The distribution of maximum a posteriori <i>η</i>.

<p>For experiments 1 to 4 (A to D), the EBEs of <i>η</i>₂ and <i>η</i>₃ are shown as red points. The regions of one and two standard deviations of a normal distribution fitted to the EBEs, and the NLME population estimate of the distribution of <i>η</i>₂ and <i>η</i>₃, are shown as black and filled gray ellipses, respectively.</p

Hog1 phosphorylation is delayed in severe hyper-osmotic stress.

<p>Western blot of Hog1 phosphorylation in wild type treated with 400mM and 800mM NaCl at time “0”. The upper blot was treated with antibody recognizing dually phosphorylated Hog1, the lower panel with an antibody that detects total Hog1.</p

Illustration of the mathematical model.

<p>Extracellular glucose is controlling the rate of production of nuclear Mig1 and a hypothetical component X. The level of X in turn modulates the degradation of nuclear Mig1.</p

Experiments.

<p>Experiments.</p

Parameter estimates.

<p>Parameter estimates.</p

Visualization of all single cell data.

<p>Time-series data of fluorescent light intensity for nuclear Mig1 in single cells, shown for the four different experiments. At time zero, the extracellular glucose concentration is changed according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0124050#pone.0124050.t001" target="_blank">Table 1</a>.</p

Distribution of the model-derived quantities response time, amplitude, and duration.

<p>A. Illustration of response time, (negative) response amplitude in % of baseline, and duration of half-maximal response. Distribution of activation (B), amplitude (C), and duration, for experiment 1 and 2 (blue), experiment 3 (pink), and experiment 4 (yellow). The typical cells (median response) are indicated by vertical dashed lines. Distributions of the model-derived quantities were determined from 100 000 Monte Carlo simulations per experiment.</p

Model simulations and data.

<p>The first row show plots of all single cell data together with a simulation of a cell using the median parameters for each experiment, respectively. Rows two to five shows data and corresponding model simulations (derived using the EBEs) for a subset of all cells, exemplifying the fit on the individual level. The simulated median cell is shown in dashed for comparison. Columns one to four correspond to experiments 1 to 4.</p

Comparing simulated Mig1 dynamics for individual cells using parameter from the STS and NLME approaches.

<p>Simulations with parameter values from the STS analysis are shown in blue, and in black for NLME. Simulations of typical cells are shown in dashed. A. An information-rich data set which by itself allows precise estimation of model parameters. The typical STS cell was simulated using the median parameters considering removal of outliers. B. The extreme case of an uninformative data set (only one data point). Here the STS approach may produce arbitrary parameter estimates which leads to questionable simulations as well as corrupting the population statistics of individual estimates. In this example the typical STS cell was simulated using the median parameters <i>without</i> considering removal of outliers, producing a different results compared to the typical NLME cell. C. A cell where the information content is too low for estimating all parameters with high precision. Model fits like this contribute to overestimation of parameter variability on the population level. The typical STS cell was simulated using the median parameters considering removal of outliers.</p

The Hog1 nuclear import rate is similar for cells in different osmotic stress conditions.

<p><b>A</b>. FRAP (Fluorescence Recovery After Photobleaching) experiments on Hog1-GFP (Nrd1-mCherry as nuclear marker) in wild type cells to measure the rate of Hog1 nuclear import under two different osmostress conditions, 400mM and 800mM NaCl. The recovery curves, i.e. the mean intensity in a nuclear bleached region as a function of time, represent the average of the individual GFP-recovery curves for 15 cells. All measurements were performed after cells were treated with salt for 2.5 minutes. Subsequently, the area of the nucleus was bleached and the times on the x-axis represent the period after which the measurements were started. The recovery curves are fitted with a double exponential fit. <b>B</b>. Box plots for the fast and slow recovery half times from double exponential fits for 400 and 800 mM NaCl. The bottom and top of the boxes present the first and third quartiles. The diamond and dash line show the mean and median respectively. Whiskers indicate the variability of recovery half times outside the upper and lower quartiles. The data are consistent with two different mechanisms of Hog1 nuclear import under osmostress, a slow and probably passive mechanism as well as a fast and probably active mechanism. </p