Edge-based relative entropy as a sensitive indicator of critical transitions in biological systems

Abstract

Abstract Background Disease progression in biosystems is not always a steady process but is occasionally abrupt. It is important but challenging to signal critical transitions in complex biosystems. Methods In this study, based on the theoretical framework of dynamic network biomarkers (DNBs), we propose a model-free method, edge-based relative entropy (ERE), to identify temporal key biomolecular associations/networks that may serve as DNBs and detect early-warning signals of the drastic state transition during disease progression in complex biological systems. Specifically, by combining gene‒gene interaction (edge) information with the relative entropy, the ERE method converts gene expression values into network entropy values, quantifying the dynamic change in a biomolecular network and indicating the qualitative shift in the system state. Results The proposed method was validated using simulated data and real biological datasets of complex diseases. The applications show that for certain diseases, the ERE method helps to reveal so-called “dark genes” that are non-differentially expressed but with high ERE values and of essential importance in both gene regulation and prognosis. Conclusions The proposed method effectively identified the critical transition states of complex diseases at the network level. Our study not only identified the critical transition states of various cancers but also provided two types of new prognostic biomarkers, positive and negative edge biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

Keywords

• Critical transition of complex disease
• Edge-based relative entropy
• Direct interaction networks
• Edge-biomarker
• Dynamic systems
• Informational entropy