Identifying the critical state of complex biological systems by the directed-network rank score method

Catastrophic transitions are ubiquitous in the dynamic progression of complex biological systems; that is, a critical transition at which complex systems suddenly shift from one stable state to another occurs. Identifying such a critical point or tipping point is essential for revealing the underlying mechanism of complex biological systems. However, it is difficult to identify the tipping point since few significant differences in the critical state are detected in terms of traditional static measurements.

In this study, by exploring the dynamic changes in gene cooperative effects between the before-transition and critical states, we presented a model-free approach, the directed-network rank score (DNRS), to detect the early-warning signal of critical transition in complex biological systems. The proposed method is applicable to both bulk and single-cell RNA-sequencing (scRNA-seq) data. This computational method was validated by the successful identification of the critical or pre-transition state for both simulated and six real datasets, including three scRNA-seq datasets of embryonic development and three tumor datasets. In addition, the functional and pathway enrichment analyses suggested that the corresponding DNRS signaling biomarkers were involved in key biological processes.

The source code is freely available at https://github.com/zhongjiayuan/DNRS.

Supplementary data are available at Bioinformatics online.