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Landscape of Target State Directed Processes in Living Systems

Nicolas Lenner1,2,3,*, Matthias Häring1,4, Stephan Eule1,5, Jörg Großhans4,6, and Fred Wolf1,4,7,8,9,10,†

  • *Contact author: lenner@ias.edu
  • †Contact author: fred.wolf@ds.mpg.de
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PRX Life 4, 013024 – Published 24 February, 2026

DOI: https://doi.org/10.1103/cx3h-q6d2

Abstract

Across the living world, from cell biology and morphogenesis to behavior and cognition, system dynamics is often directed towards functionally important goals one might call target states. Dynamics towards such target states is never in equilibrium, always nonstationary, and typically swiftly over, terminating once the goal is reached. Complicating data-driven inference of effective dynamical models, trajectories of living systems homing in on target states are not only brief but exhibit initial conditions that are typically intrinsically heterogeneous and experimentally uncontrollable. Here we present a reverse-time stochastic dynamics theory for ensembles of target state directed processes, and uncover a universal space-time core of such ensembles that is independent of initial conditions. Examining this core structure, we demonstrate that the landscape of conceivable target state directed dynamics decomposes into sectors that qualitatively differ in their accessibility to data-driven inference. Ensembles undergo a phase transition from an opaque phase, in which their space-time core is uninformative about the underlying dynamics, to a transparent phase, in which the dynamics is directly encoded in its low-order moment functions. We use the reverse-time theory of target state directed processes to construct core-based methods for data-driven dynamical systems inference. Applied to biophysical models of cytokinesis, a directed process for which different regimes of actomyosin turnover cause distinct types of terminal dynamics, our approach precisely identifies the underlying molecular mechanism. Reverse-time ensemble theory establishes a versatile toolset for understanding target state directed biological processes and reveals that the mere presence of target states in living systems induces a novel kind of phase transition in dynamical systems inference.

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PRX Life 4, 013024– Published 24 February, 2026
  • Received 17 December 2024
  • Accepted 8 December 2025
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