A quantitative study of the Hog1 MAPK response to fluctuating osmotic stress in Saccharomyces cerevisiae

Abstract

Background: Yeast cells live in a highly fluctuating environment with respect to temperature, nutrients, and especially osmolarity. The Hog1 mitogen-activated protein kinase (MAPK) pathway is crucial for the adaption of yeast cells to external osmotic changes.

Methodology/principal findings: To better understand the osmo-adaption mechanism in the budding yeast Saccharomyces cerevisiae, we have developed a mathematical model and quantitatively investigated the Hog1 response to osmotic stress. The model agrees well with various experimental data for the Hog1 response to different types of osmotic changes. Kinetic analyses of the model indicate that budding yeast cells have evolved to protect themselves economically: while they show almost no response to fast pulse-like changes of osmolarity, they respond periodically and are well-adapted to osmotic changes with a certain frequency. To quantify the signal transduction efficiency of the osmo-adaption network, we introduced a measure of the signal response gain, which is defined as the ratio of output change integral to input (signal) change integral. Model simulations indicate that the Hog1 response gain shows bell-shaped response curves with respect to the duration of a single osmotic pulse and to the frequency of periodic square osmotic pulses, while for up-staircase (ramp) osmotic changes, the gain depends on the slope.

Conclusions/significance: The model analyses suggest that budding yeast cells have selectively evolved to be optimized to some specific types of osmotic changes. In addition, our work implies that the signaling output can be dynamically controlled by fine-tuning the signal input profiles.

Figure 1. Model scheme for osmosensing network and the osmotic stress signals.

(A) Scheme of the model for osmosensing network. “Non-transcriptional feedback loop” denotes the Hog1 kinase dependent regulation of glycerol production. “Transcriptional feedback loop” stands for transcriptional regulation of the enzymes responsible for glycerol production. The gray boxes are modeled with coarse-grained black box approaches. (B) Different types of osmotic change signals considered in this work.

Figure 2. Comparison of model fits to the experimental data sets for step increase of 0.2 M NaCl in wild-type yeast and “low Pbs2” mutant.

Circles and squares represent the experimental data sets from Fig. 2D in reference . The solid curves are the simulation result from our model. For the “low Pbs2” mutant, we set Pbs2 concentration in the model to be 12.55% of the corresponding Pbs2 in the “wild type”.

Figure 3. Comparison of model fits to the experimental data sets for periodic square pulses of osmolarity.

Red squares represent the experimental data sets from Fig. S2 (A–F) and Fig. S5 (G–J) in reference . Blue curves are the simulation result from our model in this study. T₀ is the period of periodic square pulses. In all cases, the time of the pulse in on phase and off phase are equal to half of T₀ (T_on = T_off = T₀/2).

Figure 4. Model predictions for Hog1 phosphorylation response to step increase of 0.4 M NaCl in different mutants.

(A) Hog1 catalytically inactive mutant (Hog1K52R), In the model, we set ks1_Glyc = 0 for this mutant. (B) Knockout of cytoplasmic protein tyrosine phosphatase Ptp3 (ptp3 Δ). In the model, we set kdepho_Hog1PPc = 0 for this mutant. (C) Knockout of nuclear protein tyrosine phosphatase Ptp2 (ptp2Δ). In the model, we set kdepho_Hog1PPn = 0 for this mutant. (D) Knockouts of Ptp2 and Ptp3 (ptp2Δ, ptp3 Δ). In the model, we set kdepho_Hog1PPc = 0 and Kdepho_Hog1PPn = 0 for this mutant.

Figure 5. Schematic description of signal response gain (G_s).

The integral change of signal input (ΔI_s) corresponds to the area formed by the signal input curve and the basal line of signal input. The integral change of signal output (ΔI_o) corresponds to the area formed between signal output response curve and the basal line of signal output. The signal response gain is defined as the ratio of ΔI_o to ΔI_s.

Figure 6. Nuclear phosphorylated Hog1 (Hog1PPn) response to single pulses of 0.2 M NaCl.

ΔI_s: NaCl integral change, ΔI_h: integral change of Hog1PPn response, G_s: Hog1PPn response gain. The intersection curve in the lower part of panel A is a zoom-in shown in different scale.

Figure 7. Relationship between nuclear phosphorylated Hog1 (Hog1PPn) response and the duration of single pulses of NaCl change.

ΔI_h: integral change of Hog1PPn response. G_s: Hog1PPn response gain.

Figure 8. Nuclear phosphorylated Hog1 (Hog1PPn) response to different periodic square pulses of 0.2 M NaCl.

(A–E) The time of pulse in on phase (T_on = 0.1 min) of periodic square pulses is very short, while the time of pulse in off phase (T_off) of periodic square pulses varies from 0.1 min to 5 min. The intersection curve in low part of panel E is a zoom-in of Hog1PPn response in different scale. (F–J) The time of periodic square pulse in on phase (T_on = 1 min) is long enough to induce Hog1PPn response, the time of periodic square pulse in off phase (T_off) varies from 0.1 to 10 min.

Figure 9. Nuclear phosphorylated Hog1 (Hog1PPn) response to different staircase NaCl stimulations.

ΔI_s: NaCl integral change, ΔI_h: integral change of Hog1PPn response, G_s: Hog1PPn response gain, s: slope of the staircase profile of NaCl, which is the ratio of final NaCl concentration to the duration of NaCl stimulation. f: frequency of the staircase steps, which corresponds to the inverse of the interval between staircase steps.

Figure 10. Model predictions of Hog1 responses for the knockouts of different feedback loops involved in glycerol production.

We set  = 0 to simulate the knockout of the non-transcriptional feedback loop (Hog1 kinase, totalHog1PP, dependent) on glycerol production. The simulation results are shown in red curves in panel B–D. We set  = 0 to simulate the knockout of the transcriptional feedback loop (nuclear phosphorylated Hog1, Hog1PPn, dependent) on glycerol production. The simulation results are shown in blue dotted curves in panel B–D.