Modelling cell fate transitions with signal-driven attractor network bifurcations*

A major problem in development is understanding how signaling pathways mediate cell identity. Current mathematical models fall into one of two categories: geometric landscape models of cell fate bifurcations driven by signals, or gene network models that capture the interactions between a handful of genes. However, no models currently bridge the gap between signal-driven bifurcations in an abstract cell fate landscape and the dynamics of gene expression. To address this, we introduce a new model for cell fate transitions that combines modern Hopfield networks with geometric landscapes and bifurcations. The dynamics occur in gene expression space while minimizing a chosen potential in cell type space, and the potential is controlled by signaling-related parameters. Any geometric landscape may be inserted into the model to generate testable predictions of the corresponding gene expression dynamics. Using single-cell RNA-sequencing data of cell types as our attractor states, we demonstrate our model's ability to predict gene expression changes during differentiation according to a changing cell fate landscape.