MIWE: detecting the critical states of complex biological systems by the mutual information weighted entropy

Abstract

Complex biological systems often undergo sudden qualitative changes during their dynamic evolution. These critical transitions are typically characterized by a catastrophic progression of the system. Identifying the critical point is critical to uncovering the underlying mechanisms of complex biological systems. However, the system may exhibit minimal changes in its state until the critical point is reached, and in the face of high throughput and strong noise data, traditional biomarkers may not be effective in distinguishing the critical state. In this study, we propose a novel approach, mutual information weighted entropy (MIWE), which uses mutual information between genes to build networks and identifies critical states by quantifying molecular dynamic differences at each stage through weighted differential entropy. The method is applied to one numerical simulation dataset and four real datasets, including bulk and single-cell expression datasets. The critical states of the system can be recognized and the robustness of MIWE method is verified by numerical simulation under the influence of different noises. Moreover, we identify two key transcription factors (TFs), CREB1 and CREB3, that regulate downstream signaling genes to coordinate cell fate commitment. The dark genes in the single-cell expression datasets are mined to reveal the potential pathway regulation mechanism.

Keywords: Critical state; Differential entropy; Dynamic network biomarker (DNB); Mutual information.

Fig.1

The schematic of the MIWE method. A Gaussian distribution is fitted for each gene. B Mutual information network is constructed by taking mutual information between genes as edge weight, and local network is extracted from global network. C The weighted differential entropy of the global network is calculated. When the system is in the critical state, the MIWE score is at a low level, and once it reaches the critical state, the MIWE score increases sharply

Fig.2

Numerical simulation dataset is used to verify the effectiveness of MIWE. A Gene regulatory network model, where the arrow represents positive regulation. B MIWE score for each parameter of 10 nodes. C Comparison of the robustness of the MIWE method with the SLE, sJSD method at various levels of noise strength

Fig.3

Detecting the signal of cell fate commitment. The MIWE value is calculated for A MEF to neurons and B mESC to MP. The landscape of local MIWE values illustrates the dynamic evolution of network entropy in a global view for C MEF-to-neuron, D mESC to MP. The dynamical evolution of gene regulatory networks for the E MEF-to-neuron, F mESC to MP

Fig.4

TFs regulation and related enrichment analysis. A TFs modulated 74% of signaling genes identified by GSE67310 critical point. B TFs modulated 86% of signaling genes identified by GSE79578 critical point. Regulatory network of C CREB1, D CREB3. E CREB1 and its regulated signaling genes participate in significant biological processes and KEGG pathways. The outer ring's left side signifies the signaling genes identified by MIWE, while the right side represents the diverse biological processes associated with these genes. The inner ring depicts various enrichment pathways, with connection color and width indicating different levels of gene function significance. F CREB3 and its regulated signaling genes participate in significant biological processes and KEGG pathways

Fig.5

Potential regulatory mechanisms related to embryonic differentiation revealed by dark genes. Dynamic changes of gene expression and entropy of dark genes for A MEF to neurons, B mESC to MP. C Pathways enriched of MEF to neurons. D GO analysis of MEF to neurons. E The enrichment and regulation of related dark genes of MEF to neurons

Fig.6

Detection of the critical point of cancer progression. The MIWE score for A COAD, B THCA. Landscapes of the local MIWE score for C COAD, D THCA. Survival analysis before and after the identified critical states for E COAD, F THCA

Fig.7

Functional analysis of common signaling genes in two cancers. A Common signaling genes involve in major biological processes. B The association of genes with biological processes. C Common signaling genes involve in cancer related pathways. D The association between genes and pathways, where the number represents the ENTREZ ID of the gene