Figure 4. A component of the fast pathway that responds to the time-derivative of the input enables its high speed.

(A) The Hog1 trajectory in the fast mutant overshoots the Hog1 trajectories of both the wild-type and the slow mutant in ramp inputs (two examples with different slopes of approximately 0.03 M min${}^{-1}$ and 0.06 M min${}^{-1}$). The mean response is shown and error bars are SEM. (B) Distributions of response times relative to the wild-type for six different ramps (Figure 4—figure supplement 1) shows that the fast mutant is even quicker than the wild-type on average ($p$-value ${\displaystyle <{10}^{-6}}$ using a t-test for distributions with at least 600 cells per strain). (C) The average amplitude of the Hog1 response for the fast mutant consistently overshoots the wild-type for ramp inputs, which responds linearly to the slope of the ramp. (D) An input with a fluctuating time-derivative shows the average Hog1 response of the fast mutant consistently over-shooting the wild-type. Errors are SEM. (E) The average of the single-cell cross-correlations of the trajectories of Hog1 with the trajectory of the (smoothed) time-derivative of the input shows that the high correlation of the wild-type comes from the fast and not the slow pathway (average of three independent experiments with fluctuating ramps and error bars as SD; $p$-value ${\displaystyle <{10}^{-6}}$ using a t-test on pooled single-cell data from the three experiments). (F) The mutual information between the time-derivative of the input in D and the level of Hog1 at each time point shows that the fast mutant best predicts the time-derivative (at 5% significance level calculated using credible intervals of the median).

DOI: http://dx.doi.org/10.7554/eLife.21415.010

Figure 4—figure supplement 1. The Hog1 response of the fast mutant in ramps of stress indicates derivative action.

(A) Ramp data from Figure 2D showing the consistent overshoot of the wild-type Hog1 by the fast mutant. The sorbitol concentration was calculated from the fluorescent signal of the cy5 dye (black dotted lines and right y-axis) and a linear approximation is shown by the orange lines. Numbers of cells are listed in order of wild-type, ste11∆, ssk1∆ for each experiment (n = 201, 195, 192 for 0.026 M/min; n = 112, 198, 97 for 0.03 M/min; n = 193, 226, 200 for 0.035 M/min; n = 175, 164, 144 for 0.041 M/min; n = 134, 86, 60 for 0.055 M/min; n = 148, 187, 186 for 0.071 M/min). (B) The cross-correlation between the single-cell trajectories of Hog1 and the time-derivative of the input in the fluctuating ramp of Figure 4D. The derivative was smoothed using a first order filter and the correlation is plotted as a function of the smoothing parameter α. Cross-correlation for three experiments were calculated in total and the average is shown in Figure 4E.

DOI: http://dx.doi.org/10.7554/eLife.21415.011