Assessing the reliability of cellular decision making from noisy, multidimensional 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 (PD) for a chosen false alarm probability (PFA), 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, PD-PFA trade-offs, and ROC curves at 30 minutes and 4 hours. The NP framework captures expected biology: PD 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, PD rises from 0.71 (30 minutes) and 0.42 (4 hours) to 0.80 at PFA = 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. A non-parametric (kernel-density) detector applied to the raw single-cell data reproduces these detection probabilities (|ΔPD| ≤ 0.092), confirming the conclusions do not rely on the Gaussian approximation. 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.