A Neyman-Pearson Framework for Modeling Cellular Decision Making Using Single-Cell TNF-NF-κB Signaling Data

Cells make hard calls under noise. When signaling is abnormal, those calls can go wrong and drive pathological conditions and diseases. In this research, we develop a Neyman-Pearson (NP) detection-theory framework that maximizes probability of detection (P _D) for a chosen false alarm probability (P _FA), without requiring prior probabilities, using experimental single-cell measurements of NF-κB responses to tumor necrosis factor (TNF), a critical pathway involved in cell survival, apoptosis, immune signaling, and stress response, in wild-type and A20-deficient fibroblasts. We model log-responses as (multi)variate Gaussian and compute optimal thresholds, P _D-P _FA trade-offs, and ROC curves at 30 minutes and 4 hours. The NP framework captures expected biology: P _D increases with TNF dose; wild-type cells outperform A20^-/- at matched conditions; and combining two time points (bivariate analysis) improves detection (e.g., for 0.0052 vs. 0.2 ng/mL, P _D rises from 0.71 (30 minutes) and 0.42 (4 hours) to 0.80 at P _FA = 0.1). The analysis recovers expected biology (higher TNF causes higher detectability; negative feedback lowers late responses) and flags cases where decision quality degrades (e.g., perturbations that blunt separation between conditions). The same recipe extends to multivariate readouts without changing the logic. Overall, the NP detection framework provides a compact, quantitative score of pathway performance and failure. It turns noisy single-cell readouts into actionable decision metrics that compare doses, time points, and perturbations, and ultimately, can help explain when and how cellular decisions drift toward pathology.