Immune gene co-expression networks are constrained by a non-linear topology spectral relationship
Inter-individual heterogeneity poses a fundamental challenge to systems-level characterization of immune states. When examined in isolation, network metrics exhibit extensive distributional overlap between conditions, providing little discriminatory power at the donor level. We hypothesized that immune states differ not in isolated properties but in the geometric constraints governing their joint distribution. We constructed donor-level gene co-expression networks from peripheral blood mononuclear cells across a Discovery cohort (CLARITY/SLE; n[~]Healthy[~] = 74, n[~]Disease[~] = 86) and an independent Validation cohort (STEPHENSON/COVID-19), totaling 259 unique donors. Network modularity (Q) and leading eigenvalue ({lambda}[~]max[~]) distributions overlapped substantially between conditions (Q: Wilcoxon p = 0.913, Cliffs {delta} = 0.01, 95% CI [-0.17, 0.19]; {lambda}[~]max[~]: p = 0.108, {delta} = 0.15, 95% CI [-0.04, 0.34]). However, mapping donors into a joint modularity-spectral energy space revealed a non-monotonic organizational constraint: networks with high modularity exhibit constrained spectral energy, while low-modularity networks permit dominant collective modes. Critically, configurations combining high modularity with high spectral leakage are empirically absent--defining an empirically unoccupied (forbidden) zone in the state space. The two cohorts occupy opposite arms of this U-shaped crossover (Discovery: {rho} = -0.39; Validation: {rho} = +0.41), explaining their opposite correlation signs as sampling different regions of a single underlying constraint. This geometry persists across network densities (5-10%), sampling depths (500-800 cells), and within major cell lineages (CD4+ T cells, Monocytes). These findings characterize immune network organization not by univariate biomarkers, but by geometric boundaries that constrain permissible configurations. Significance StatementImmune responses vary substantially across individuals, frustrating efforts to identify universal organizational principles. We analyzed gene co-expression networks from peripheral blood mononuclear cells across 259 donors in two independent cohorts and found that neither network modularity nor spectral dominance alone distinguishes healthy from disease states--distributions overlap extensively. However, plotting these properties jointly reveals that observed immune networks are confined to a restricted region of the modularity-spectral energy space, while configurations combining high modularity with high spectral energy are empirically absent. This geometric constraint persists across cohorts, sampling depths, and cell lineages, suggesting a robust structural trade-off between compartmentalization and collective coordination in immune network architecture.