The propagation of information through signaling cascades spans a wide range of time-scales, including the rapid ligand-receptor interaction and the much slower response of downstream gene expression. To determine which dynamic range dominates a response, we used periodic stimuli to measure the frequency dependence of signal transduction in the osmo-adaptation pathway of Saccharomyces cerevisiae. We applied system identification methods to infer a concise predictive model. We found that the dynamics of the osmo-adaptation response are dominated by a fast-acting negative feedback through the kinase Hog1 that does not require protein synthesis. After large osmotic shocks, an additional, much slower, negative feedback through gene expression allows cells to respond faster to future stimuli.The mechanisms cells use to sense and respond to environmental changes include complicated systems of biochemical reactions that occur with rates spanning a wide dynamic range. Reactions can be fast, such as association and dissociation between a ligand and its receptor (< 1 s), or slow, such as protein synthesis (> 10 3 s). Though a system may comprise hundreds of reactions, often only a few of them dictate the system dynamics. Unfortunately, identification of the dominant processes is often difficult, and many models instead incorporate knowledge of all reactions in the system. Although occasionally successful (1-4), this exhaustive approach often suffers from missing information, such as unknown interactions or parameters.Here we used systems engineering tools to study how oscillatory signals propagate through a signal transduction cascade, allowing us to identify and concisely model the interactions that dominate system dynamics. The cornerstone of this approach is to measure the cascade output in response to input signals oscillating at a range of frequencies (5,6). By comparing the frequency response of the wild-type network to that of mutants, the molecular underpinnings of network dynamics can be determined. Studies of neural and other physiological systems have used systems theory (6), while control-theory has also been applied to cellular networks (7-14).We focused on the high osmolarity glycerol (HOG) Mitogen-activated protein kinase (MAPK) cascade in the budding yeast Saccharomyces cerevisiae. This cascade forms a core module of the hyperosmotic-shock-response system and is particularly well suited to frequency-response * To whom correspondence should be addressed: avano@mit.edu. NIH Public Access Author ManuscriptScience. Author manuscript; available in PMC 2010 August 5. analysis for several reasons. First, both the input (extracellular osmolyte concentration) and output (activity of the MAPK Hog1) of the network are easily measured and manipulated. Second, the molecular components of the network have been well studied, facilitating connection of dynamic models with molecular events. Finally, the system contains multiple negative feedback loops that operate on different time-scales (4,15,16). It is still unc...

SUMMARY Negative feedback can serve many different cellular functions, including noise reduction in transcriptional networks and the creation of circadian oscillations. However, only one special type of negative feedback (“integral feedback”) ensures perfect adaptation, where steady-state output is independent of steady-state input. Here we quantitatively measure single-cell dynamics in the Saccharomyces cerevisiae hyperosmotic shock network, which regulates membrane turgor pressure. Importantly, we find that the nuclear enrichment of the MAP kinase Hog1 perfectly adapts to changes in external osmolarity, a feature robust to signaling fidelity and operating with very low noise. By monitoring multiple system quantities (e.g., cell volume, Hog1, glycerol) and using varied input waveforms (e.g., steps and ramps), we assess the network location of the mechanism responsible for perfect adaptation in a minimally invasive manner. We conclude that the system contains only one effective integrating mechanism, which requires Hog1 kinase activity and regulates glycerol synthesis but not leakage.