Signal processing by the HOG MAP kinase pathway

Abstract

Signaling pathways relay information about changes in the external environment so that cells can respond appropriately. How much information a pathway can carry depends on its bandwidth. We designed a microfluidic device to reliably change the environment of single cells over a range of frequencies. Using this device, we measured the bandwidth of the Saccharomyces cerevisiae signaling pathway that responds to high osmolarity. This prototypical pathway, the HOG pathway, is shown to act as a low-pass filter, integrating the signal when it changes rapidly and following it faithfully when it changes more slowly. We study the dependence of the pathway's bandwidth on its architecture. We measure previously unknown bounds on all of the in vivo reaction rates acting in this pathway. We find that the two-component Ssk1 branch of this pathway is capable of fast signal integration, whereas the kinase Ste11 branch is not. Our experimental techniques can be applied to other signaling pathways, allowing the measurement of their in vivo kinetics and the quantification of their information capacity.

Fig. 1.

Analysis of a model pathway and the hyperosmolar response pathway in S. cerevisiae. (A) The hyperosmolar glycerol response HOG pathway consists of two input branches. The SLN1 phosphorelay represses the kinase Ssk1 under osmotically neutral conditions. Hyperosmotic stress results in deactivation of Sln1. The subsequent derepression of Ssk1 allows Ssk1 to activate the MAPKKKs Ssk2 and Ssk22, which in turn phosphorylate Pbs2. The SHO1 branch activates Pbs2 through the MAPKK Ste11. Activation of Hog1 by Pbs2 leads to its nuclear localization and a hyperosmolar transcriptional response. (B) A model three-level branched signaling cascade with both X*₁ and X′*₁ activating X₂, which in turn activates X₃. Each level of the cascade activates the next through phosphorylation consuming one molecule of ATP. (C) The steady-state level of X*₃ is plotted as a function of time. For an input oscillating slowly, the level of X*₃ (in red) oscillates between zero and a maximum value, following the input in time. For an input oscillating rapidly, the level of X*₃ (in green) oscillates with a very small amplitude and shows a response primarily to the time-averaged value of the input. (D) The amplitude of the oscillating response of X*₃ is plotted as a function of the frequency of the input signal oscillation. The points corresponding to the input frequencies in B are shown as a red square and a green square, respectively. This amplitude of the oscillatory response drops off sharply at a characteristic frequency ω_b of the input, which is the bandwidth of this model pathway. How fast information propagates through such a cascade is proportional to this pathway bandwidth ω_b.

Fig. 2.

Microfluidic device for studying frequency response of single cells. (A) One of the input arms of a Y-shaped flow chamber is fed by a solution of 1 M sorbitol in SC medium (in red) from reservoir R3 at a hydrostatic pressure head at P₀. The other arm is fed by SC (in blue) from one of two reservoirs, R1 at a hydrostatic pressure head at P₊ and R2 at P₋. The choice between the two reservoirs, R1 or R2, is made by a programmable three-way electrovalve. When reservoir R2 is chosen, the fluid from reservoir R3 fills most of the chamber, whereas when R1 is chosen, the fluid from R1 fills the chamber. Periodic changes in the state of the electrovalve allow a change in the environment of the cells at a tunable period T. (B) To characterize the device, water was filled in reservoirs R1 and R2, and a dilute solution of fluorescein was filled in R3. The state of a cross-section of the flow chamber was imaged by fluorescent microscopy. This state is shown as a function of flow-cell width (along the x axis) and time (along the y axis) for both T = 1-s oscillations (Left) and T = 0.5-s oscillations (Right). The bright regions indicate fluorescein solution, and the dark regions indicate water. The sharp interfaces between the dark and bright regions show the efficiency of our device in changing conditions rapidly. (C) The fluorescence intensity for a typical point in the middle of the channel is shown for oscillation periods ranging from T = 0.5 s to T = 4 s. The curves have been offset along the y axis for clarity, and for each curve, time has been scaled by its input frequency ω. All the curves oscillate between the same minimum and maximum fluorescence intensities. The transition from one medium to the other gets less sharp as T = 0.5 s is approached, indicating the limit of resolution for our experimental device.

Fig. 3.

The mechanical and Hog1 localization responses of the HOG pathway in S. cerevisiae behave as low-pass filters with distinct bandwidths. (A) The response of Hog1 localization to oscillating 1 M sorbitol input behaves like a low-pass filter with bandwidth ω_b = 4.6 × 10⁻³ ± 1.1 × 10⁻³ Hz. Each point represents the average response amplitude as measured by Hog1-GFP colocalization with Htb2-mCherry over, typically, 15 cells (391 cells total). Error bars denote one standard deviation from the mean. (B) At input frequencies below ω_b = 4.6 × 10⁻³ Hz, the pathway output faithfully records the input: Hog1-GFP localizes and delocalizes in phase with the ω = 1.25 × 10⁻³-Hz input oscillations (filled circles and red lines). (C) At input frequencies above the bandwidth (ω = 6.7 × 10⁻² Hz, ω = 3.3 × 10⁻² Hz, or ω = 1.4 × 10⁻² Hz), the pathway does not respond faithfully to the input oscillations but, rather, integrates the signal. The traces for response to a 1 M sorbitol (black line) and a 0.5 M sorbitol (red line) step shock show that for input at frequencies above the bandwidth, the pathway responds approximately to the mean change in input. (D) The transcriptional response of the HOG pathway, as reported by Gpd1-GFP, reflects its low-pass behavior. Below the bandwidth, (ω = 8 × 10⁻⁴ Hz, green line) the level of Gpd1-GFP follows the input faithfully by initiating a new round of transcription during each period. At input frequencies above ω_b (ω = 0.5 Hz, purple line) the transcriptional response of Gpd1-GFP integrates the signal and responds to the mean change in input. (E) The mechanical response of an S. cerevisiae cell to oscillating 1 M sorbitol input is measured as variation in cytoplasmic fluorescence and is plotted versus input frequency. Each point represents 5–10 cells. Error bars denote one standard deviation from the mean. Size response is a low-pass filter with a bandwidth ω_b = 0.033 ± 0.01 Hz. Comparison of the mechanical response of cells exposed to 1 M sorbitol (open squares) with the response of cells exposed to 2 M sorbitol (filled circles) scaled by a factor of 0.5 indicates that cell-size response is linear in the input magnitude. (F) At frequencies slower than ω_b (ω = 2.5 × 10⁻³ Hz, black line), the cell-size response follows the input faithfully. At frequencies higher than the bandwidth (ω = 0.33 Hz, red line) the magnitude of cell-size response drops dramatically. Time has been normalized by the input frequency, and fluorescence intensity variations are shown around their mean intensity.

Fig. 4.

The SHO1 and SLN1 branches have different bandwidths. (A) Deletion of STE11 (red ) or SHO1 (▴) blocks input to Hog1 from the SHO1 branch. Strains with this branch blocked show no change in bandwidth compared with the wild-type strain. Time scales are in good agreement for wild type (ω_b = 4.6 × 10⁻³ ± 1.10 × 10⁻³ Hz), sho1Δ mutants (ω_b = 4.6 × 10⁻³ ± 0.9 × 10⁻³ Hz), and ste11Δ mutants (ω_b = 4.6 × 10⁻³ ± 1 × 10⁻³ Hz), indicating that the SSK1 branch dominates the activation dynamics of the HOG pathway. (B) Deletion of SSK1 (●) blocks input to Hog1 from the SLN1 branch. The ssk1Δ strains (ω_b = 2.6 × 10⁻³ ± 0.4 × ¹⁰⁻³ Hz) show close to 2-fold decrease in bandwidth compared with the wild-type strain (■, ω_b = 4.6 × 10⁻³ ± 1.1 × 10⁻³ Hz). Each point represents the amplitude of Hog1-GFP and Htb2-mCherry colocalization over, typically, 10 cells. The error bars represent one standard deviation from the mean. (C) The time course of nuclear Hog1-GFP levels for the input oscillating 0.2 Hz (larger than the pathway bandwidth) is shown for cells of ste11Δ (in green) and ssk1Δ (in red) strain backgrounds. At such high frequencies, the cells possessing only the Ssk1 branch (ste11Δ) integrate the input just as the wild type (see Fig. 3C), whereas the cells possessing just the Sho1 branch (ssk1Δ) do not respond at all. Thus it is the Ssk1 branch of the pathway that allows the cells to integrate fluctuating inputs from the environment. (D) Time course of nuclear Hog1::GFP intensity as a function of time shown for different temporally changing inputs. In both Upper and Lower graphs, the input amplitude (shown in red) oscillates between 0 and 1 M sorbitol starting at time t = 0 s. In Upper, the input stays at 1 M for t_on = 100 s and at 0 M for t_off = 50 s. In Lower, t_on = 100 s, whereas t_off = 400 s. The nuclear Hog1::GFP intensity oscillates according to the input. The amplitude of the oscillation for t_off = 400 is larger than for t_off = 50 s. (E) The amplitude of the oscillations in Hog1 nuclear intensity is plotted as a function of t_off for a fixed t_on = 100 s. With increasing t_off, the amplitude of Hog1::GFP oscillations in steady-state increase, reaching a maximum at and above t_off = 800 s. (F) The log of the difference in the amplitude of the oscillation at a given t_off (shown in D) from that at t_off = 800 s is plotted as a function of t_off. This plot gives an accurate measure of the rate constant for the turn off of the osmolar pathway when the osmolar input is turned off, and from the slope of this plot, we find it to be 0.0041 ± 0.0005 Hz, which corresponds to within error bars to the bandwidth of the Hog pathway shown in Fig. 3. This shows that the rate-limiting step is the turn off of the Hog pathway.