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A bistable model of cell polarity.

Semplice M, Veglio A, Naldi G, Serini G, Gamba A - PLoS ONE (2012)

Bottom Line: Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms.We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics.The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Mathematics, Università dell'Insubria, Como, Italy.

ABSTRACT
Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

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Related in: MedlinePlus

Physical analogy: membrane polarization and precipitation from a supersaturated solution.At initial time, the concentration of some molecule  is higher than the critical value , so that a small fluctuation, or an impurity, can easily give rise to the formation of small germs of precipitate. Germs larger than a critical size  grow steadily, while germs smaller than  are dissolved by diffusion. As the size of the germs grows, the molecule  is extracted from the hydrated phase and transferred to the solid phase, moving the concentration  closer to the critical value , increasing the value of , and correspondingly slowing down the process of germ growth. Grains that were initially larger than  are dissolved, so that larger grains grow at the expense of the smaller grains. Eventually, an equilibrium is reached when  and a single large grain of precipitate survives.
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pone-0030977-g005: Physical analogy: membrane polarization and precipitation from a supersaturated solution.At initial time, the concentration of some molecule is higher than the critical value , so that a small fluctuation, or an impurity, can easily give rise to the formation of small germs of precipitate. Germs larger than a critical size grow steadily, while germs smaller than are dissolved by diffusion. As the size of the germs grows, the molecule is extracted from the hydrated phase and transferred to the solid phase, moving the concentration closer to the critical value , increasing the value of , and correspondingly slowing down the process of germ growth. Grains that were initially larger than are dissolved, so that larger grains grow at the expense of the smaller grains. Eventually, an equilibrium is reached when and a single large grain of precipitate survives.

Mentions: As soon as the plasmamembrane is driven towards the phase coexistence line, the potential difference decreases and the critical radius gets larger, so that patches that were previously growing fall below the critical size and start shrinking. Thus, large patches grow at the expense of smaller patches until a single patch survives. This kind of competitive growth of patches has been known for a long time in the physics of materials as Lifshitz-Slyozov coarsening[2], [3], [20], [21]. The corresponding dynamics may be understood via a simple physical analogy with the nonequilibrium process taking place during the formation of precipitate from a supersaturated solution (see Fig. 5). At initial time, the concentration of some molecule is higher than the critical value , so that a small fluctuation, or an impurity, can easily give rise to the formation of small germs of precipitate. Germs larger than a critical size grow steadily, while germs smaller than are dissolved by diffusion. As the size of the germs grows, the molecule is extracted from the hydrated phase and transferred to the solid phase, moving the concentration closer to the critical value , increasing the value of , and correspondingly slowing down the process of germ growth. Grains that were initially larger than are dissolved, so that larger grains grow at the expense of the smaller grains. Eventually, an equilibrium is reached when and a single large grain of precipitate survives.


A bistable model of cell polarity.

Semplice M, Veglio A, Naldi G, Serini G, Gamba A - PLoS ONE (2012)

Physical analogy: membrane polarization and precipitation from a supersaturated solution.At initial time, the concentration of some molecule  is higher than the critical value , so that a small fluctuation, or an impurity, can easily give rise to the formation of small germs of precipitate. Germs larger than a critical size  grow steadily, while germs smaller than  are dissolved by diffusion. As the size of the germs grows, the molecule  is extracted from the hydrated phase and transferred to the solid phase, moving the concentration  closer to the critical value , increasing the value of , and correspondingly slowing down the process of germ growth. Grains that were initially larger than  are dissolved, so that larger grains grow at the expense of the smaller grains. Eventually, an equilibrium is reached when  and a single large grain of precipitate survives.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3285628&req=5

pone-0030977-g005: Physical analogy: membrane polarization and precipitation from a supersaturated solution.At initial time, the concentration of some molecule is higher than the critical value , so that a small fluctuation, or an impurity, can easily give rise to the formation of small germs of precipitate. Germs larger than a critical size grow steadily, while germs smaller than are dissolved by diffusion. As the size of the germs grows, the molecule is extracted from the hydrated phase and transferred to the solid phase, moving the concentration closer to the critical value , increasing the value of , and correspondingly slowing down the process of germ growth. Grains that were initially larger than are dissolved, so that larger grains grow at the expense of the smaller grains. Eventually, an equilibrium is reached when and a single large grain of precipitate survives.
Mentions: As soon as the plasmamembrane is driven towards the phase coexistence line, the potential difference decreases and the critical radius gets larger, so that patches that were previously growing fall below the critical size and start shrinking. Thus, large patches grow at the expense of smaller patches until a single patch survives. This kind of competitive growth of patches has been known for a long time in the physics of materials as Lifshitz-Slyozov coarsening[2], [3], [20], [21]. The corresponding dynamics may be understood via a simple physical analogy with the nonequilibrium process taking place during the formation of precipitate from a supersaturated solution (see Fig. 5). At initial time, the concentration of some molecule is higher than the critical value , so that a small fluctuation, or an impurity, can easily give rise to the formation of small germs of precipitate. Germs larger than a critical size grow steadily, while germs smaller than are dissolved by diffusion. As the size of the germs grows, the molecule is extracted from the hydrated phase and transferred to the solid phase, moving the concentration closer to the critical value , increasing the value of , and correspondingly slowing down the process of germ growth. Grains that were initially larger than are dissolved, so that larger grains grow at the expense of the smaller grains. Eventually, an equilibrium is reached when and a single large grain of precipitate survives.

Bottom Line: Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms.We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics.The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Mathematics, Università dell'Insubria, Como, Italy.

ABSTRACT
Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

Show MeSH
Related in: MedlinePlus