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Mesoscopic bio-systems typically evolve towards functionally important targetstates, such as cell-cycle checkpoints or decision boundaries for the releaseof specific behaviors. For the data-driven inference of the underlyingdirectional out-of-equilibrium dynamics, we here develop a theory of targetstate aligned (TSA) ensembles. Target state alignment allows to analyzedirectional dynamics in reverse time, starting from the final conditions of theforward process. Knowledge about the initial conditions of the forward processis not required for the analysis. Our theory reveals whether and when such asystem can be represented by a single, effective stochastic equation of motion.We show how, in these effective dynamics, genuine biological forces can beseparated from spurious forces, which invariably arise from target statealignment. We apply our inference scheme to the example of cytokinetic ringconstriction, and derive the universal low-noise and short-term behavior of TSAensembles. Our theory establishes a transparent mathematical foundation for theanalysis and inference of directed biological dynamics by target statealignment.

Reverse-time analysis uncovers universality classes in directional biological dynamics