driven by predictions made by various mathematical models for the
regulatory networks involved in EMT [4, 5, 9–14]. These mathematical models have focused on characterizing the properties of
EMT and have predicted that cells can stably maintain one or more
hybrid E/M phenotypes [15]. Moreover, these models have also
driven insights into how cells may spontaneously switch between
various phenotypes due to stochasticity, and thereby determine
how cellular plasticity leads to phenotypic heterogeneity associated
with EMT as observed experimentally [16, 17]. These models have
also offered mechanistic insights into experimental observations
showing that EMT and MET are not necessarily symmetric processes [12, 18], i.e., cells may take different paths during EMT and
MET in the multi-dimensional landscape of epithelialmesenchymal plasticity. Finally, these models have helped us gain
insights into the interconnection between EMT and other cellular
traits such as stemness; for instance, the prediction that a hybrid
E/M phenotype is more stem-like and metastatically aggressive
than cells exhibiting extremely epithelial or extremely mesenchymal
phenotypes [19] was recently confirmed both in vitro and in vivo
[20–22]. Here, we introduce a generic framework for developing
mathematical models of EMT regulation and share examples of
how these models can be used as tools to generate predictions
that will guide the next set of experiments.
2 Mathematical Modeling of EMT
The choice of a systems biology approach to study a biological
process is highly context-dependent. We here describe a generic
procedure for choosing an appropriate approach and detail how this
procedure was applied to modeling EMT.
2.1 Identify a
Problem that
Mathematical
Modeling Can Help
Address and Form a
Team of Experimental
and Modeling
Researchers
This is a key and probably the most challenging step in modeling
studies. There are questions that modeling studies can address and
others that they cannot address. It is typically constructive to form a
team of experimental and modeling researchers. The team members hold thorough literature review and extensive, in-depth discussions to review existing knowledge and identify open questions
regarding the system. One may find it pedagogically illuminating to
read accounts of how some successful collaborations were established [23, 24].
2.2 Choose an
Appropriate Modeling
Framework
Several modeling frameworks have been used to analyze EMT
regulatory networks. A Boolean network has dynamics that are
discrete in time and involve discrete variable values. The variable
values are updated based on a set of Boolean functions that reflect
the regulatory relations [25]. Conversely, an ordinary differential
equation (ODE)-based model treats time and variables as taking
386
Shubham Tripathi et al.
regulatory networks involved in EMT [4, 5, 9–14]. These mathematical models have focused on characterizing the properties of
EMT and have predicted that cells can stably maintain one or more
hybrid E/M phenotypes [15]. Moreover, these models have also
driven insights into how cells may spontaneously switch between
various phenotypes due to stochasticity, and thereby determine
how cellular plasticity leads to phenotypic heterogeneity associated
with EMT as observed experimentally [16, 17]. These models have
also offered mechanistic insights into experimental observations
showing that EMT and MET are not necessarily symmetric processes [12, 18], i.e., cells may take different paths during EMT and
MET in the multi-dimensional landscape of epithelialmesenchymal plasticity. Finally, these models have helped us gain
insights into the interconnection between EMT and other cellular
traits such as stemness; for instance, the prediction that a hybrid
E/M phenotype is more stem-like and metastatically aggressive
than cells exhibiting extremely epithelial or extremely mesenchymal
phenotypes [19] was recently confirmed both in vitro and in vivo
[20–22]. Here, we introduce a generic framework for developing
mathematical models of EMT regulation and share examples of
how these models can be used as tools to generate predictions
that will guide the next set of experiments.
2 Mathematical Modeling of EMT
The choice of a systems biology approach to study a biological
process is highly context-dependent. We here describe a generic
procedure for choosing an appropriate approach and detail how this
procedure was applied to modeling EMT.
2.1 Identify a
Problem that
Mathematical
Modeling Can Help
Address and Form a
Team of Experimental
and Modeling
Researchers
This is a key and probably the most challenging step in modeling
studies. There are questions that modeling studies can address and
others that they cannot address. It is typically constructive to form a
team of experimental and modeling researchers. The team members hold thorough literature review and extensive, in-depth discussions to review existing knowledge and identify open questions
regarding the system. One may find it pedagogically illuminating to
read accounts of how some successful collaborations were established [23, 24].
2.2 Choose an
Appropriate Modeling
Framework
Several modeling frameworks have been used to analyze EMT
regulatory networks. A Boolean network has dynamics that are
discrete in time and involve discrete variable values. The variable
values are updated based on a set of Boolean functions that reflect
the regulatory relations [25]. Conversely, an ordinary differential
equation (ODE)-based model treats time and variables as taking
386
Shubham Tripathi et al.