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Dynamical equations describing physical systems in contact with a thermal bath are commonly extended by mathematical tools called "thermostats." These tools are designed for sampling ensembles in statistical mechanics. Here we propose a dynamic principle underlying a range of thermostats which is derived using fundamental laws of statistical physics and ensures invariance of the canonical measure. The principle covers both stochastic and deterministic thermostat schemes. Our method has a clear advantage over a range of proposed and widely used thermostat schemes that are based on formal mathematical reasoning. Following the derivation of the proposed principle, we show its generality and illustrate its applications including design of temperature control tools that differ from the Nosé-Hoover-Langevin scheme.

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The organisation and form of most organisms is generated during theirembryonic development and involves precise spatial and temporal controlof cell division, cell death, cell differentiation and cell movement.Differential cell movement is a particularly important mechanism in thegeneration of form. Arguably the best understood mechanism of directedmovement is chemotaxis. Chemotaxis plays a major role in the starvationinduced multicellular development of the social amoebae Dictyostelium.Upon starvation up to 10(5) individual amoebae aggregate to form afruiting body. In this paper we review the evidence that the movement ofthe cells during all stages of Dictyostelium development is controlled bypropagating waves of cAMP which control the chemotactic movement ofthe cells. We analyse the complex interactions between cell-cell signallingresulting in cAMP waves of various geometries and cell movement whichresults in a redistribution of the signalling sources and therefore changes thegeometry of the waves. We proceed to show how the morphogenesis,including aggregation stream and mound formation, slug formation andmigration, of this relatively simple organism is beginning to be understoodat the level of rules for cell behaviour, which can be tested experimentallyand theoretically by model calculations.

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Differential cell movement is an important mechanism in the development and morphogenesis of many organisms. In many cases there are indications that chemotaxis is a key mechanism controlling differential cell movement. This can be particularly well studied in the starvation-induced multicellular development of the social amoeba Dictyostelium discoideum. Upon starvation, up to 10(5) individual amoebae aggregate to form a fruiting body The cells aggregate by chemotaxis in response to propagating waves of cAMP, initiated by an aggregation centre. During their chemotactic aggregation the cells start to differentiate into prestalk and prespore cells, precursors to the stalk and spores that form the fruiting body. These cells enter the aggregate in a random order but then sort out to form a simple axial pattern in the slug. Our experiments strongly suggest that the multicellular aggregates (mounds) and slugs are also organized by propagating cAMP waves and, furthermore, that cell-type-specific differences in signalling and chemotaxis result in cell sorting, slug formation and movement.

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Dictyostelium slug movement results from the coordinated movement of its 10(5)constituent cells. We have shown experimentally that cells in the tip of the slug show a rotational cell movement while the cells in the back of the slug move periodically forward (Siegert & Weijer, 1992). We have put forward the hypothesis that cell movement in slugs is controlled by chemotaxis to scroll waves generated in the tip which convert to twisted scroll or planar waves in the back of the slug (Bretschneider et al., 1995). The coordinated movement of all individual cells in response to these waves could then result in forward movement of the slug. We now test this hypothesis by extending our model for mound formation (Bretschneider et al., 1997) to include two cell types with different signalling and movement properties. All cells are able to relay cAMP and move chemotactically in response to cAMP gradients. Cells interact by adhesion, pressure and friction with neighbouring cells and the extracellular matrix. The model can generate stable scroll waves propagating from the tip to the back of a slug which coordinate forward cell movement and result in slug migration. We use the model to investigate the influence of cell type specific differences in excitability, adhesion and cell interactions on slug motion. Copyright 1999 Academic Press.

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Coordinated cell movement is a major mechanism of the multicellular development of most organisms. The multicellular morphogenesis of the slime mould Dictyostelium discoideum, from single cells into a multicellular fruiting body, results from differential chemotactic cell movement. During aggregation cells differentiate into prestalk and prespore cells that will form the stalk and spores in the fruiting body. These cell types arise in a salt and pepper pattern after what the prestalk cells chemotactically sort out to form a tip. The tip functions as an organizer because it directs the further development. It has been difficult to get a satisfactory formal description of the movement behavior of cells in tissues. Based on our experiments, we consider the aggregate as a drop of a viscous fluid and show that this consideration is very well suited to mathematically describe the motion of cells in the tissue. We show that the transformation of a hemispherical mound into an elongated slug can result from the coordinated chemotactic cell movement in response to scroll waves of the chemoattractant cAMP. The model calculations furthermore show that cell sorting can result from differences in chemotactic cell movement and cAMP relay kinetics between the two cell types. During this process, the faster moving and stronger signaling cells collect on the top of the mound to form a tip. The mound then extends into an elongated slug just as observed in experiments. The model is able to describe cell movement patterns in the complex multicellular morphogenesis of Dictyostelium rather well and we expect that this approach may be useful in the modeling of tissue transformations in other systems.

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The morphogenesis of Dictyostelium results from the coordinated movement of starving cells to form a multicellular aggregate (mound) which transforms into a motile slug and finally a fruiting body. Cells differentiate in the mound and sort out to form an organised pattern in the slug and fruiting body. During aggregation, cell movement is controlled by propagating waves of the chemo-attractant cAMP. We show that mounds are also organised by propagating waves. Their geometry changes from target or single armed spirals during aggregation to multi-armed spiral waves in the mound. Some mounds develop transiently into rings in which multiple propagating wave fronts can still be seen. We model cell sorting in the mound stage assuming cell type specific differences in cell movement speed and excitability. This sorting feeds back on the wave geometry to generate twisted scroll waves in the slug. Slime mould morphogenesis can be understood in terms of wave propagation directing chemotactic cell movement.

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Dictyostelium development is based on cell-cell communication by propagating cAMP signals and cell movement in response to these signals. In this paper we present a model describing wave propagation and cell movement during the early stages of Dictyostelium development, i.e. aggregation and mound formation. We model cells as distinct units whose cAMP relay system is described by the Martiel-Goldbeter model. To describe cell movement we single out three components: chemotactic motion, random motion and motion due to pressure between cells. This pressure result in cells crawling on top of each other and therefore to the extension of the aggregate into the third dimension. Using this model we are able to describe aggregation up to the mound stage. The cells in the mound move in a rotational fashion and their movement is directed by the counter-rotating spiral of the chemo-attractant cAMP. Furthermore, we show that the presence of two subpopulations with different inherent chemotactic velocities can lead to cell sorting in the mound. The fast moving cells collect into the centre while the slow cells occupy the rest of the mound. This model allows the direct comparison of the properties of the cAMP waves properties and movement behavior of individual cells with experimental data. Thereby it allows a critical test of our understanding of the basic cellular principles involved in the morphogenesis of a simple eukaryote.Copyright 1997 Academic Press Limited Copyright 1997 Academic Press Limited

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Investigation of the membrane potential of Neurospora crassa mycelial cells was carried out by standard microelectrode technique. The resting potential is equal to--156 +/- 11 mV (negative inside the cell). The light of the spectrum blue-violet zone causes transient hyperpolarization of the cell membrane reaching --38 +/- 5 mV after 25 minutes of illumination.

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