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Description
Epigenetic transitions in the tumor microenvironment exhibit history-dependent memory effects and abrupt phenotypic shifts that classical smooth dynamical systems fail to capture from a physical perspective \cite{Esteller2002}. We present a novel mathematical framework grounded in the theory of rate-independent systems to describe the evolution of epigenetic marks—specifically DNA methylation—under hypoxic stress.
Using the Mielke-Theil energetic formulation \cite{Mielke2015}, we model the epigenetic state as an internal variable governed by a double-well energy function coupled with Michaelis-Menten hypoxia kinetics and a 1-homogeneous dissipation potential, which axiomatically enforces the energy-dissipation balance and the Clausius-Duhem inequality, driving biological irreversibility.
By deriving the Kuhn-Tucker differential inclusions governing the system evolution, we demonstrate that the model captures key experimental phenomena: epigenetic catastrophes such as Epithelial-Mesenchymal Transitions \cite{Yoo2011}, reversible-irreversible damage under hypoxia and long-term adaptation \cite{Thienpont2016} as well as the imprint of epigenetic scars \cite{Kwoun2025}. In addition, it allows for quantitative predictions of cellular state stability based on the thermodynamic potentials.
This work provides a rigorous physical basis for computational epigenetics and lays the groundwork for a systematic analysis of the energetic barriers and irreversibility of tumor progression.
Bibliography
@book{Mielke2015, address={New York, NY}, series={Applied Mathematical Sciences}, title={Rate-Independent Systems: Theory and Application}, volume={193}, rights={https://www.springernature.com/gp/researchers/text-and-data-mining}, ISBN={9781493927050}, url={https://link.springer.com/10.1007/978-1-4939-2706-7}, DOI={10.1007/978-1-4939-2706-7}, publisher={Springer New York}, author={Mielke, Alexander and Roubíček, Tomáš}, year={2015}, collection={Applied Mathematical Sciences}, language={en} }
@article{Thienpont2016, title={Tumour hypoxia causes DNA hypermethylation by reducing TET activity}, volume={537}, ISSN={0028-0836, 1476-4687}, url={https://www.nature.com/articles/nature19081}, DOI={10.1038/nature19081}, number={7618}, journal={Nature}, author={Thienpont, Bernard and Steinbacher, Jessica and Zhao, Hui and D’Anna, Flora and Kuchnio, Anna and Ploumakis, Athanasios and Ghesquière, Bart and Van Dyck, Laurien and Boeckx, Bram and Schoonjans, Luc and Hermans, Els and Amant, Frederic and Kristensen, Vessela N. and Koh, Kian Peng and Mazzone, Massimiliano and Coleman, Mathew L. and Carell, Thomas and Carmeliet, Peter and Lambrechts, Diether}, year={2016}, month=sept, pages={63–68}, language={en} }
@article{Yoo2011, title={HIF-1α Mediates Tumor Hypoxia to Confer a Perpetual Mesenchymal Phenotype for Malignant ProgressionA presentation from the Keystone Symposium on Epithelial Plasticity and Epithelial-to-Mesenchymal Transition, Vancouver, British Columbia, Canada, 21 to 26 January 2011.}, volume={4}, ISSN={1945-0877, 1937-9145}, url={https://www.science.org/doi/10.1126/scisignal.2002072}, DOI={10.1126/scisignal.2002072}, abstractNote={Hypoxia-induced genetic alterations induce epithelial-mesenchymal transition and tumor progression. , Although tumor progression involves genetic and epigenetic alterations to normal cellular biology, the underlying mechanisms of these changes remain obscure. Numerous studies have shown that hypoxia-inducible factor 1α (HIF-1α) is overexpressed in many human cancers and up-regulates a host of hypoxia-responsive genes for cancer growth and survival. We recently identified an alternative mechanism of HIF-1α function that induces genetic alterations by suppressing DNA repair. Here, we show that long-term hypoxia, which mimics the tumor microenvironment, drives a perpetual epithelial-mesenchymal transition (EMT) through up-regulation of the zinc finger E-box binding homeobox protein ZEB2, whereas short-term hypoxia induces a reversible EMT that requires the transcription factor Twist1. Moreover, we show that the perpetual EMT driven by chronic hypoxia depends on HIF-1α induction of genetic alterations rather than its canonical transcriptional activator function. These mesenchymal tumor cells not only acquire tumorigenicity but also display characteristics of advanced cancers, including necrosis, aggressive invasion, and metastasis. Hence, these results reveal a mechanism by which HIF-1α promotes a perpetual mesenchymal phenotype, thereby advancing tumor progression.}, number={178}, journal={Science Signaling}, author={Yoo, Young-Gun and Christensen, Jared and Gu, Jie and Huang, L. Eric}, year={2011}, month=june, language={en} }
@article{Kwoun2025, title={Epigenetic memories induced by hypoxia in AKI-to-CKD transition}, volume={29}, ISSN={1342-1751, 1437-7799}, url={https://link.springer.com/10.1007/s10157-025-02745-1}, DOI={10.1007/s10157-025-02745-1}, abstractNote={Abstract Chronic kidney disease (CKD) is a global health burden associated with increasing mortality rates. Aging populations and declining fertility rates exacerbate this issue, particularly in countries such as Japan. Acute kidney injury (AKI) was previously considered temporary and reversible condition. However, in recent years, multiple studies on kidney diseases have shown that AKI survivors are at an increased risk of developing CKD. During the AKI-to-CKD transition, a subset of AKI-induced epigenetic alterations persists in cells, potentially driving the progression of tubulointerstitial fibrosis. Therefore, targeting epigenetic mechanisms may represent a promising therapeutic approach for preventing AKI-to-CKD transition. Among the epigenetic mechnisms involved, “hypoxic memory” plays a crucial role in this transition by inducing persistent epigenetic changes. Hypoxic memory induces DNA methylation, histone modification, changes in chromatin conformation, and long non-codingRNA (lncRNA) expression. Herein, we review the latest evidence on epigenetic memory in the AKI-to-CKD transition, identifying that the detailed mechanisms of epigenetic memory and temporal specificity are crucial for developing effective treatments.}, number={12}, journal={Clinical and Experimental Nephrology}, author={Kwoun, Giyoung and Nangaku, Masaomi and Mimura, Imari}, year={2025}, month=dec, pages={1712–1723}, language={en} }
@article{Esteller2002, title={Cancer as an epigenetic disease: DNA methylation and chromatin alterations in human tumours}, volume={196}, ISSN={0022-3417, 1096-9896}, url={https://pathsocjournals.onlinelibrary.wiley.com/doi/10.1002/path.1024}, DOI={10.1002/path.1024}, abstractNote={Abstract Cancer is an epigenetic disease at the same level that it can be considered a genetic disease. In fact, epigenetic changes, particularly DNA methylation, are susceptible to change and are excellent candidates to explain how certain environmental factors may increase the risk of cancer. The delicate organization of methylation and chromatin states that regulates the normal cellular homeostasis of gene expression patterns becomes unrecognizable in the cancer cell. The genome of the transformed cell undergoes simultaneously a global genomic hypomethylation and a dense hypermethylation of the CpG islands associated with gene regulatory regions. These dramatic changes may lead to chromosomal instability, activation of endogenous parasitic sequences, loss of imprinting, illegitimate expression, aneuploidy, and mutations, and may contribute to the transcriptional silencing of tumour suppressor genes. The hypermethylation‐associated inactivation affects virtually all of the pathways in the cellular network, such as DNA repair ( hMLH1 , BRCA1 , MGMT , …︁), the cell cycle ( p16 INK4a , p14 ARF , p15 INK4b , …︁), and apoptosis ( DAPK , APAF‐1 , …︁). The aberrant CpG island methylation can also be used as a biomarker of malignant cells and as a predictor of their behaviour, and may constitute a good target for future therapies. Copyright © 2002 John Wiley & Sons, Ltd.}, number={1}, journal={The Journal of Pathology}, author={Esteller, Manel and Herman, James G.}, year={2002}, month=jan, pages={1–7}, language={en} }
