Negative Result Note: Spectral "Collapse" Signals in Longitudinal Gene Coexpression Landscapes under Anti–PD-1 Therapy

We explored whether longitudinal gene coexpression networks during anti–PD-1 therapy exhibit robust signatures consistent with a global spectral “collapse” or critical transition (e.g., proliferation of soft modes reflected in spectral entropy / effective rank changes). Using a patient-level pre-treatment vs on-treatment design and focusing on three immunology-motivated gene modules (CYTOLYTIC_CORE, IFNG_AP_CORE, CHECKPOINTS), we computed multiple threshold-swept (“landscape”) network metrics and tested responder vs non-responder differences via permutation and empirical nulls (random gene sets matched by size). We did not find stable, reproducible evidence for a global collapse narrative in this cohort. A modest module-specific signal appeared for a cytolytic module in a threshold/transition-like feature (Δτ*), but several curve-based spectral-window analyses proved numerically fragile (NaNs and overlap loss across patients). This note documents the workflow, observed limitations, and why the attempted “universal spectral collapse” framing is not currently well-supported here, aiming to help others avoid similar dead ends.