Finding signatures of low-dimensional geometric landscapes in high-dimensional cell fate transitions

Hundreds of highly specialized cell phenotypes cooperate together to enable healthy functioning in many animals. When growing or injured, cells can self-organize and transition between these cell types. The consistency and robustness of developmental cell fate trajectories suggests that complex gene regulatory networks effectively act as low-dimensional cell fate landscapes. We introduce a phenomenological model of cell fate transitions that predicts signatures of these landscapes observable in gene expression measurements. By combining low-dimensional gradient dynamical systems and high-dimensional Hopfield networks, our model captures the interplay between cell fate, gene expression, and signals. Using existing single-cell RNA-sequencing time-series data, we compare experimental observations to theoretical landscape candidates belonging to different bifurcation classes. These results show that a geometric landscape approach can reveal new insights in time series single-cell RNA-sequencing data of cell fate transitions. Additionally, spatial interactions between cells can be integrated into the model to recreate cell type patterning such as the striped patterning of lung ciliated and secretory cells caused by lateral Notch inhibition.