Propagation and mutual annihilation of circular and spiral NADH and proton waves were detected by spatially resolved spectrophotometry and fluorescent proton indicators in a biological in vitro system: an organelle-free yeast extract. Spontaneous wave generation during glycolytic sugar degradation is established after an induction period of about 1 h. Controlled wave initiation could be performed by local injection of the strong activator of phosphofructokinase, fructose 2,6-bisphosphate. A crucial role for wave initiation and control of pattern dynamics is attributed to the key enzyme of glycolysis, the allosterically regulated phosphofructokinase. An overall increase in the concentration of its positive effector AMP leads to the formation of rotating spirals. The dynamics of the observed wave patterns resemble that of self-organized calcium waves as recently found in frog eggs and heart cells.Living cells represent thermodynamically open systems, characterized by a nonequilibrium state. Their metabolism is often regulated by the action of enzymes with nonlinear, oscillatory reaction kinetics. A well known example is periodic oscillations in the degradation of sugar via glycolysis in resting yeast or heart cells (1-3). Investigations of spatially extended chemical nonequilibrium systems have demonstrated that nonlinear reaction kinetics, coupled with a transport process such as molecular diffusion, lead to the formation of self-organized waves (4, 5). Since similar thermodynamic principles apply for biological pathways, it has been suggested that wave patterns should occur in living cells, too (6, 7). First evidence for intracellular waves came from measurements of the spatial distribution of calcium in inositol 1,4,5-trisphosphate-activated frog eggs and in heart cells (8, 9). The observed calcium patterns and wave dynamics share great similarity with the patterns generated in chemical systems, suggesting that principles of self-organization hold for both systems.For a detailed examination of the underlying mechanisms of intracellular self-organization one needs an in vitro system for experimental manipulations that are hard to perform with living cells. For this purpose, we chose glycolytic degradation of sugars in a yeast extract as a model system for such investigations. Under appropriate metabolic conditions glycolysis is characterized by oscillatory reaction kinetics (10 -12) and fulfills all requirements for the generation of excitation waves: a nonequilibrium state and nonlinear reaction kinetics. Glycolytic degradation of sugars has been the subject of intense experimental and theoretical work regarding its metabolic control points and its nonlinear dynamic properties (13-17). Although several attempts were made to detect spatiotemporal patterns associated with oscillatory glycolysis in a yeast extract (18,19), traveling excitation waves have yet not been shown. The aim of the present work is to demonstrate the generation of excitation waves during oscillatory glycolysis and to give first insights into...

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The coordination of cellular behavior is a prerequisite of functionality of tissues and organs. Generally, this coordination occurs by signal transduction, neuronal control, or exchange of messenger molecules. The extent to which metabolic processes are involved in intercellular communication is less understood. Here, we address this question in layers of resting yeast cells and report for the first time the observation of intercellular glycolytic waves. We use a combined experimental and theoretical approach and explain the radial velocity of the waves to arise from the substrate gradient due to local substrate addition. Our results show that metabolic processes introduce an additional level of local intercellular coordination.

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