Early Detection of Transcriptomic State-Transition Dynamics in Cancer Through Nonlinear Dynamical Systems Analysis

Background: Understanding transcriptomic state-transition dynamics is important for elucidating cancer progression and therapeutic response, yet existing single-cell transcriptomic approaches primarily characterize gene-expression changes or pseudotemporal ordering rather than the dynamical organization of cellular-state progression. Methods: We developed a nonlinear dynamical systems framework that reconstructs transcriptomic state spaces from single-cell RNA-sequencing data by integrating diffusion pseudotime, data-driven observable selection, Takens-inspired delay-coordinate reconstruction, nonlinear dynamical analysis, trajectory-aware bootstrap uncertainty estimation, and a novel Transcriptomic Dynamical Instability Score (TDIS). The framework was evaluated using the GSE147405 epithelial-to-mesenchymal transition dataset, with complementary external analysis using the GSE149428 treatment-response dataset. Results: At the prespecified 120-bin resolution, TDIS values differed among treatments (EGF = 0.778, TNF = 0.657, TGFβ1 = 0.091); however, sensitivity analyses demonstrated that both absolute scores and treatment ordering depended on pseudotime discretization. TDIS is therefore interpreted as a resolution-dependent comparative descriptor rather than a resolution-invariant biological ranking. Local TDIS preceded the detected onset of held-out composite EMT-associated transcriptional remodeling with robust bootstrap support for EGF and TNF, whereas the temporal ordering under TGFβ1 was uncertain, demonstrating treatment-dependent pseudotemporal early-warning behavior. Complementary external analysis demonstrated a strong association between transcriptomic trajectory geometry and experimentally measured treatment response. Conclusions: These findings support nonlinear dynamical systems analysis as a complementary systems-level framework for quantifying relative transcriptomic dynamical instability, characterizing transcriptomic state-transition dynamics, and investigating treatment-dependent cellular-state reorganization in cancer.