Detection of pre-transition phases during biological development using single-sample network entropy (SNE)

Complex biological systems often undergo a pre-transition phase prior to the onset of catastrophic event, during which a sharp and essential shift occurs. There is a pressing need to develop a swift and effective method for identifying such pre-transition phase or critical state, facilitating the timely implementation of tailored interventions to prevent irreversible and catastrophic transitions. Nonetheless, the identification of the pre-transition phase at the single-sample or single-cell level remains an exceedingly daunting task in modern clinical medicine, as reliance on small sample sizes often undermines the efficacy of traditional statistical methodologies. In this study, we propose a novel critical state algorithm based on individual sample data, termed single-sample network entropy (SNE), which effectively quantifies the disturbance caused by an individual sample relative to a set of reference samples, thereby revealing the pre-transition phases during biological development at the specific sample level. Our proposed method successfully identified pre-transition phases in both numerical simulations and eight real-world datasets, including an influenza infection dataset, three single-cell data (one associated with epithelial-mesenchymal transition (EMT) and two related to embryo development), and four tumor datasets: esophageal carcinoma (ESCA), head and neck squamous cell carcinoma (HNSC), and uterine corpus endometrial carcinoma (UCEC). In contrast to the existing single-sample approaches, our SNE method demonstrates enhanced effectiveness in detecting potential pre-transition phase. Moreover, it identifies two novel prognostic indicators: optimistic SNE (O-SNE) and pessimistic SNE (P-SNE) biomarkers for subsequent practical applications. Additionally, the reliability of computational findings is further strengthened by the functional roles of signaling biomarkers. Therefore, we present a novel computational approach that uncovers the pre-transition phases and signaling biomarkers of complex biological processes at the single sample or single-cell level, offering new insights and applications for early personalized biological analysis, including disease diagnosis and prognosis evaluation.