Information Geometry of Intracellular Compartment Coupling Reveals Transcriptomic State Transitions in Single Cells

Single-cell transcriptomic analyses typically characterize cellular states using gene-expression variability, dimensionality reduction, and trajectory inference. However, existing approaches provide limited insight into how transcriptomic information is organized across interacting intracellular compartments. Here we introduce Compartment Coupling Entropy (CCE), an information-geometric framework that quantifies the organization of transcriptomic coupling between spliced and unspliced RNA compartments. CCE constructs a cross-compartment coupling operator from compartment-resolved transcriptomic profiles and characterizes its singular-value spectrum using coupling entropy, effective coupling dimension, and coupling susceptibility. These metrics measure how transcriptomic information is distributed across coupling modes and provide a quantitative description of transcriptomic organization beyond conventional expression-based statistics. Applying CCE to pancreatic endocrine differentiation revealed substantial remodeling of coupling architecture along developmental trajectories. Coupling entropy and effective coupling dimension underwent transient collapse and re-expansion during lineage progression, while coupling susceptibility identified discrete intervals of rapid transcriptomic reorganization corresponding to candidate cell-state transition regimes. Across cell states, coupling entropy showed weak correspondence with classical mutual information, indicating that spectral coupling organization captures information not represented by conventional information-theoretic measures. An organization ratio and spectral excess information further quantified the divergence between classical and coupling-based descriptions of transcriptomic structure. Robustness analyses demonstrated stability of the framework under bootstrap resampling, gene subsampling, spectral truncation, and trajectory discretization. Application to an independent dentate gyrus developmental dataset revealed similar hierarchical coupling spectra and susceptibility-defined transition regimes, suggesting that transient reorganization of compartment-coupling architecture may represent a general feature of cellular state transitions. CCE provides a general methodology for quantifying the information geometry of intracellular transcriptomic organization and complements existing single-cell analytical approaches by revealing coupling architectures that are inaccessible to conventional expression-based analyses.