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.