Predictive dynamical models are critical for the analysis of complex biological systems. However, methods to systematically develop and discriminate among systems biology models are still lacking. Here, we describe a computational method that incorporates all hypothetical mechanisms about the architecture of a biological system into a single model, and automatically generates a set of simpler models compatible with observational data. As a proof-of-principle, we analyzed the dynamic control of the transcription factor Msn2 in Saccharomyces cerevisiae, specifically the short-term mechanisms mediating the cells’ recovery after release from starvation stress. Our method determined that twelve out of 192 possible models were compatible with available Msn2 localization data. Iterations between model predictions and rationally designed phosphoproteomics and imaging experiments identified a single circuit topology with a relative probability of 99% among the 192 models. Model analysis revealed that the coupling of dynamic phenomena in Msn2 phosphorylation and transport could lead to efficient stress-response signaling by establishing a rate-of-change sensor. Similar principles could apply to mammalian stress-response pathways. Systematic construction of dynamic models may yield detailed insight into non-obvious molecular mechanisms.