Identifying Critical States of Complex Diseases by Single-Sample Jensen-Shannon Divergence

Abstract

MotivationThe evolution of complex diseases can be modeled as a time-dependent nonlinear dynamic system, and its progression can be divided into three states, i.e., the normal state, the pre-disease state and the disease state. The sudden deterioration of the disease can be regarded as the state transition of the dynamic system at the critical state or pre-disease state. How to detect the critical state of an individual before the disease state based on single-sample data has attracted many researchers’ attention.MethodsIn this study, we proposed a novel approach, i.e., single-sample-based Jensen-Shannon Divergence (sJSD) method to detect the early-warning signals of complex diseases before critical transitions based on individual single-sample data. The method aims to construct score index based on sJSD, namely, inconsistency index (ICI).ResultsThis method is applied to five real datasets, including prostate cancer, bladder urothelial carcinoma, influenza virus infection, cervical squamous cell carcinoma and endocervical adenocarcinoma and pancreatic adenocarcinoma. The critical states of 5 datasets with their corresponding sJSD signal biomarkers are successfully identified to diagnose and predict each individual sample, and some “dark genes” that without differential expressions but are sensitive to ICI score were revealed. This method is a data-driven and model-free method, which can be applied to not only disease prediction on individuals but also targeted drug design of each disease. At the same time, the identification of sJSD signal biomarkers is also of great significance for studying the molecular mechanism of disease progression from a dynamic perspective.

Tipping the Balance: A Criticality Perspective

“…Some of the concepts and methodologies of the statistical mechanical description of phase transitions, like the state transition from a unimodal to a bimodal frequency distribution through a flattened unimodal profile (Figure 1) and the depiction of the state-transitions via potential landscapes and hysteresis curves (Figures 3 and 6), have made their appearance in recent studies on cancer. In such studies, cancer is interpreted in terms of a state-transition in the time series of transcriptome (gene expression) data with the transition points (bifurcation/phase transition points) identified as the points in state space at which dynamical regime shifts take place [17,28,34,40,41] .…”

“…It is, however, not a bonafide distance measure as it is not symmetric and does not satisfy the triangle inequality. The Jensen-Shannon divergence is defined to be [33,34] 𝐷 𝐽𝑆 (𝑃||𝑄) = 1 2 𝐷 𝐾𝐿 (𝑃||𝑀) + 1 2 𝐷 𝐾𝐿 (𝑄||𝑀), 𝑀 = 1 2 (𝑃 + 𝑄) (27) One can check that 𝐷 𝐽𝑆 (𝑃||𝑄) = 𝐷 𝐽𝑆 (𝑄||𝑃) (symmetry) and 0 ≤ 𝐷 𝐽𝑆 (𝑃||𝑄) ≤ 1. The zero (one) value indicates perfect (zero) overlap between the distributions.…”

“…Figure8shows the plot of the Jensen-Shannon divergence, 𝐷 𝐽𝑆 (𝑃||𝑄) ((27))[34], versus the parameter λ. The steady state probability distributions 𝑃 and 𝑄 are as given in(9) with 𝜎 2 = 4, 𝜆 ≠ 0 for the distribution 𝑃 and 𝜎 2 = 2, 𝜆 = 0 for the distribution Q.…”

Noninvasive cervicovaginal proteomic biomarkers for spontaneous preterm birth

“…Pair-wise proteomics divergences were quantified as the Jensen-Shannon divergence [66][67][68] . Groups of samples with similar proteomics were identified by hierarchical clustering using the sample-sample divergence matrix with the following parameters: Euclidean distance as the distance metric, average linkage clustering as the linkage selection method, and distance threshold = 3.…”

Detecting the Critical States of Type 2 Diabetes Mellitus Based on Degree Matrix Network Entropy by Cross-Tissue Analysis

“…Single-cell graph entropy (SGE) can explore the gene–gene associations among cell populations based on single-cell RNA sequencing data [ 6 ]. The single-sample-based Jensen–Shannon divergence (sJSD) method is used to detect the early-warning signals of complex diseases before critical transitions based on individual single-sample data [ 7 ]. The temporal network flow entropy (TNFE) method, which is based on network fluctuation of molecules, can detect the critical states of complex diseases on the basis of each individual [ 8 ].…”