Biophysical properties of Saccharomyces cerevisiae and their relationship with HOG pathway activation

Abstract

Parameterized models of biophysical and mechanical cell properties are important for predictive mathematical modeling of cellular processes. The concepts of turgor, cell wall elasticity, osmotically active volume, and intracellular osmolarity have been investigated for decades, but a consistent rigorous parameterization of these concepts is lacking. Here, we subjected several data sets of minimum volume measurements in yeast obtained after hyper-osmotic shock to a thermodynamic modeling framework. We estimated parameters for several relevant biophysical cell properties and tested alternative hypotheses about these concepts using a model discrimination approach. In accordance with previous reports, we estimated an average initial turgor of 0.6 ± 0.2 MPa and found that turgor becomes negligible at a relative volume of 93.3 ± 6.3% corresponding to an osmotic shock of 0.4 ± 0.2 Osm/l. At high stress levels (4 Osm/l), plasmolysis may occur. We found that the volumetric elastic modulus, a measure of cell wall elasticity, is 14.3 ± 10.4 MPa. Our model discrimination analysis suggests that other thermodynamic quantities affecting the intracellular water potential, for example the matrix potential, can be neglected under physiological conditions. The parameterized turgor models showed that activation of the osmosensing high osmolarity glycerol (HOG) signaling pathway correlates with turgor loss in a 1:1 relationship. This finding suggests that mechanical properties of the membrane trigger HOG pathway activation, which can be represented and quantitatively modeled by turgor.

Fig. 1

Qualitative representation of cell volume concepts. Solid line: V _ap , the apparent cell wall enclosed volume. Dotted line: V _m, the membrane enclosed volume. V _m^P=0 is the volume at which the turgor becomes zero and V _m^τ is the volume where negative hydrostatic effects or matrix potential effects become important, corresponding to hyperosmotic shock levels of c _P=0^e and c _τ^e, respectively. c _pl^e and V _ap^pl are the stress and volume thresholds, respectively, where V _m detaches from V _ap. V _pl is the periplasmic volume. V _b is the minimum solid cytosolic volume. Note, that it is not necessarily true that c _τ^e < c _pl^e and V _m^τ > V _ap^pl. The diagrams of the cells illustrate the cell wall and the membrane in different states after hyper-osmotic shock

Fig. 2

Illustration of turgor and matrix potential. Turgor (black line), which has an initial value of P ₀ at the initial turgid cell volume of 100%, is displayed on the positive y-axis. When the cell shrinks, the turgor decreases to zero at the volume V _m^P=0. This is referred to as the “one-sided turgor model”. The matrix potential or other effects that reduce the water potential are displayed on the negative y-axis. These are assumed to become important below a specific threshold volume V _m^τ. The model represented by the solid line up to V _m^τ together with the dashed line is referred to as the “two-sided turgor model”

Fig. 3

Best fit models and data. The data and the best fit model (solid line) refer to the left y-axis. The dark gray region depicts the 95% confidence region of the fitted model. The right y-axis refers to the estimated turgor pressure (dashed line). The light gray region depicts the 95% confidence region of the estimated turgor pressure. The x-axis refers to concentrations of the respective stress agent. The confidence regions were calculated on the basis of the confidence intervals of the estimated parameters (Table 3). The four data sets are described in the “Methods” sections and the “Supplementary material”

Fig. 4

Hog1 activation data. Circles: maximum Hog1 nuclear concentration after osmotic shock. Squares: Hog1 phosphorylation after 2 min of shock treatment. Data are scaled to the respective measured maximum

Fig. 5

Turgor-HOG pathway activation relationship. The x-axes are relative turgor (%) as predicted by the parameterized models for different shocks of NaCl (dotted line in Fig. 3). The y-axes are relative HOG pathway activation (%) according to different shocks of NaCl (Fig. 4). The black lines are a fitted linear relationship (y = a + bx) based on a weighted orthogonal regression. The gray lines represent the null hypothesis H₀: y = 100 − x, i.e., a direct 1:1 linear relationship between relative loss of turgor and relative HOG pathway activation. The insets are plots of the (25, 50, 75, 90, 95%)-confidence regions of the respective estimated parameter pair (a, b) of a + bx with the outermost line being the 95% confidence region. The black points correspond to the black lines in the plots, the gray points correspond to the gray lines. The confidence regions are obtained by a Monte–Carlo analysis with 1,000 runs