Fig. 3

The probabilistic method can simulate dampening of oscillations in a linear signaling pathway with negative feedback. a Simplified model of the high osmolarity glycerol (HOG) pathway visualized as a regulatory graph [11]. The simplified HOG pathway consists of two modules: a phosphotransfer module and a MAP kinase module [13]. When turgor is sufficient, the phosphotransfer module is active and keeps the downstream MAP kinase module inactive. On the other hand, increased external osmolarity causes loss of turgor, which leads to inactivation of the phosphotransfer module and activation of MAP kinase module. The output of the signal cascade activates the phosphotransfer module again via glycerol accumulation, which leads to turgor recovery. b Descriptions of the simplified HOG pathway in the rxncon format. The upper panel displays the qualitative HOG model, and the lower panel the quantitative HOG pathway in which all contingency symbols were changed from “!” or “×” into “K+” or “K-”, respectively, indicating a certain probability of the occurrence of a reaction if its contingencies are met or not met. c, d Results of the time course simulation of the qualitative HOG model with a non-zero failure rate (p _FALSE > 0) and the quantitative HOG model. The average probabilities of being active or inactive are calculated over 1000 time series of 280 time points. c The amplitude and phase for the 1st and 7th periods are represented by the size and colors of nodes, respectively. The parameters p and k shown in each panel indicate false-rate and k-base value, respectively. d Individual state transitions of Hog1-{P} with different probabilities of false-rate and different scale factors of k-base. The upper (“!/×”) and lower (“K+ / K-”) panels show the average value for the phosphorylated state of the terminal MAP kinase (Hog1-{P}) in the qualitative HOG model and the quantitative HOG model, respectively