Detecting bifurcations in tissue development

During embryonic development, pluripotent cells undergo fate transitions, yielding functionally specialized cells. These transitions are often visualized as bifurcations, points in time when the landscape of cell fates changes from having one steady state to multiple, or different steady states. Experimental tools such as single-cell RNA sequencing, which measures the full distribution of a cell’s possible genetic compositions, can be used to obtain trajectories of gene expression during a developmental transition, but it remains unclear how RNA dynamics relate to changes in cellular state space. We show that bifurcations in cellular state space can be analytically pinpointed and qualitatively assessed directly from the temporal covariance of gene expression. We apply our bifurcation time measurement to a well characterized sequence of cell fate decisions, the transition of hematopoietic stem cells to neutrophils, to identify genes that drive fate decisions. Our work provides a robust mathematical framework for categorizing developmental transitions that can aid in gene network inference and help determine features of cell differentiation, such as when and why cell fate transitions are reversible or generate multiple cell types.