281-283 Yoshikawa, Κ Mechanism of stratification in a thin-layered excitable 284-286 reaction-diffusion system with an oxygen gradient Zhabotinsky, A.M., Kiyatkin, A.B. and Epstein, LR. Effects of disorder in convective systems 287-288 Zimmermann, W. Kinematics of spiral wave with indistinct front 289-290 Zykov, V.S. 244 Wave propagation and cell movement control morphogenesis of the cellular slime mould Dictyostelium discoideum Florian Siegert and Cornells J. Weijer, Zoologisches Institut, Universität München, Luisenstraße 14, 8000 Manchen 2, Germany. FAX: 089-5902450 The cellular slime mould Dictyostelium discoideum is well suited to study cellular communication and the role of biological oscillations in spatio-temporal pattern formation. Dictyostelium cells live as solitary amoebae in the soil where they feed on bacteria. Upon starvation up to cells aggregate over large distances into a multicellular mass, the slug (see fig. 1A). The slug transforms during a complicated morphogenesis into a fruiting body consisting of a spore head supported by a stalk composed of dead vacuolated stalk cells. The spores disperse and germinate to single amoeba again. The aggregation and coordinated cell movement during slug morphogenesis require extensive cell-cell communication. The aggregation of single cells into multicellular structures is directed by periodic cyclic-AMP signals and Chemotaxis. Cells in the aggregation center periodically produce the chemoattractant cyclic Adenosine-Monophosphate (cAMP). cAMP is secreted into the extracellular medium, where it diffuses away. Neighbouring cells detect cAMP via cell surface receptors. These stimulated cells now produce themselves huge amounts of cAMP, which they in turn secrete. This feed-back process results in a wave-like propagation of the cAMP signal from cell to cell and from the center outwards. Extracellular phosphodiesterases degrades cAMP. After stimulation the cells are refractory to further stimulation. This property ensures unidirectional outward propagation of the signal. Stimulated cells respond with periodic chemotactic movement. Theys move in the direction of increasing cAMP concentrations. This leads to periodic waves of inward directed chemotactic movement. As a result the cells collect in the aggregation center. The cAMP wave propagation can be seen as outward propagating concentric or spiral optical density waves (see fig. IB) . These waves are only visible in monolayers of cells ,i.e during the early stages of aggregation (1). In later aggregates these waves are no longer visible. After aggregation the cells form a multicellular "slug" which contains up to cells. The slug has a defined polarity and is composed of at least three different cell types. The front quarter (tip) consists of two types of prestalk cells (pstA, pstB), the back three quarters consists of prespore cells. The prestalk cells will form the stalk of the fruiting body and the prespore cells the spores. We investigated whether the same principles that govern aggregation, i.e wave propagation and chemotactic cell movement, are responsible for the complex slug morphogenesis. Since optical density waves are no longer visible we investigated cell behaviour and cell movement in late aggregates and slugs. Cell movement of labeled single cells in Dictyostelium slugs were 245 analysed by high resolution digital image processing. We found that all cells in a slug move in a periodic and chemotactic fashion as juged by their periodic shape and velocity changes (2). This implies that the cells respond to periodic signals. In order to deduce the spatial geometry of these signals we determined the movement trajectories of many cells in various parts of the slug. Cells in the front and the back of a slug move along completely different trajectories (see fig. 1C). Prestalk cells move around the long axis of the slug, while prespore cells move forward parallel to the long axis. The cell movement data show that the chemotactic signal in the slug propagates as a three dimensional scroll wave in the front (prestalk zone), which transforms into planar waves in the back (prespore zone). This behavior is postulated to result from a difference in excitability of the cells along the long axis of the slug (2,3). The cells in the prestalk zone are more excitable than cells in the prespore zone. The biological significance of this particular type of wave propagation is that the core of the scroll wave will be a region of low continuous cAMP, conditions that favor the expression of stalk cell specific genes. In summary our experiments show that the morphogenesis of this relative simple biological system is controlled in two as well as in three dimensions largely by the dynamics of the underlying excitable system. 1. F.Siegertand C.J.Weijer, (1989) J. Cell.Sci. 93, 325 2. F.Siegert and C.J.Weijer, (1991) Physica D 49, 224 3. F Siegertand C.J.Weijer, (1992) Proc.Natl.Acad.Sei. 89, 6433 Figure: The life cycle of Dictyostelium discoideum The scheme (A) starts with single cells that aggregate in spirals as seen in darkfield optics. Moving cells are elongated and are seen as white bands due to increased light scattering (B). Cells which are not moving directionally are rounded and detected as dark bands. After stream formation waves emanating from the center propagate through the aggregation streams, while the cells move inward. The aggregation center can either be a mass of cells or temporarly form a loop. After tight aggregates (mounds) have formed the cells differentiate. Due to a higher oscillation frequency the prestalk cells form the tip in which the signals propagates as a (twisted) scroll wave as derived from the analysis of cell movement tracks (C, white lines). The wave rotates along its long axis as indicated by the black arrow. The mound now extends up in the air and forms a slug, which falls over and migrates away. The prestalk region stays a twisted scroll wave which decomposes upon arrival in the prespore zone in planar waves, due to the lower excitability of the prespore cells. The core of the slug is a region of low cAMP and this favors pstB expression, while the perifery of the tip with high cAMP favours pstA expression. The slug then converts by a series of not yet understood morphogenetic changes into a fruiting body, during which process the differentiation in the final cell types spore and stalk cells takes place. 246 

Wave propagation and cell movement control morphogenesis of the cellular slime mould Dictyostelium discoideum

Universität München: Elektronischen Publikationen

Spatio-Temporal Organization 
in Nonequilibrium Systems 
Contributions to the 
Dortmunder Dynamische Woche 
June 1992 
Edited by Stefan C. Müller and Theo Plesser 
Projekt verlag 
Table of Contents 
BZ-waves propagation along a line of diffusion-jump 1-7 
Agladze, KI. and De Kepper, P. 
Models of cytoplasmic motion 8-10 
Alt, W. 
Pattern formation and topological defects in nonlinear optics 11-12 
Arecchi, F.T. 
Wave phenomena in an excitable surface reaction 13-15 
Bär, Μ., Eiswirth, Μ , Rotermund, H.H. and Eni, G. 
Dynamic instabilities in a coupled electrochemical and 16-18 
biochemical reaction system 
Baier, G. and Urban, P. 
Bifurcations and symmetries of spiral waves 19-20 
Barkley, D. 
Experiments on interacting electrochemical oscillators 21-24 
Bell, J.C, Wang, Y., Jaeger, N.I. and Hudson, J.L. 
Convection in gasses at elevated pressures 25 
Bodenschatz, Ε, Morris, S.W., deBruyn, J.R., Cannell, D.S. and 
Ahlers, G. 
Evolutionary consequences of spatial pattern formation 26-28 
Boerlijst, M.C. and HogewegP. 
Spatial structures in reaction-diffusion systems 29-31 
Borckmans, P., De Wit, A. and Dewel, G. 
Localized solutions of envelope and phase equations 32-33 
Brand, HR andDeissler, RJ. 
Spiral drift in a light-sensitive active medium with spatial 34-36 
gradient of excitability 
Braune, Μ. and Engel, Η. 
Mathematical modeling of oscillations and waves of oxidation 37-39 
and reduction in the cerium and ferroin-catalyzed BZ-reaction 
Buchholtz, F. 
Pattern formation in populations of chemotactic bacteria 40 
Budrene, E.O. 
Transitions to tertiary and quaternary states of fluid flows 
Busse, H.-G. and Clever, R.M. 
41-43 
I I 
Stochastic effects in nonlinear chemical systems 44-45 
Careta, A. and Sagues, F. 
Pattern formation in oscillators submitted to a parametric 46-58 
forcing close to the frequency cut-off 
Coullet, P., Frisch, Τ. and Sonn'mo, G. 
Spiral waves of excitation in isolated cardiac muscle 59-62 
Davidenko, J.M., Pertsov, A.M., Salomonsz, R. Baxter, W.T. and 
Jalife, J. 
Spiral waves in a small disk and on a small sphere 63-64 
Davydov, V.A. and Zykov, V.S. 
Cellular automaton modeling of pattern formation by 65-67 
filamentous fungi 
Deutsch, Α., Dress, A. and Rensing, L . 
Oscillations and waves of cytosolic calcium: properties of a 68-70 
model based on calcium-induced calcium release 
Dupont, G. and Goldbeter, A. 
Symmetry breaking instability in a model of chemical reaction 71-74 
and molecular diffusion 
Dutt, A.K. 
Chemical pattern formation: An overview 75-77 
Epstein, LR. 
Pattern formation in the oscillatory regime of the CO-oxidation 78-81 
on Pt(110) 
Falcke, M. and Engel, Η. 
Period doublings, period three, chaos, and quasiperiodicity in 82-84 
the peroxidase - oxidase reaction: Experimental and 
theoretical studies 
Geest, Τ., Larter, R, Steinmetz, C. and Oben, L.F. 
A cellular automaton model of excitable media 85-88 
Gerhardt, Μ. 
Developmental complexity and evolutionary order 89 
Goodwin, B. 
Theorist's view of a beautiful experiment: how many states of 90-92 
Rayleigh-Benard turbulence? 
Grossmann, S. and Lohse, D. 
I I I 
Dependence of the spatial and temporal dynamics on the 93-95 
acidity in the ferroin-catalyzed Belousov-Zhabotinsky reaction 
Guria, G.T., Zhabotinsky, A.M., Plesser, Tlx., Kiyatkin, A.B. and 
Epstein, LR 
Pattern formation in the early Drosophila embryo 96-99 
Hoch, M. and Jackie, H. 
Instabilities in propagating reaction-diffusion fronts 100-101 
Honrath, D., Petrov, V., Scott, S.K and Showalter, Κ 
The role of "excess work" in nonequilibrium thermodynamic 102-104 
systems 
Hunt, K.L.C., Hunt, P.M., Peng, B., Chu, X. and Ross, J. 
Ginzburg-Landau parameters for reaction-diffusion systems 105-107 
Hynne, F., S0rensen, P.G., Ipsen, M., Kristiansen, K.R. and 
Florian, Μ. 
Transition from order to spatiotemporal turbulence in 108-110 
catalytic NO reduction 
Imbihl, R. 
Nonlinear forecasting as a tool to diagnose heart disease 111-112 
J0rgensen, B.L., Junker, Α., Mickley, H, Mobiler, Μ., 
Christiansen, Ε. and Olsen L.F. 
Transient bimodality in turbulence 1-turbulence 2 transition in 113-116 
electrohydrodynamic convection in nematic liquid crystals 
Kai, S., Andoh, M. and Yamaguchi, S. 
Reactive dynamics in a multi-species lattice-gas automaton 117-118 
Kapral, R, Lawniczak, A. and Masiar, P. 
Scroll waves in myocardium 119-121 
Keener, J.P. and Panfilov, Α. V. 
Excitation wave propagation through narrow pathways 122-127 
Kogan, B.Y., Karplus, W.J. and Billett, B.S. 
Coupled excitable cells 128-131 
Kosek, Κ and Marek, Μ. 
Hyperchaos in a surface reaction 132-134 
Kruel, Tfu-M., Eiswirth, M., Schneider, F.W. andErtl, G. 
Intracellular calcium waves: propagation, annihilation and 135-137 
excitability 
Lechleiter, J.D. and Clapham, D. 
IV 
Scaling relations in thermal turbulence: global measurements 138-140 
and boundary layers estimate 
Libchaber, A. 
Patterns of temperature waves on electrically heated catalytic 141-143 
ribbons 
Luss, D. 
Reaction-diffusion patterns in heterogeneous media 144-145 
Malchow, Η. and Sattler, C. 
Microtubules: Structure, dynamics, oscillations, and spatial 146-150 
patterns 
Mandelkow, K, Marx, Α., Trinczek, B. and Mankelkow, E.-M. 
Pattern formation in neural activator-inhibitor networks 151-153 
Markus, Μ. and Schepers, H.E. 
Spatial long-range coherence in squid giant axons 154-155 
Matsumoto, G. 
Molecular evolution iin traveling waves 156-157 
McCaskill, IS. 
Complex biological pattern formation by linking several 158-161 
pattern forming reactions 
Meinhardt, Η. 
A big chemical-wave: accelerating propagation and surface 162-165 
deformation induced by a spontaneous convection 
Miike, H., Yamamoto, H. and Kai, S. 
Diffusive coupling of spatio-temporal patterns in 166-170 
nonequilibrium systems 
Mimura, M. 
Spiral waves in the Oregonator model: A study of time-space 171-175 
correlations 
Müller, KH. and Plesser, Th. 
Growth patterns in two-phase systems 176 
Müller-Krumbhaar, H. 
Formation of temporal patterns in the swimming behaviour of 177-179 
Halobacteria: Possible dynamical mechanisms 
Naber, H. 
Dynamics of spiral waves in the Belousov-Zhabotinsky reaction 180-181 
Nagy-Ungyarai, Zs. 
ν 
Unstable wave propagation in the Belousov-Zhabotinsky 
reaction 
Nagy-Ungvarai, Zs., Ungvarai, J., Hess, B., Pertsov, A.M. and 
Müller, S.C. 
182-183 
Reaction diffusion patterns in the catalytic CO oxidation on 
Pt(llO) - Front propagation and spiral waves -
Nettesheim, S., v. Oertzen, Α., Rotermund, H.H. and Eni, G. 
184-186 
Measuring an accelerating propagation of a big wave by 
sequential image processing 
Nomura, Α., Miike, H. and Hashimoto, H. 
187-189 
Experiments at the boundary of two worlds: Reaction, 
diffusion, electric conduction and multicomponent convection 
in gel and fluid reactors 
Noszticzius, Z., Farkas, H, Schubert, Α., SwiftJ., 
McCormic, W.D. and Swinney, H.L. 
190-193 
Turing instability in the CI MA reaction 
Ouyang, Q. and Swinney, H.L. 
194-196 
Self-organized criticality in a semiconducting charge density 
wave compound 
Parisi, J., Peinke, J., Dumas, J. and Kittel, A. 
197-199 
Asymptotics of spiral waves 200-204 
Pelci, P. and Sun, J. 
Turing-Hopf localized structures 205-210 
Perraud, J.-l, Dulos, E., De Kepper, P., De Wit, Α., Dewel, G. and 
Borckmans, P. 
Electrohydrodynamic convection in nematics: The homeotropic 
case 
Pesch, W., Hertrich, A. and Kramer, L . 
211-213 
Interaction of chemical waves with convective flows induced by 
density gradients: A comparison between experiments and 
computer simulations 
Plesser, Th., Wilke, H. and Winters, KH. 
214-216 
Scaling exponents, wrinkled graphs, and the high Reynolds 
number geometry of turbulence 
Procaccia, I. 
2Y7-21Q 
Spatio-temporal patterns in gas discharge systems 
Purwins, H.-G. and Willebrand, Η 
221 
Self-trapping of travelling-wave pulses 
Riecke, H. 
222-223 
VI 
Spiral turbulence in Taylor-Couette-flow 
Roesner, KG. 
Chemical implementation of computers 
Ross, J. 
Induction of temporal patterns in the locomotor behavior of 
Halobacterium - an indication of nonlinear dynamics 
Schimz, A. and Hildebrand, Ε. 
Pattern formation in molecular evolution - A physicist's look at 
biology 
Schuster, P. 
Observation of defect dynamics in small system 
Sepulchre, JA. and Babloyantz, A. 
Spatio-temporal patterns of on-going and evoked activity in cat 
visual cortex 
Shoham, D., Oilman, S. and Grinvald, A. 
Three-dimensional autowaves control cell motion in 
Dictyostelium slugs 
Siegert, F., Steinbock, Ο., Weijer, C.J. and Müller, S.C. 
Wave propagation and cell movement control morphogenesis 
of the cellular slime mould Dictyostelium discoideum 
Siegert, F. and Weijer, C.J. 
Spatio-temporal patterns in ionic diffusion chemical system 
Snita, D., Dvorak, L . and Marek, Μ. 
Pairs of pacemakers 
Spoerel, U., Peuker, A. and Busse, H.-G. 
Rotating vortex initiation in excitable media: pulse chemistry 
control 
Starm.er, C.F., Krinsky, V.l., Romashko, D.N., Aliev, R.R. and 
Stepanov, M.R 
Light-controlled spiral waves 
Steinbock, Ο. and Müller, S.C. 
Second control loop in the Belousov-Zhabotinsky reaction 
investigated at different acidities 
Varga, M. and Försterling, H.-D. 
Waves in a liquid, locally heated along a wire 
Vince, J.M., Dubois, M. and Berge, P. 
V I I 
Spontaneous nucleation in a reactive lattice gas automaton 266-269 
Weimar, J.R. 
Numerical experiments on filament motion 270-273 
Winfree,A.T. 
Hydrodynamic fluctuations in nematics 274-276 
Winkler, B.L., Hörner, F., Richter, Η. and Rehberg, I. 
Artificial retina - photo image processing in the Belousov- 277-280 
Zhabotinsky reaction in gels 
Yamaguchi, T., Ohmori, T. and Matumura-Inoue, T. 
Dynamic mode of entrainment in coupled chemical oscillators 281-283 
Yoshikawa, Κ 
Mechanism of stratification in a thin-layered excitable 284-286 
reaction-diffusion system with an oxygen gradient 
Zhabotinsky, A.M., Kiyatkin, A.B. and Epstein, LR. 
Effects of disorder in convective systems 287-288 
Zimmermann, W. 
Kinematics of spiral wave with indistinct front 289-290 
Zykov, V.S. 
244 
Wave propagation and cell movement 
control morphogenesis of the cellular slime mould 
Dictyostelium discoideum 
Florian Siegert and Cornells J. Weijer, Zoologisches Institut, Universität München, Luisenstraße 14, 
8000 Manchen 2, Germany. FAX: 089-5902450 
The cellular slime mould Dictyostelium discoideum is well suited to study cellular 
communication and the role of biological oscillations in spatio-temporal pattern formation. 
Dictyostelium cells live as solitary amoebae in the soil where they feed on bacteria. Upon 
starvation up to cells aggregate over large distances into a multicellular mass, the slug (see 
fig. 1A). The slug transforms during a complicated morphogenesis into a fruiting body 
consisting of a spore head supported by a stalk composed of dead vacuolated stalk cells. The 
spores disperse and germinate to single amoeba again. The aggregation and coordinated cell 
movement during slug morphogenesis require extensive cell-cell communication. 
The aggregation of single cells into multicellular structures is directed by periodic cyclic-AMP 
signals and Chemotaxis. Cells in the aggregation center periodically produce the 
chemoattractant cyclic Adenosine-Monophosphate (cAMP). cAMP is secreted into the 
extracellular medium, where it diffuses away. Neighbouring cells detect cAMP via cell surface 
receptors. These stimulated cells now produce themselves huge amounts of cAMP, which they 
in turn secrete. This feed-back process results in a wave-like propagation of the cAMP signal 
from cell to cell and from the center outwards. Extracellular phosphodiesterases degrades 
cAMP. After stimulation the cells are refractory to further stimulation. This property ensures 
unidirectional outward propagation of the signal. Stimulated cells respond with periodic 
chemotactic movement. Theys move in the direction of increasing cAMP concentrations. This 
leads to periodic waves of inward directed chemotactic movement. As a result the cells collect 
in the aggregation center. The cAMP wave propagation can be seen as outward propagating 
concentric or spiral optical density waves (see fig. IB) . These waves are only visible in 
monolayers of cells ,i.e during the early stages of aggregation (1). In later aggregates these 
waves are no longer visible. After aggregation the cells form a multicellular "slug" which 
contains up to cells. The slug has a defined polarity and is composed of at least three 
different cell types. The front quarter (tip) consists of two types of prestalk cells (pstA, pstB), 
the back three quarters consists of prespore cells. The prestalk cells will form the stalk of the 
fruiting body and the prespore cells the spores. 
We investigated whether the same principles that govern aggregation, i.e wave propagation 
and chemotactic cell movement, are responsible for the complex slug morphogenesis. Since 
optical density waves are no longer visible we investigated cell behaviour and cell movement 
in late aggregates and slugs. Cell movement of labeled single cells in Dictyostelium slugs were 
245 
analysed by high resolution digital image processing. We found that all cells in a slug move in 
a periodic and chemotactic fashion as juged by their periodic shape and velocity changes (2). 
This implies that the cells respond to periodic signals. In order to deduce the spatial geometry 
of these signals we determined the movement trajectories of many cells in various parts of the 
slug. Cells in the front and the back of a slug move along completely different trajectories (see 
fig. 1C). Prestalk cells move around the long axis of the slug, while prespore cells move 
forward parallel to the long axis. The cell movement data show that the chemotactic signal in 
the slug propagates as a three dimensional scroll wave in the front (prestalk zone), which 
transforms into planar waves in the back (prespore zone). This behavior is postulated to result 
from a difference in excitability of the cells along the long axis of the slug (2,3). The cells in 
the prestalk zone are more excitable than cells in the prespore zone. The biological 
significance of this particular type of wave propagation is that the core of the scroll wave will 
be a region of low continuous cAMP, conditions that favor the expression of stalk cell specific 
genes. In summary our experiments show that the morphogenesis of this relative simple 
biological system is controlled in two as well as in three dimensions largely by the dynamics 
of the underlying excitable system. 
1. F.Siegertand C.J.Weijer, (1989) J. Cell.Sci. 93, 325 
2. F.Siegert and C.J.Weijer, (1991) Physica D 49, 224 
3. F Siegertand C.J.Weijer, (1992) Proc.Natl.Acad.Sei. 89, 6433 
Figure: The life cycle of Dictyostelium discoideum 
The scheme (A) starts with single cells that aggregate in spirals as seen in darkfield optics. 
Moving cells are elongated and are seen as white bands due to increased light scattering (B). 
Cells which are not moving directionally are rounded and detected as dark bands. After stream 
formation waves emanating from the center propagate through the aggregation streams, while 
the cells move inward. The aggregation center can either be a mass of cells or temporarly form 
a loop. After tight aggregates (mounds) have formed the cells differentiate. Due to a higher 
oscillation frequency the prestalk cells form the tip in which the signals propagates as a 
(twisted) scroll wave as derived from the analysis of cell movement tracks (C, white lines). 
The wave rotates along its long axis as indicated by the black arrow. The mound now extends 
up in the air and forms a slug, which falls over and migrates away. The prestalk region stays a 
twisted scroll wave which decomposes upon arrival in the prespore zone in planar waves, due 
to the lower excitability of the prespore cells. The core of the slug is a region of low cAMP 
and this favors pstB expression, while the perifery of the tip with high cAMP favours pstA 
expression. The slug then converts by a series of not yet understood morphogenetic changes 
into a fruiting body, during which process the differentiation in the final cell types spore and 
stalk cells takes place. 
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Wave propagation and cell movement control morphogenesis of the cellular slime mould Dictyostelium discoideum

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