Signaling mechanisms enable cells to sense, respond, and adapt to changing environments. Understanding signal transduction mechanisms at both molecular and network levels is critical to characterize key proteins and reaction rates in the cellular response in normal and pathophysiological conditions. This insight is important to discover unknown regulatory mechanisms, to identify abnormal protein interactions, and to computationally screen drug targets in disease. However, it remains a challenge to predict time-dependent signaling response dynamics upon genetic, pharmacological, or environmental perturbations. In particular, it is unknown how cells sense and respond to dynamic signal inputs that change over time. This project uses the conserved High Osmolarity Glycerol (HOG) Mitogen-Activated Protein Kinase (MAPK) stress signaling pathway in the yeast S. cerevisiae model system to address this knowledge gap. Here, I present an integrated experimental and theoretical framework to build predictive mathematical models which lead to the discovery of a new mechanism of cell signaling using time-varying cell stimulations. In comparison to standard step-like cell stimulations, different dynamic stimulations result in different signaling responses that lead to better model predictions. We then predict and experimentally confirm that this eukaryotic MAPK pathway employs a logarithmic signal transduction mechanism, similar to E. coli chemotaxis. This signaling mechanism induces persistent pathway activation upon gradual stimulations that maximizes cell survival in severe stress conditions. A long-term goal of my research project is to expand both experimental and computational approaches to investigate physiological signaling mechanisms upon dynamic environmental changes in human cells relevant to human health and disease.