Differential entropy as a measure of initial heterogeneity driving differentiation in the early mouse embryo

Background: Heterogeneity in gene expression among single cells is critical for cell differentiation. In the preimplantation mammalian embryo, stochastic cell-to-cell expression heterogeneity is followed by signal reinforcement to initiate the differentiation of the Inner Cell Mass (ICM) cells into Epiblast (Epi) or Primitive Endoderm. A key question is to identify genes that initiate and drive coordination of pluripotency factors and specification of Epi cells alongside the key transcription factor NANOG. Results: To address this question, we fit single-cell expression data to gamma distributions and compute their inter-cellular differential entropy profile. Using five single-cell transcriptomic datasets (RT-qPCR and RNA-seq), we recover genes that are well-known to play a key role in Epi specification and identify candidate genes, whose coordinated heterogeneity in expression, alongside Nanog drives ICM cells differentiation. We show that other typical measures of variability, such as the Fano factor or the coefficient of variation, show a less robust temporal profile than differential inter-cellular entropy. Moreover, candidate genes would not have been identified with principal component and correlation analyses. Conclusions: The identified candidate genes, with a differential entropy time profile similar to that of Nanog, could play a crucial role in the differentiation of ICM cells. The estimation of cell-to-cell variability in gene expression based on inter-cellular differential entropy is robust among datasets and reveals insights that other standard methods such as principal component analysis and Fano factors do not. Differential entropy thus provides a useful quantity to assess gene regulation during early embryonic development.