The Early-warning Method For Critical Points Of Biological Systems Based On Molecular Omics Data

There is a critical state(critical point)in many complex systems,such as ecosystems,climate systems,the dynamic progression of complex diseases,and early embryonic development.Once the system crosses the critical state,it would switch from one state to another state and is nearly impossible to reverse.Appropriate and timely intervention can be taken to prevent or halt the negative consequences generated from the after-transition stage if we can detect early-warning signals of critical transitions in complex systems.For instance,for the dynamic progression of complex diseases,the disease would deteriorate rapidly after the critical point,and it is difficult to achieve effective treatment.For another example,for early embryonic development,the cells would differentiate into other cell types after the system undergoes the critical transition.Therefore,it is of great significance to detect the early-warning signal of critical transition of these complex biological systems in order to prevent disease deterioration in a timely manner and induce early embryonic stem cells to differentiate in a favorable direction.In this paper,from the perspective of a data-driven model,based on both the theory and methods of computational biology,we can identify critical points just before disease deterioration and predict cell fate commitment during early embryonic development.Focusing on complex biological systems,the following three algorithms are developed to detect the early-warning signal for the critical transition of complex biological systems based on different features of different data types.(1)For the high-dimensional data with a small sample size,we developed a single-samplebased hidden Markov model(HMM)algorithm.It is an unsupervised learning method,which makes the association between the steady-state to unstable Markov process and the process of sudden catastrophic transition into the disease state from the relatively normal state,and detect early warning signal of critical transition into the disease state by exploring the dynamic difference between the normal state and the pre-disease state.This method is a detection algorithm for the critical point based on a small sample size,which detects the critical point of complex diseases at a single sample level.(2)For data with stronger noise,we developed a single-sample-based Kullback-Leibler divergence(s KLD)based on the distribution information of molecules.The background distribution is fitted based on the normal samples,and then a novel index constructed by Kullback–Leibler divergence was proposed to explore and quantify the disturbance on the background distribution caused by a case single sample.The critical transition into the disease deterioration is then signaled by the significant change of index.This method is a detection algorithm for the critical point under the strong noise condition.The proposed method is featured with robustness against sample noises and can detect the critical point of biomedical data with large noise.(3)For single-cell RNA sequencing data characterized with sparsity.we developed a single-cell graph entropy(SGE)algorithm to predict cell fate commitment during early embryonic development.The algorithm is composed of constructing a cell-specific network for each cell,transforming the sparse gene expression matrix into the network entropy matrix,and predicting the critical signal of cell fate commitment based on entropy values.This method is a detection algorithm of the critical point based on single-cell RNA sequencing datasets.