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),

*sho1*Δ mutants (ω

_{b} = 4.6 × 10

^{−3} ± 0.9 × 10

^{−3} Hz), and

*ste11*Δ 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

*ssk1*Δ 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

*ste11*Δ (in green) and

*ssk1*Δ (in red) strain backgrounds. At such high frequencies, the cells possessing only the Ssk1 branch (

*ste11*Δ) integrate the input just as the wild type (see

*C*), whereas the cells possessing just the Sho1 branch (

*ssk1*Δ) 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 . This shows that the rate-limiting step is the turn off of the Hog pathway.

## PubMed Commons