Early Detection of Critical Transcriptomic State Transitions in Cancer Through Nonlinear Dynamical Systems Analysis

<jats:p>Understanding critical transcriptomic state transitions is essential for elucidating cancer progression and therapeutic response. Although single-cell transcriptomics has transformed the study of cellular heterogeneity, existing approaches primarily characterize gene expression changes or pseudotemporal ordering rather than the underlying dynamics of cellular state transitions. Here, we present a nonlinear dynamical systems framework for the early detection and quantitative characterization of transcriptomic state transitions. The proposed framework integrates diffusion pseudotime, data-driven observable selection, Takens delay-coordinate embedding, nonlinear dynamical analysis, trajectory-aware bootstrap uncertainty estimation, and a novel Transcriptomic Dynamical Instability Score (TDIS). The framework was evaluated using the publicly available single-cell RNA-sequencing dataset GSE147405, which captures epithelial-to-mesenchymal transition (EMT) in A549 cells following EGF, TGFβ1, and TNF stimulation. The reconstructed transcriptomic state spaces exhibited distinct treatment-specific dynamics, with TGFβ1 showing the highest dynamical instability (LLE = 0.0344; TDIS = 0.700), followed by EGF (LLE = 0.0136; TDIS = 0.309) and TNF (LLE = 0.0131; TDIS = 0.188). Local TDIS preceded canonical EMT-associated transcriptional reprogramming for EGF, provided moderate evidence for TGFβ1, and showed no detectable lead for TNF, indicating that its early-warning capability is pathway dependent. Trajectory-aware bootstrap analysis confirmed the robustness and reproducibility of the nonlinear dynamical measures, while independent validation using the GSE149428 treatment-response dataset demonstrated a strong association between transcriptomic trajectory geometry and cell viability (Pearson r = 0.891, p = 0.007; Spearman ρ = 0.821, p = 0.023). These findings establish TDIS as a robust and reproducible framework for quantifying transcriptomic instability and identifying pathway-dependent early-warning signals of critical cellular state transitions, providing a new systems-level approach for investigating cancer progression, therapeutic response, and other dynamic biological processes.</jats:p>