Recovering Candidate Circadian Regulators of Arrhythmic Pituitary Hormone Genes Using Reliability-Weighted Magnetic Laplacian with rwMagLap

2026-07-02

AI Summary

This study addresses the challenge of identifying regulatory factors for hormone-related genes in the pituitary that lack overt 24-hour rhythmicity yet are crucial for women’s health. The authors propose a novel method that integrates circadian phase information by constructing a Hermitian graph based on rhythmically expressed backbone genes. They derive a magnetic Laplacian operator incorporating both goodness-of-fit and peak-phase estimates, and introduce a reliability-weighted nearest-neighbor projection to anchor non-rhythmic genes. Candidate regulators are then ranked using complex-valued personalized PageRank. This approach uniquely combines magnetic Laplacian embedding with reliability weighting to effectively recover latent rhythmic regulatory signals. Applied to pituitary data, the top 50 candidates show significant enrichment—7.95-fold (p_BH = 4×10⁻⁶) in KEGG and 4.54-fold (p_BH = 1.6×10⁻⁴) in Reactome circadian pathways—substantially outperforming phase-agnostic baselines, with a magnetic embedding accuracy of 0.971.

Abstract

We study how to recover candidate circadian-clock regulators of pituitary hormone genes that are important for women's health but do not show a clear 24-hour rhythm in bulk tissue, aiming to nominate clock-linked regulatory targets that could inform future chronopharmacologic and chronotherapeutic strategies. We propose \textbf{rwMagLap}, which builds a graph on rhythmic backbone genes. For each edge, we combine 24-hour fit quality with peak-time phase, represented as a complex unit-circle value, yielding a Hermitian adjacency matrix and a magnetic Laplacian. We insert arrhythmic hormone genes, treated as anchors, by a reliability-weighted nearest-neighbor projection. The projected anchor-neighbor weights are pooled into a soft teleport distribution, and complex personalized PageRank then ranks rhythmic backbone genes by the magnitude of their PageRank scores. In pituitary data, we find that all 11 women's-health anchors are arrhythmic. Even so, we find that the top-50 list is $7.95\times$ enriched for the 13-gene KEGG circadian set (7 of the 8 set genes in the 454-gene backbone; corrected Benjamini-Hochberg (BH) $p_{\mathrm{BH}}=4\times10^{-6}$) and $4.54\times$ enriched for the 111-gene Reactome set (8 of 16 genes; $p_{\mathrm{BH}}=1.6\times10^{-4}$), while a phase-blind real-valued baseline recovers none. We recover candidates through reliability weighting and phase-aware seeding rather than through magnetic propagation. The magnetic phase adds a different capability: it represents temporal order. On pituitary backbone, the magnetic embedding recovers measured peak-time order of connected pituitary genes with accuracy $0.971$, while $q{=}0$, i.e., no magnetic charge, is at chance.

Problem

• circadian regulators
• arrhythmic genes
• pituitary hormone
• chronopharmacology
• women's health

Innovation

• magnetic Laplacian
• circadian rhythm
• complex personalized PageRank
• phase-aware graph embedding
• reliability-weighted projection