Chapter 28
Mathematical Modeling of Plasticity and Heterogeneity
in EMT
Shubham Tripathi, Jianhua Xing, Herbert Levine, and Mohit Kumar Jolly
Abstract
The epithelial-mesenchymal transition (EMT) and the corresponding reverse process, mesenchymalepithelial transition (MET), are dynamic and reversible cellular programs orchestrated by many changes
at both biochemical and morphological levels. A recent surge in identifying the molecular mechanisms
underlying EMT/MET has led to the development of various mathematical models that have contributed
to our improved understanding of dynamics at single-cell and population levels: (a) multi-stability—how
many phenotypes can cells attain during an EMT/MET?, (b) reversibility/irreversibility—what time
and/or concentration of an EMT inducer marks the “tipping point” when cells induced to undergo
EMT cannot revert?, (c) symmetry in EMT/MET—do cells take the same path when reverting as they
took during the induction of EMT?, and (d) non-cell autonomous mechanisms—how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT? These dynamical traits may facilitate a
heterogenous response within a cell population undergoing EMT/MET. Here, we present a few examples
of designing different mathematical models that can contribute to decoding EMT/MET dynamics.
Key words Mathematical modeling, Epithelial-mesenchymal plasticity, Nongenetic heterogeneity,
Multi-stability, Epithelial-mesenchymal heterogeneity
1 Introduction
The epithelial-mesenchymal transition (EMT) is a cellular process
involving changes in multiple aspects of cellular behavior, including
cell–cell adhesion, cell polarity, cell migration and invasion, and cell
shape [1]. EMT and the corresponding reverse process, mesenchymal-epithelial transition (MET), are regulated at multiple levels.
These include transcriptional, posttranscriptional, translational,
and epigenetic [2] controls, along with non-cell autonomous
mechanisms acting through matrix density [3] or cell–cell communication [4–7]. Largely thought of in the past as a binary process,
EMT is now known to involve multiple stable intermediates
referred to as hybrid epithelial/mesenchymal (hybrid E/M) phenotypes [8]. This updated view of the process has, in part, been
Kyra Campbell and Eric Theveneau (eds.), The Epithelial-to Mesenchymal Transition: Methods and Protocols,
Methods in Molecular Biology, vol. 2179, https://doi.org/10.1007/978-1-0716-0779-4_28,
© Springer Science+Business Media, LLC, part of Springer Nature 2021
385
Mathematical Modeling of Plasticity and Heterogeneity
in EMT
Shubham Tripathi, Jianhua Xing, Herbert Levine, and Mohit Kumar Jolly
Abstract
The epithelial-mesenchymal transition (EMT) and the corresponding reverse process, mesenchymalepithelial transition (MET), are dynamic and reversible cellular programs orchestrated by many changes
at both biochemical and morphological levels. A recent surge in identifying the molecular mechanisms
underlying EMT/MET has led to the development of various mathematical models that have contributed
to our improved understanding of dynamics at single-cell and population levels: (a) multi-stability—how
many phenotypes can cells attain during an EMT/MET?, (b) reversibility/irreversibility—what time
and/or concentration of an EMT inducer marks the “tipping point” when cells induced to undergo
EMT cannot revert?, (c) symmetry in EMT/MET—do cells take the same path when reverting as they
took during the induction of EMT?, and (d) non-cell autonomous mechanisms—how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT? These dynamical traits may facilitate a
heterogenous response within a cell population undergoing EMT/MET. Here, we present a few examples
of designing different mathematical models that can contribute to decoding EMT/MET dynamics.
Key words Mathematical modeling, Epithelial-mesenchymal plasticity, Nongenetic heterogeneity,
Multi-stability, Epithelial-mesenchymal heterogeneity
1 Introduction
The epithelial-mesenchymal transition (EMT) is a cellular process
involving changes in multiple aspects of cellular behavior, including
cell–cell adhesion, cell polarity, cell migration and invasion, and cell
shape [1]. EMT and the corresponding reverse process, mesenchymal-epithelial transition (MET), are regulated at multiple levels.
These include transcriptional, posttranscriptional, translational,
and epigenetic [2] controls, along with non-cell autonomous
mechanisms acting through matrix density [3] or cell–cell communication [4–7]. Largely thought of in the past as a binary process,
EMT is now known to involve multiple stable intermediates
referred to as hybrid epithelial/mesenchymal (hybrid E/M) phenotypes [8]. This updated view of the process has, in part, been
Kyra Campbell and Eric Theveneau (eds.), The Epithelial-to Mesenchymal Transition: Methods and Protocols,
Methods in Molecular Biology, vol. 2179, https://doi.org/10.1007/978-1-0716-0779-4_28,
© Springer Science+Business Media, LLC, part of Springer Nature 2021
385