Contour plot of activated regulator concentration <i>r</i>_<i>a</i> = <i>r</i>₄ = [R₂S₂] around the time of ignition as a function of time and distance from the center of the colony.

<p>The plot contains the exact solution of the system of equations presented in Eqs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e002" target="_blank">2</a>)–(<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e005" target="_blank">5</a>) as well as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e013" target="_blank">Eq (8)</a>, i. e. the system describing total signal molecule concentration. The concentration necessary for ignition ( in the static case) is marked by the red contour. A logarithmic colour-scheme has been chosen due to the large range of values pre- and post-ignition.</p

Reaction scheme of a generic quorum sensing process with regulator (R with promoter <i>P</i>_<i>R</i>) and signal molecules (S with promoter <i>P</i>_<i>S</i>).

<p>In this example dimerization takes place prior to signal molecule binding. As the signal molecules produced by the cell itself diffuse quickly away, the signal molecules binding to the regulator typically come from other cells. Figure modified form [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.ref015" target="_blank">15</a>]</p

Plot of activated regulator concentration, <i>r</i>_<i>a</i> = <i>r</i>₄, at the center of the colony as a function of geometric size measure, Σ.

<p>Both axes are in natural units. The exact solution depicts the solution found when solving Eqs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e002" target="_blank">2</a>)–(<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e005" target="_blank">5</a>) and (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e013" target="_blank">8</a>), whereas non-buffered solution uses <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e008" target="_blank">Eq (6)</a>. The quasi-static solution uses Eqs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e008" target="_blank">6</a>) and (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180199#pone.0180199.e014" target="_blank">9</a>). The ignition point, , is indicated, as well as the dissociation constant <i>K</i>_<i>s</i> and maximum regulator concentration <i>r</i>_<i>m</i>. The exact solution is displayed with circles corresponding to 10 second intervals to indicate the speed of the ignition.</p

Table of parameters.

<p>Table of parameters.</p

Quantitative Analysis of Glycerol Accumulation, Glycolysis and Growth under Hyper Osmotic Stress

<div><p>We provide an integrated dynamic view on a eukaryotic osmolyte system, linking signaling with regulation of gene expression, metabolic control and growth. Adaptation to osmotic changes enables cells to adjust cellular activity and turgor pressure to an altered environment. The yeast <i>Saccharomyces cerevisiae</i> adapts to hyperosmotic stress by activating the HOG signaling cascade, which controls glycerol accumulation. The Hog1 kinase stimulates transcription of genes encoding enzymes required for glycerol production (Gpd1, Gpp2) and glycerol import (Stl1) and activates a regulatory enzyme in glycolysis (Pfk26/27). In addition, glycerol outflow is prevented by closure of the Fps1 glycerol facilitator. In order to better understand the contributions to glycerol accumulation of these different mechanisms and how redox and energy metabolism as well as biomass production are maintained under such conditions we collected an extensive dataset. Over a period of 180 min after hyperosmotic shock we monitored in wild type and different mutant cells the concentrations of key metabolites and proteins relevant for osmoadaptation. The dataset was used to parameterize an ODE model that reproduces the generated data very well. A detailed computational analysis using time-dependent response coefficients showed that Pfk26/27 contributes to rerouting glycolytic flux towards lower glycolysis. The transient growth arrest following hyperosmotic shock further adds to redirecting almost all glycolytic flux from biomass towards glycerol production. Osmoadaptation is robust to loss of individual adaptation pathways because of the existence and upregulation of alternative routes of glycerol accumulation. For instance, the Stl1 glycerol importer contributes to glycerol accumulation in a mutant with diminished glycerol production capacity. In addition, our observations suggest a role for trehalose accumulation in osmoadaptation and that Hog1 probably directly contributes to the regulation of the Fps1 glycerol facilitator. Taken together, we elucidated how different metabolic adaptation mechanisms cooperate and provide hypotheses for further experimental studies.</p></div

Yeast strains used in this study.

<p>*Strain YMR84 was kindly provided by Martijn Rep (Amsterdam) and contains a replacement of the GPD1 upstream region (−883 to +91) by the URA3 gene. The strains was generated using a PCR approach and does not express the GPD1 gene product.</p

Effect of salt stress on growth rate.

<p><b>A</b>: <i>In vivo</i> doubling times (−: before, +: after addition of 0.4 M NaCl) strongly differ between strains. <b>B</b>: Model simulations of the flux towards biomass production (left) and glycerol production (right) in the different strains at 0, 20, and 90 minutes after osmotic upshift to 0.4 M NaCl indicate a link between insufficient glycerol accumulation and a prolonged decrease in growth rate.</p

Contribution of glycerol accumulation mechanisms in different strains.

<p>(<b>A, B</b>) Absolute fluxes towards glycerol as well as relative contributions of specific mechanisms differ between wild type WT (<b>A</b>) and <i>gpd1Δ</i> (<b>B</b>). (<b>C</b>) Changes in relative contributions of Fps1, Gpd1, and other effects (basal glycerol production, uptake through Stl1, effects of volume change) over time are depicted for WT, <i>fps1</i>-<i>Δ1</i> and <i>hog1Δ</i>. Colors in (C) indicate time as shown on the x-axis in (A).</p

Figure 2

<p>Time courses of (<b>A</b>) phosphorylated Hog1, (<b>B</b>) Gpd1, and (<b>C</b>) intracellular glycerol following hyperosmotic stress of 0.4 M NaCl at time point 0. The full dataset is provided in Datasets S1, S2, S3, S4, S5, S6, S7.</p

Model analysis with time-dependent response coefficients.

<p><b>A</b>: Model simulation for phosphorylated Hog1, intracellular glycerol, and abundance of open Fps1. <b>B</b>: Effect of small changes in Pfk26/27 activation on different model variables as expressed by normalized response coefficient indicates that Pfk26/27 contributes to a rerouting of flux towards lower glycolysis. <b>C</b>: Response of intracellular glycerol concentration to perturbations in Stl1 gene expression as measured by normalized response coefficients in different strains indicates a specific time- and context-dependent role of Stl1in osmoadaptation. <b>D</b>: Simulation of genetic perturbations of Stl1 results in time courses as expected from C: in wild type, deletion of STL1 affects intracellular glycerol levels only at later time points. In <i>gpd1Δ</i> background, the effect of additional deletion of STL1 is early and transient.</p