Systems Biology (Methods in Molecular Biology)

Chapter 7

Systems Biology Approach and Mathematical Modeling

for Analyzing Phase-Space Switch During

Epithelial-Mesenchymal Transition

Chiara Simeoni, Simona Dinicola, Alessandra Cucina,

Corrado Mascia, and Mariano Bizzarri

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 Differen-
tial Equations (ODEs).

Key wordsEpithelial-mesenchymal transition, Metastable states, Systems biology, Mesoscopic

description, Mathematical modeling, Multiscale differential equations, Slow–fast dynamics, Stability

analysis

1 Introduction

1.1 Complex
Systems and Phase
Transition

Cell transition from a phenotype into another constitutes a critical

event during development, differentiation, and eventually the onset

of degenerative diseases, like cancer. Phenotypic differentiation

involves several changes at molecular, physiological, and morpho-

logical level. Yet, rather than a progressive process, such transfor-

mation behaves like afirst order phase transition, also involving the

overall system in a coherent and global (phase) change.

A phase of a thermodynamic system and the states of matter

typically have uniform physical properties. During a phase transi-

tion, certain properties of the given medium change, as a result of

the variation of some external conditions (for example, tempera-

ture, pressure, or others). In Physics, first order phase transitions

are characterized by a discontinuity in one or more state variables,

and those we are particularly interested in also imply a change in

Mariano Bizzarri (ed.),Systems Biology, Methods in Molecular Biology, vol. 1702,
https://doi.org/10.1007/978-1-4939-7456-6_7,©Springer Science+Business Media LLC 2018

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