1. M.A. Al-Radhawi and E.D. Sontag. Analysis of a reduced model of epithelial-mesenchymal fate determination in cancer metastasis as a singularly-perturbed monotone system. In C.A. Beattie, P. Benner, M. Embree, S. Gugercin, and S. Lefteriu, editors, Realization and model reduction of dynamical systems. Springer Nature, 2022. Note: (Previous version: 2020 preprint in arXiv:1910.11311.). [PDF] Keyword(s): epithelial-mesenchymal transition, miRNA, singular perturbations, monotone systems, oncology, cancer, metastasis, reaction networks, reaction networks, systems biology. Abstract:

   Metastasis can occur after malignant cells transition from the epithelial phenotype to the mesenchymal phenotype. This transformation allows cells to migrate via the circulatory system and subsequently settle in distant organs after undergoing the reverse transition. The core gene regulatory network controlling these transitions consists of a system made up of coupled SNAIL/miRNA-34 and ZEB1/miRNA-200 subsystems. In this work, we formulate a mathematical model and analyze its long-term behavior. We start by developing a detailed reaction network with 24 state variables. Assuming fast promoter and mRNA kinetics, we then show how to reduce our model to a monotone four-dimensional system. For the reduced system, monotone dynamical systems theory can be used to prove generic convergence to the set of equilibria for all bounded trajectories. The theory does not apply to the full model, which is not monotone, but we briefly discuss results for singularly-perturbed monotone systems that provide a tool to extend convergence results from reduced to full systems, under appropriate time separation assumptions.




2. M.A. Al-Radhawi, S. Tripathi, Y. Zhang, E.D. Sontag, and H. Levine. Epigenetic factor competition reshapes the EMT landscape. Proc Natl Acad Sci USA, 119:e2210844119, 2022. [WWW] [PDF] Keyword(s): gene networks, Epithelial-Mesenchymal Transition, EMT, epigenetics, systems biology, cancer. Abstract:

   The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene regulatory elements. These elements include chromatin remodelers, histone modifiers, transcription factors, and regulatory RNAs. Mathematical models known as Gene Regulatory Networks (GRNs) are an increasingly important tool to unravel the workings of such complex networks. In such models, epigenetic factors are usually proposed to act on the chromatin regions directly involved in the expression of relevant genes. However, it has been well-established that these factors operate globally and compete with each other for targets genome-wide. Therefore, a perturbation of the activity of a regulator can redistribute epigenetic marks across the genome and modulate the levels of competing regulators. In this paper, we propose a conceptual and mathematical modeling framework that incorporates both local and global competition effects between antagonistic epigenetic regulators in addition to local transcription factors, and show the counter-intuitive consequences of such interactions. We apply our approach to recent experimental findings on the Epithelial-Mesenchymal Transition (EMT). We show that it can explain the puzzling experimental data as well provide new verifiable predictions.

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