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.Author summary: Cells constantly sense their environment and make decisions based on chemical signals, but biological noise makes these decisions error-prone. When decision-making goes wrong, for instance due to mutations—diseases like chronic inflammation or cancer can result. In this study, we applied a well-established framework from signal detection theory, the Neyman-Pearson approach, to quantify how reliably cells can distinguish between different levels of the signaling molecule TNF. Using single-cell measurements from both normal cells and cells lacking the A20 feedback regulator, we computed detection and false alarm probabilities at different time points. We found that analyzing multiple time points together improves detection, that stronger signals are easier to detect, and that loss of A20 degrades decision quality—consistent with known biology. Our framework does not require assumptions about how likely each signal is, making it generalizable and broadly applicable. We believe this approach offers a practical, quantitative “scorecard” for cellular signaling performance that could help researchers understand when and why cellular decisions go wrong in disease.