Information Geometry and the Eukaryotic Architecture: Mapping Energy Transfers and Progression Dynamics (Volume II)

The complex spatial compartmentalization of eukaryotic cells, defined by interacting membrane-bound organelles and specialized membrane contact sites (MCS), can be rigorously analyzed by treating the cellular architecture as a physical and statistical manifold. Metabolic states, derived from imaging or transcriptomics, are modeled as probability distributions and projected onto an information-geometric space defined by the Fisher-Rao metric. Within this geometry, cellular energetic progression, including critical phase transitions like proliferation or apoptosis, is mapped as continuous geodesic flows, which follow paths of "least action" dictated by the manifold's curvature. Analyzing these dynamics reveals "sloppiness," a property where a few "stiff parameters" guard the critical path while other "sloppy parameters" are permitted variance. To reconstruct continuous cell progression trajectories from static data, the methodology employs entropic Sinkhorn optimal transport. Crucially, modern models utilize unbalanced Sinkhorn optimal transport with the Wasserstein-Fisher-Rao metric to dynamically account for cellular growth rates and stochastic biological noise, such as proliferation or apoptosis. This geometric rendition allows for the highly predictive modeling of eukaryotic cell differentiation, migration, and unchecked proliferative pathologies directly from static imaging and transcriptomic data.

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