16Cell fate commitment occurs during early embryonic development, that is, the embryonic 17 differentiation sometimes undergoes a critical phase transition or "tipping point" of cell fate 18 commitment, at which there is a drastic or qualitative shift of the cell populations. In this study, we 19 presented a novel computational approach, the single-cell graph entropy (SGE), to explore the gene-20 gene associations among cell populations based on single-cell RNA sequencing (scRNA-seq) data. 21 Specifically, by transforming the sparse and fluctuating gene expression data to the stable local network 22 entropy, the SGE score quantitatively characterizes the criticality of gene regulatory networks among 23 cell populations, and thus can be employed to predict the tipping point of cell fate or lineage 24 commitment at the single cell level. The proposed SGE method was applied to five scRNA-seq datasets. 25 For all these datasets of embryonic differentiation, SGE effectively captures the signal of the 26 impending cell fate transitions, which cannot be detected by gene expressions. Some "dark" genes that 27 are non-differential but sensitive to SGE values were revealed. The successful identification of critical 28 transition for all five datasets demonstrates the effectiveness of our method in analyzing scRNA-seq 29 data from a network perspective, and the potential of SGE to track the dynamics of cell differentiation. 30 31 gene; cell fate commitment. 33 34 35Predicting cell-fate commitment by SGE 2 This is a provisional file, not the final typeset article 36 1. Introduction 37 Complex systems may switch abruptly to a contrasting state through a critical transition [1]. In recent 38 years, detecting critical transitions for general systems, such as ecosystems systems [2-3], climates 39 systems [4-5], financial systems [6,7], and epidemic model [8][9], has drawn more and more attentions.
40In biomedical fields, the rapid growth of single-cell datasets has shed new light on the complex 41 mechanisms of cellular heterogeneity. In these single-cell experiments, the cell fate commitment 42 represents a critical state transition or "tipping point" at which complex systems undergo a qualitative 43 shift. Characterizing and predicting such critical transition is crucial for patient-specific disease 44 modeling and drug testing [10]. Recent studies provided a plethora of statistical quantities such as 45 variance, correlation coefficient, and coordination of gene expression, to detect a cell fate transition of 46 embryonic differentiation [10,11]. However, these statistical quantities mainly focused on the analyses 47 at the gene expression level, while single-cell RNA sequencing (scRNA-seq) may offer more 48 information of an insight into the cell-specific network systems. In contrast to gene expression, cell-49 specific network is a stable form against the time and condition [12], and thus reliably characterize the 50 biological processes such as cell fate commitment. Such a network system is viewed as a nonlinear 5...