Identification of critical states in complex biological systems using cell-specific causal network entropy (CCNE)

Abrupt shifts, referred to as critical transitions, are frequently observed in complex biological systems, characterized by marked qualitative changes occurring from one stable state to another through a pre-transitional/critical state. Pinpointing such critical states, along with the signaling molecules, can provide valuable insights into the fundamental mechanisms of intricate biological processes. However, the identification and early warning of the critical state remains a challenge, particularly in model-free cases with high-dimensional single-cell data, where traditional statistical methods often prove inadequate due to the inherent sparsity, noise, and heterogeneity of the data. In this study, we propose a novel quantitative method, cell-specific causal network entropy (CCNE), to infer the specific causal network for each cell and quantify dynamic causal changes, thereby enabling the identification of critical states in complex biological processes at the single-cell level. We validated the accuracy and effectiveness of the proposed approach through numerical simulations and 5 distinct real-world single-cell datasets. Compared to existing methods for detecting critical states, the proposed CCNE exhibits enhanced effectiveness in identifying critical transition signals. Moreover, CCNE score is a computational tool for distinguishing temporal changes in cellular heterogeneity and demonstrates satisfactory performance in clustering cells over time. In addition, the reliability of CCNE is further emphasized through the functional enrichment and pathway analysis of signaling molecules.