Ergodic patterns of cell state transitions underlie the reproducibility of embryonic development

The reproducibility of embryonic development is a remarkable feat of biological organization, but the underlying mechanisms are poorly understood. Clearly, gene regulatory networks are central to the orderly progression of development, but noisy molecular and cellular processes should reduce reproducibility. Here, we identify ergodicity, a type of dynamical stability, as underlying the reproducibility of development. In ergodic systems, a single timepoint measurement equals a time average. Focusing on the zebrafish tailbud, we define gene expression and cell motion states using a parallel statistical analyses of single cell RNA sequencing data and in vivo timelapse cell tracking data and a change point detection algorithm. Strikingly, the cell motion state transitions in each embryo exhibit the same patterns for both a single timepoint and a 2-3 hour time average. Both the cell motion and gene expression cell states exhibit balanced influx and outflux rates reflecting a spatiotemporal stability. Stated simply, these data indicate the pattern of changes in the tailbud doesnt change. This ergodic pattern of cell state transitions may represent an emergent meta-state that links gene networks to the reproducible progression of embryogenesis.