Cellular Density Homeostasis Is Governed by an Anisotropic Attractor and Predictive Feedback Control

Cell density is a fundamental biophysical property of living cells, yet the dynamical architecture underlying density homeostasis remains unknown. Here, we reconstruct the geometry, dynamics, and control structure governing cellular density regulation from single-cell mass-volume measurements acquired during recovery from osmotic perturbation. We identify a persistent anisotropic attractor in mass-volume state space that permits coordinated density-preserving fluctuations while strongly suppressing density-changing deviations. Optimal transport analysis reveals directed recovery trajectories confined to this attractor, enabling inference of an effective density-restoring control law. Density deviations are associated with coordinated changes in biomass accumulation and volume expansion that together generate an effective density-restoring control law. Moreover, density error contains significant predictive information regarding future corrective behavior, revealing an information-rich component of cellular regulation. Together, these findings establish cellular density homeostasis as an emergent dynamical control process and demonstrate how attractor reconstruction, optimal transport, and information theory can be combined to uncover the organizing principles of biological homeostasis.