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Methods Mol Biol. 2018;1702:95-123. doi: 10.1007/978-1-4939-7456-6_7.

Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Transition.

Author information

1
Department of Mathematics, University of Nice Sophia Antipolis, Parc Valrose, 06108, Nice Cedex 02, France. simeoni@unice.fr.
2
Department of Clinical and Molecular Medicine, Sapienza University of Rome, Viale Regina Elena 336, 00161, Rome, Italy.
3
Department of Surgery "Pietro Valdoni", Sapienza University of Rome, via A. Scarpa 14, 00161, Rome, Italy.
4
Department of Mathematics, Sapienza University of Rome, piazzale A. Moro 2, 00185, Rome, Italy.
5
Department of Experimental Medicine, Systems Biology Group Lab, Sapienza University of Rome, Rome, Italy. mariano.bizzarri@uniroma1.it.

Abstract

In this report, we aim at presenting a viable strategy for the study of Epithelial-Mesenchymal Transition (EMT) and its opposite Mesenchymal-Epithelial Transition (MET) by means of a Systems Biology approach combined with a suitable Mathematical Modeling analysis. Precisely, it is shown how the presence of a metastable state, that is identified at a mesoscopic level of description, is crucial for making possible the appearance of a phase transition mechanism in the framework of fast-slow dynamics for Ordinary Differential Equations (ODEs).

KEYWORDS:

Epithelial-mesenchymal transition; Mathematical modeling; Mesoscopic description; Metastable states; Multiscale differential equations; Slow–fast dynamics; Stability analysis; Systems biology

PMID:
29119504
DOI:
10.1007/978-1-4939-7456-6_7
[Indexed for MEDLINE]

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