Complex biological systems do not always develop smoothly but occasionally undergo a sharp transition; i.e. there exists a critical transition or tipping point at which a drastic qualitative shift occurs. Hunting for such a critical transition is important to prevent or delay the occurrence of catastrophic consequences, such as disease deterioration. However, the identification of the critical state for complex biological systems is still a challenging problem when using high-dimensional small sample data, especially where only a certain sample is available, which often leads to the failure of most traditional statistical approaches. In this study, a novel quantitative method, sample-perturbed network entropy (SPNE), is developed based on the sample-perturbed directed network to reveal the critical state of complex biological systems at the single-sample level. Specifically, the SPNE approach effectively quantifies the perturbation effect caused by a specific sample on the directed network in terms of network entropy and thus captures the criticality of biological systems. This model-free method was applied to both bulk and single-cell expression data. Our approach was validated by successfully detecting the early warning signals of the critical states for six real datasets, including four tumor datasets from The Cancer Genome Atlas (TCGA) and two single-cell datasets of cell differentiation. In addition, the functional analyses of signaling biomarkers demonstrated the effectiveness of the analytical and computational results.

The critical point or pivotal threshold of cell transition occurs in early embryonic development when cell differentiation culminates in its transition to specific cell fates, at which the cell population undergoes an abrupt and qualitative shift. Revealing such critical points of cell transitions can track cellular heterogeneity and shed light on the molecular mechanisms of cell differentiation. However, precise detection of critical state transitions proves challenging when relying on single-cell RNA sequencing data due to their inherent sparsity, noise, and heterogeneity. In this study, diverging from conventional methods like differential gene analysis or static techniques that emphasize classification of cell types, an innovative computational approach, single-cell gene association entropy (SGAE), is designed for the analysis of single-cell RNA-seq data and utilizes gene association information to reveal critical states of cell transitions. More specifically, through the translation of gene expression data into local SGAE scores, the proposed SGAE can serve as an index to quantitatively assess the resilience and critical properties of genetic regulatory networks, consequently detecting the signal of cell transitions. Analyses of five single-cell datasets for embryonic development demonstrate that the SGAE method achieves better performance in facilitating the characterization of a critical phase transition compared with other existing methods. Moreover, the SGAE value can effectively discriminate cellular heterogeneity over time and performs well in the temporal clustering of cells. Besides, biological functional analysis also indicates the effectiveness of the proposed approach.

Tipping points or critical transitions widely exist during the progression of many biological processes. It is of great importance to detect the tipping point with the measured omics data, which may be a key to achieving predictive or preventive medicine. We present the tipping point detector (TPD), a web tool for the detection of the tipping point during the dynamic process of biological systems, and further its leading molecules or network, based on the input high-dimensional time series or stage course data. With the solid theoretical background of dynamic network biomarker (DNB) and a series of computational methods for DNB detection, TPD detects the potential tipping point/critical state from the input omics data and outputs multifarious visualized results, including a suggested tipping point with a statistically significant P value, the identified key genes and their functional biological information, the dynamic change in the DNB/leading network that may drive the critical transition and the survival analysis based on DNB scores that may help to identify 'dark' genes (nondifferential in terms of expression but differential in terms of DNB scores). TPD fits all current browsers, such as Chrome, Firefox, Edge, Opera, Safari and Internet Explorer. TPD is freely accessible at http://www.rpcomputationalbiology.cn/TPD.

The dynamics of complex diseases are not always smooth; they are occasionally abrupt, i.e. there is a critical state transition or tipping point at which the disease undergoes a sudden qualitative shift. There are generally a few significant differences in the critical state in terms of gene expressions or other static measurements, which may lead to the failure of traditional differential expression-based biomarkers to identify such a tipping point. In this study, we propose a computational method, the direct interaction network-based divergence, to detect the critical state of complex diseases by exploiting the dynamic changes in multivariable distributions inferred from observable samples and local biomolecular direct interaction networks. Such a method is model-free and applicable to both bulk and single-cell expression data. Our approach was validated by successfully identifying the tipping point just before the occurrence of a critical transition for both a simulated data set and seven real data sets, including those from The Cancer Genome Atlas and two single-cell RNA-sequencing data sets of cell differentiation. Functional and pathway enrichment analyses also validated the computational results from the perspectives of both molecules and networks.

MOTIVATION: 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. RESULTS: 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. AVAILABILITY AND IMPLEMENTATION: The source code is freely available at https://github.com/zhongjiayuan/DNRS. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.