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

Multicellular organisms develop a wide variety of highly-specialized 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. A complementary set of works draws on the theory of dynamical systems to argue that cell fate transitions can be categorized into universal decision-making classes. However, the theory connecting geometric landscapes and decision-making classes to high-dimensional gene expression space is still in its infancy. Here, we introduce a phenomenological model that allows us to identify gene expression signatures of decision-making classes from single-cell RNA-sequencing time-series data. Our model combines low-dimensional gradient-like dynamical systems and high-dimensional Hopfield networks to capture the interplay between cell fate, gene expression, and signaling pathways. We apply our model to the maturation of alveolar cells in mouse lungs to show that the transient appearance of a mixed alveolar type 1/type 2 state suggests the triple cusp decision-making class. We also analyze lineage-tracing data on hematopoetic differentiation and show that bipotent neutrophil-monocyte progenitors likely undergo a heteroclinic flip bifurcation. Our results suggest it is possible to identify universal decision-making classes for cell fate transitions directly from data.