Calibrating developmental dynamics from single-cell atlases: lineage paths outrun least-action routes

Abstract

Single-cell atlases infer developmental dynamics from destructive snapshots, yet how far realized lineage paths depart from such inferred dynamics has never been measured with controls. We introduce LADD (Least-Action Developmental Dynamics), a measurement framework that learns a stochastic developmental vector field from time-series single-cell RNA-seq and computes minimum-action and minimum-time paths, together with a three-layer calibration protocol that separates genuine path deviation from the generic cost of centroid measurement, and we compare its forecasting component with optimal-transport and flow-matching methods. In the lineage-resolved Caenorhabditis elegans atlas, the raw action ratio of observed lineage-centroid trajectories to optimal paths is 3.79, yet forward-simulated ensembles of the learned model itself score 2.07, leaving a genuine excess of about two-fold. In zebrafish (Danio rerio), the observed ratio sits entirely at the model's floor. Three mechanisms that could explain the residual deviation (detours, flow-opposition, and fate-map complexity) are each excluded; what remains is speed, with lineages moving 30-43% faster along the learned flow. We report validity boundaries for temporal resolution, cross-species comparison, and energetic interpretation, delimiting where action-based trajectory comparisons are meaningful.