Global Quantitative Dynamics and Early Warning Signals of Hepatocellular Carcinoma: Integrating Theoretical Modeling...

Early detection of hepatocellular carcinoma (HCC) is critical for improving patient outcomes, yet existing methods lack the predictive power to reliably anticipate malignant transition. Here, we introduce a quantitative framework integrating gene regulatory networks with nonequilibrium landscape and flux theory to identify early warning signals (EWS) of HCC from both dynamical and thermodynamic perspectives. Within this framework, the entropy production rate (EPR) quantifies the thermodynamic dissipation associated with carcinogenesis, while the mean flux captures the dynamical driving force of state transitions. We show that both indicators undergo marked changes near critical transition points (e.g., from normal tissue to HCC or from hepatic homeostasis to malignancy), providing reliable EWS for impending HCC emergence. To bridge theoretical predictions with clinical application, we derived two measurable signatures from time-series gene expression data: variance and the forward-backward cross-correlation difference (ΔC), a metric of time irreversibility. These signatures increased significantly during premalignant stages, offering a practical strategy for detecting early HCC risk. Validation using the longitudinal transcriptomic data set GSE17384─spanning normal liver, chronic hepatitis, and HCC stages─confirmed strong consistency with model predictions. By uncovering the thermodynamic and dynamical principles underlying HCC progression, this work not only elucidates the mechanisms of critical transitions in carcinogenesis but also provides a foundation for future strategies in precision monitoring and early intervention.