A Phase-Gated Autoregressive Framework Reveals Tissue-Specific Circadian Gating of Cancer-Relevant Genes Across Mammalian Tissues

Circadian clocks orchestrate tissue homeostasis by gating cell cycle, DNA repair, metabolism, and immune responses in time. However, the precise form, strength, and tissue specificity of this gating—and how it fails in cancer—remain poorly characterised. Here we introduce PAR(2), a stability-constrained, phase-dependent autoregressive framework of order two that systematically quantifies temporal coupling between core clock genes and downstream targets across diverse tissues and conditions. We applied PAR(2) to over 28,000 clock–target expression time series drawn from 22 publicly available circadian transcriptomic datasets spanning mouse liver, heart, cerebellum, intestinal organoids, and additional tissues. For each pair, PAR(2) jointly estimates phase-dependent linear coupling (via sinusoidal Fourier expansion of autoregressive coefficients) and eigenvalues summarising dynamical stability and oscillatory character. Residual-based permutation testing (\(\:B=1,000\)) and cross-tissue replication criteria control false discoveries; hits are classified into three confidence tiers. PAR(2) recovers known circadian gating relationships and reveals new candidate architectures. In mouse liver, Wee1 emerges as the most robustly gated target—a Tier 0 hit achieving FDR significance across two independent datasets (GSE54650 and GSE11923) and replicating in heart and cerebellum, with inferred eigenperiods of 22.8–24.5 hours consistent with circadian periodicity. In heart, Tead1 /YAP1-linked gating connects circadian timing with Hippo pathway regulation; in cerebellum, Cdk1 and related cell-cycle regulators form the primary circadian-coupled module. In intestinal organoids, Apc mutation increases FDR-significant gating density (3.8% to 6.7%) and elevates target-gene eigenvalues, collapsing the clock/target hierarchy gap (\(\:+0.35\) wild-type, \(\:-0.025\) ApcKO), while Bmal1 loss destroys the hierarchy through clock gene suppression (gap \(\:-0.04\)). Strikingly, the Apc/Bmal1 double mutant paradoxically restores the hierarchy gap (\(\:+0.11\)) through non-additive compensatory effects. Phase-gating terms consistently improved in-sample fit but did not reliably improve out-of-sample prediction, confirming PAR(2) as a descriptive discovery framework rather than a predictive model. PAR(2) provides a principled, permutation-tested approach to mapping clock–target gating architectures across tissues and perturbations, yielding testable hypotheses about circadian temporal organisation and its disruption in cancer. All analyses are reproducible via the PAR(2) Discovery Engine (https://par2-discovery-engine.replit.app).