Thomas Mair

Traveling waves in yeast extract and in cultures of Dictyostelium discoideum

Biological self-organization was investigated in a biochemical and a cellular system: yeast extract and cultures of the slime mold Dictyostelium discoideum. In both systems traveling reaction-diffusion waves occur in response to oscillatory reactions. Glycolytic degradation of sugar in a yeast extract leads to the spontaneous formation of NADH and proton waves. Manipulation of the adenine nucleotide pool by addition of purified plasma membrane ATPase favors the formation of both reaction-diffusion waves and phase waves. The results indicate that the energy charge has an important impact for the dynamics of glycolytic patterns. When affecting the lower part of glycolysis by pyruvate addition the frequency of wave generation was increased with concomitant formation of rotating NADH and proton spirals. During morphogenesis of the cellular system Dictyostelium discoideum, circular and spiral shaped aggregation patterns of motile amoeboid cells form in response to traveling cAMP waves. Velocity analysis of the cell movements reveals that the cAMP waves guide the cells towards the site of wave initiation along optimized trajectories. The minimization of aggregation paths is based on a mechanism exploiting general properties of excitation waves. The resulting aggregation territories are reminiscent of Voronoi diagrams.

Extracellular potassium alters frequency and profile of retinal spreading depression waves

The phenomenon of spreading depression (SD) was observed in chicken retina by means of optical registration via a microscope and a CCD camera applying modern methods of image processing for optimized evaluation of the wave profiles. The propagation dynamics of SD waves was investigated as a function of extracellular potassium. Two main findings were obtained. Firstly, the frequency of spontaneous wave generation increased with the increase of K+ concentration. Secondly, there was an effect of potassium on the wave profile. In particular, the recovery zone of SD waves was shortened at increased K+. This effect was not only due to the dispersion relation of waves in excitable media as shown by the result of the mechanically induced wave trains. Applying the basic principles of chemical excitability for the interpretation of the data led us to the conclusion that these potassium effects are due to perturbations of an autocatalytic reaction to be further explored.

Spatio-temporal dynamics in glycolysis

During the glycolytic degradation of sugar in a thin layer of yeast extract, travelling waves of NADH and protons can be generated that carry a state of high enzymatic activity through the system. The controlled initiation of such waves with an activator of the enzyme phosphofructokinase (PFK) and the influence of various salts and co-factors on the propagation dynamics are investigated. Furthermore a first study of the dispersion of waves is presented. The experimental characterisation of this in vitro system contributes to unravelling the possible role of glycolysis for biological information processing. In this context, the provision of chemically available energy in the absence of compartmentation by glycolysis is of primary importance.

Excitation-induced dynamics of external pH pattern in Chara corallina cells and its dependence on external calcium concentration

The influence of cell excitation and external calcium level on the dynamics of light-induced pH bands along the length of Chara corallina cells is studied in the present paper. Generation of an action potential (AP) transiently quenched these pH patterns, which was more pronounced at 0.05-0.1 mM Ca2+ than at higher concentrations of Ca2+ (0.6-2 mM) in the medium. After transient smoothing of the pH bands, some alkaline peaks reemerged at slightly shifted positions in media with low Ca2+ concentrations, while at high Ca2+ concentrations, the alkaline spots reappeared exactly at their initial positions. This Ca2+ dependency has been revealed by both digital imaging and pH microelectrodes. The stabilizing effect of external Ca2+ on the locations of recovering alkaline peaks is supposedly due to formation of a physically heterogeneous environment around the cell owing to precipitation of CaCO3 in the alkaline zones at high Ca2+ during illumination. The elevation of local pH by dissolving CaCO3 facilitates the reappearance of alkaline spots at their initial locations after temporal suppression caused by cell excitation. At low Ca2+ concentrations, when the solubility product of CaCO3 is not attained, the alkaline peaks are not stabilized by CaCO3 dissolution and may appear at random locations.

Spatial Desynchronization of Glycolytic Waves as Revealed by Karhunen−Loeve Analysis

The dynamics of glycolytic waves in a yeast extract have been investigated in an open spatial reactor. At low protein contents in the extract, we find a transition from inwardly moving target patterns at the beginning of the experiment to outwardly moving spiral- or circular-shaped waves at later stages. These two phases are separated by a transition phase of more complex spatiotemporal dynamics. We have analyzed the pattern dynamics in these three intervals at different spatial scales by means of a Karhunen-Loeve (KL) decomposition. During the initial phase of the experiment, the observed patterns are sufficiently described by the two dominant KL modes independently of the spatial scale. However, during the last stage of the experiment, at least 6 KL modes are needed to account for the observed patterns at spatial scales larger than 3 mm, while for smaller scales, 2 KL modes are still sufficient. This indicates that in the course of the experiment, the local glycolytic oscillators become desynchronized at spatial scales larger than 3 mm. Possible reasons for the desynchronization of the glycolytic waves are discussed.

Modeling of glycolytic wave propagation in an open spatial reactor with inhomogeneous substrate influx

The spatio-temporal dynamics of traveling waves in glycolysis as it occurs in yeast extract have been studied, both theoretically and experimentally. We describe this phenomenon with the distributed Selkov model that accounts for the reactions of phosphofructokinase, which is a key enzyme of the glycolytic reaction cascade. To describe the experimentally observed phase waves in an open spatial reactor we introduce a non-homogeneous flux of substrate in the model. The experimental observation that waves can change their direction of propagation during the experiment is considered in the model. The mechanism for such a change in wave direction is discussed.

Inward Rotating Spiral Waves in Glycolysis

We report on the first observation of inward rotating spiral waves (antispirals) in a biochemical reaction-diffusion system. Experiments are performed with extracts from yeast cells in an open spatial reactor. By increasing the protein concentration of the extract we observe a transition from outward to inward propagating waves of glycolytic activity. Numerical simulations with an allosteric model for the phosphofructokinase can reproduce these inward propagating waves over a wide range of parameters if the octameric structure of yeast phosphofructokinase is taken into account.

Spatiotemporal dynamics of glycolytic waves provides new insights into the interactions between immobilized yeast cells and gels

The immobilization of cells or enzymes is a promising tool for the development of biosensors, yet the interactions between the fixative materials and the cells are not fully understood, especially with respect to their impact on both cell metabolism and cell-to-cell signaling. We show that the spatiotemporal dynamics of waves of metabolic synchronization of yeast cells provides a new criterion to distinguish the effect of different gels on the cellular metabolism, which otherwise could not be detected. Cells from the yeast Saccharomyces carlsbergensis were immobilized into agarose gel, silica gel (TMOS), or a mixture of TMOS and alginate. We compared these immobilized cells with respect to their ability to generate temporal, intracellular oscillations in glycolysis as well as propagating, extracellular synchronization waves. While the temporal dynamics, as measured by the period and the number of oscillatory cycles, was similar for all three immobilized cell populations, significant differences have been observed with respect to the shape of the waves, wave propagation direction and velocity in the three gel matrices used.

Spatial control of the energy metabolism of yeast cells through electrolytic generation of oxygen

The metabolic dynamics of yeast cells is controlled by electric pulses delivered through a spatially extended yeast cell/Au electrode interface. Concomitant with voltage pulses, oxygen is generated electrolytically at the electrode surface and delivered to the cells. The generation of oxygen was investigated in dependence of the applied voltage, width of the voltage pulses and temperature of the electrolytic solution. The local oxygen pulses at the electrodes lead to a transient activation of the aerobic energy metabolism of the yeast cells causing a perturbation in their energy balance. The effect of these local perturbations on the temporal dynamics of glycolysis in yeast cells is quantified in dependence of the energy state of cells.

Spatio-Temporal Aspects of a Dynamical Disease: Waves of Spreading Depression

Nearly all functions of the body exhibit nonlinear behaviour, a prominent example being the physiological rhythms that are autonomous in nature, e.g. heart beat, respiration or peristaltic of the gut. According to the different functions of the body rhythms, the time scale of their periodic activity can vary from seconds (heart) to hours (sleep-awake cycle) to days or months (e.g. menstruation). Moreover, they appear at nearly all levels of morphological organisation, ranging from the intracellular space to tissue and organs. One important feature of rhythmic behaviour is its ability to respond in a characteristic manner to different external requirements. Increase in the frequency of the heart beat to increased stress is one impressive example.