Precursors for cell-state transitions: Stability, resilience, and predictability in Notch signaling pathways

The Notch signaling pathway is an evolutionarily conserved mechanism crucial for directing cell-state decisions during embryonic development and maintaining adult tissue homeostasis, with aberrations linked to diseases, including oncogenesis. Hence, reliable markers of impending transitions in Notch signaling are essential for predicting deleterious shifts and guiding therapeutic interventions. To develop a reliable predictive framework, we consider a deterministic model incorporating the principal components of the Notch pathway-namely, the Notch receptor; its ligands, Delta and Jagged; and the Notch intracellular domain (NICD)-to elucidate key biochemical processes at the single-cell level [Boareto et al., Proc. Natl. Acad. Sci. U.S.A. 112, E402 (2015)]. This model is then extended into a stochastic formulation via the corresponding chemical master equation to capture intrinsic cellular noise. A bifurcation analysis coupled with stochastic simulations reveals that variations in external Jagged levels induce multiple cell-state transitions among sender, receiver, and hybrid states. These transitions are predicted using statistical measures, including autocorrelation, variance, heteroskedasticity, and mutual information, whose significance and robustness are rigorously evaluated. Although individual metrics provide effective predictions, composite measures often underperform despite the transitions' association with a fold catastrophe. In addition, we assess the resilience landscape using time-series analyses and observe that the variability index outperforms the Jacobian indices. Further basin stability and stochastic potential-well evaluations indicate that the hybrid state is the fittest. In summary, our study demonstrates cellular transitions in a biologically relevant system and explores the application and limitations of statistical tools as dynamic biomarkers of cellular plasticity.