Signalling Entropy Across Measurement Scales: A Compositional Dilution Lemma and Cross-Modality Invariance for Information-Theoretic Analysis of Cancer Transcriptomes
Entropy, vol.28, no.7, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 28 Issue: 7
- Publication Date: 2026
- Doi Number: 10.3390/e28070781
- Journal Name: Entropy
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: cancer transcriptomics, cross-modality validation, information theory, mixed-effects regression, protein–protein interaction networks, signalling entropy, single-cell RNA sequencing, total correlation
- Dokuz Eylül University Affiliated: No
Abstract
We develop a unified information-theoretic framework for the analysis of cancer transcriptomic dysregulation across measurement modalities. Three functionals capture distributional, network-aware, and joint-dependence aspects of expression: the Shannon entropy with a Miller–Madow correction, the signalling entropy rate over the protein interaction graph, and the Gaussian total correlation on a principal-component projection. A closed-form algebraic expression yields a linear-time algorithm for the signalling entropy rate. A Compositional Dilution Lemma decomposes bulk entropy into intrinsic and compositional contributions, and a Cross-Modality Invariance Proposition provides an empirically falsifiable null hypothesis. Validation uses 700,202 single cells and 3942 bulk samples across five cancer types. Pan-cancer tumour elevation is significant at (Formula presented.), and cross-modality testing on 4230 observations does not reject the interaction null at (Formula presented.). The invariance conclusion is corroborated by cancer-level paired sign-flip permutation, cancer-block bootstrap, and empirical distribution function tests, and the prognostic Cox regressions satisfy proportional-hazards diagnostics with cross-validation concordance of (Formula presented.). Immune deconvolution against the LM22 signature validates cell-type-specific predictions, partitioning cancers into myeloid-driven and lymphoid-driven classes. Breast cancer Cox regressions instantiate the predicted orthogonality of distributional and network-aware functionals after immune adjustment.