Single-cell data-driven mathematical model reveals possible molecular mechanisms of embryonic stem-cell differentiation.

Embryonic development is widely studied due to its application in disease treatment. The published literature demonstrated that Krüppel-like factor 8(KLF8) plays an important role in modulating mesendoderm to definitive endoderm (DE) differentiation. However, it is not clear how KLF8 interacts with other key genes and affects the differentiation process. To qualitatively and quantitatively explore the molecular mechanisms of KLF8 during the differentiation of human embryonic stem cells (hESCs) in detail, we developed a mathematical model to describe the dynamics between KLF8 and two other significant genes, E-cadherin(CDH1) and Zinc-finger E-box-binding homeobox1(ZEB1). Based on the single-cell RNA-seq data, the model structure and parameters were obtained using particle swarm optimization (PSO). The bifurcation analysis and simulation results reveal that the system can exhibit a complex tristable transition, which corresponds to the three states of embryonic development at the single-cell level. We further predict that the novel important gene KLF8 promotes the formation of DE cells by reciprocal inhibition between CDH1 and KLF8 and promotion of the expression of ZEB1. These results may help to shed light on the biological mechanism in the differentiation process of hESCs.