Osmotic stress triggers the activation of the HOG (high osmolarity glycerol) pathway in Saccharomyces cerevisiae. This signaling cascade culminates in the activation of the MAPK (mitogen-activated protein kinase) Hog1. Quantitative single cell measurements revealed a discrepancy between kinase- and transcriptional activities of Hog1. While kinase activity increases proportionally to stress stimulus, gene expression is inhibited under low stress conditions. Interestingly, a slow stochastic gene activation process is responsible for setting a tunable threshold for gene expression under basal or low stress conditions, which generates a bimodal expression pattern at intermediate stress levels.