(A) An upward spike in external osmotic pressure at t=0 is sensed by Sln1, which propagates a signal via a MAPK cascade that culminates in the dual phosphorylation and nuclear import of Hog1. In the nucleus, Hog1 activates gene expression; active Hog1 also plays various roles in the cytoplasm to facilitate osmoadaptation. Together with Hog1-independent stress responses, these mechanisms increase internal glycerol, thereby restoring turgor pressure across the membrane. Our “wildtype” strain has YFP fused to Hog1, and the Sln1 branch is the primary osmosensor, since SHO1 is deleted.
(B) Network diagram inferred from (A) showing the system input and measurable outputs.
(C) Schematic of our simple flow chamber. The pump draws media through the flow-cell, with the osmolarity controlled by a valve. Cells adhere to the coverslip coated with 1 mg/ml conA in water.
(D) Phase-contrast (top row), Hog1-YFP (middle row), and Nrd1-RFP (bottom row) images are captured at each time point. In the absence of hyperosmotic shock, Hog1-YFP is distributed throughout the cell (left column). Only transiently does Hog1 accumulate appreciably in the nucleus after a shock (middle column), restoring the pre-stress distribution at steady state (right column).

(A) In response to hyperosmotic shocks with indicated concentrations of NaCl, the steady-state Hog1 nuclear enrichment returns exactly to the same level as in unshocked cells. All cells were grown and loaded into the flow cell using media with 0.0 M NaCl. Dotted lines show the average response, obtained by averaging population averages from independent experiments (N=3 or 4); error boundaries depict +/− SEM.
(B) Cell volume traces corresponding to the experiments in (A), except that all post-shock data points are the average of measurements at three consecutive time points.
(C) Hog1 nuclear enrichment perfectly adapts even in cells with compromised MAPK signaling. The TetO7 promoter was integrated upstream of the endogenous PBS2 gene. In the experiments shown, [doxycycline] = 0.06 μg/ml.
(D) The area under the Hog1 curves in (A) and (C) scales linearly with [NaCl] consistent with a single integrator between Hog1 activation and glycerol accumulation (Supplemental Data); dotted gray lines are guides for the eye. Data points indicate mean +/− STD of the area calculated from at least three independent Hog1-nuclear-enrichment traces. The inset shows the double integral of Hog1 curves in (A), calculated up to the point where the data curves adapt.

(A) Nuclear enrichment of (hog1-as)-YFP in cells treated with 24 μM PP1 prior to hyperosmotic shock with 0.4 M NaCl. This trace is corrected to highlight the salt-specific response (Figure S3). In the inset, the same strain is stressed in the same manner, except PP1 is omitted. In both the main curve and the inset, the mean (N=3) +/− SEM is plotted.
(B) Mean volume traces (N=3) +/− SEM from the corresponding experiments in (A), again corrected to highlight the salt-specific response (Figure S3).
(C) Dynamics in the concentration of intracellular glycerol (OD₅₄₀ measurement from glycerol kit; see Experimental Procedures), corrected for cell-growth (OD₆₀₀ measurement) by taking the ratio, were measured in hog1-as cells in the presence and absence of 24 μM PP1 (administered 30 minutes before experiment) and hyperosmotic shock with 0.4 M NaCl (administered at t = 0). Data points represent the mean (N=3) +/− STD.
(D) The glycerol accumulation rate was computed as the slope of the traces in (A), and the time of each plotted point corresponds to the midpoint of the two time points used in the slope computation (e.g., the slope between the 0-minute and 15-minute time points is plotted at 7.5 minutes). Error bars represent the combined standard deviation from data points in (A), assuming measurements were independent at different time points.
(E) and (F): Dynamics in the extracellular (E) and total (F) glycerol concentration (see Experimental Procedures) in experiments outlined in (C) and described in the main text. Data points and error bars are as described in (C).

Cartoon representation of key features of yeast hyperosmotic shock response, explained in detail in the Discussion. Hyperosmotic shock is applied at t = 0. Green membrane channels are open, allowing the transport of glycerol, shown as purple circles. Upon closure, the channel is depicted in red.

(A) In response to a step shock of 0.4M NaCl, dynamics in single-cell Hog1 nuclear enrichment (shown for three cells in green, orange, and purple; defined in Experimental Procedures) strongly resemble the population average (dark-blue dotted line) obtained from a single experiment (>100 cells). The shaded region is +/− STD around the population average and represents the cell-to-cell variability of a single experiment.
(B) Cell volume traces are low in noise (salt stimulus, single cells, mean, and shaded area are as in (A)). After an abrupt decrease in cell volume after t = 0, volume recovers and exceeds the pre-stimulus value, indicative of cell growth within the flow cell once turgor pressure is restored.
(C) and (D) Two-second sampling of single-cell Hog1 nuclear enrichment (C) and cellular volume (D) (salt stimulus, single cells, mean, and blue shaded area are as in (A)). Yellow shaded region depicts +/− SEM for >3 independent flow cells.
(E) For each time point in panels (A) through (D), the cell volume and Hog1 nuclear enrichment values are positioned on this scatter plot of Hog1 versus volume, illustrating four distinct regions. Spots are false-colored for clarity, becoming black near the boundaries between regions.

We permute the model from Figure 1B (shown in reduced form at top-left) such that each of the subsystems H, D, I, and G, is an integrator (shaded orange) or not (shaded green), yielding the sixteen possibilities (a) through (m). For the reasons listed at top-right, which consider data from Figures 2, 3, 5, and 6, certain network schematics can be rejected. Only network (d) satisfies all the constraints.

(A) The calculated concentration of NaCl in the flow chamber as a function of time (see Experimental Procedures). We measured the fluorescence intensity of rhodamine diluted in water and converted to [NaCl] based on the respective dilutions. The mean (N=3) +/− SEM is shown.
(B) and (C) Temporal changes in relative volume increase (B) and Hog1 nuclear enrichment (C) in response to ramp input shown in (A) (mean and error are same as in (A)). During the ramp period, volume and Hog1 fail to perfectly adapt, but they later adapt during the plateau period.