continuous values. Both Boolean network and ODE-based models
can be deterministic (meaning that one can precisely predict the
temporal evolution of the variables from a set of initial conditions),
or stochastic (meaning that the prediction is only probabilistic).
There is no best modeling framework for all cases, and one needs to
determine what is appropriate and justified for the biological system
and process under study. Some general aspects that may be considered include:
1. What is the qualitative and quantitative information available?
Compared to a Boolean model, an ODE model typically has
more parameters and requires more quantitative data to constrain these model parameters. Therefore, for a large regulatory
network without much quantitative data such as the one studied by Steinway et al. [11], the Boolean framework is appropriate. It would be questionable whether an alternative
ODE-based model with dozens or even hundreds of free parameters can provide further additional information (but see
systematic statistical analyses of model ensembles discussed
below).
2. Is the framework sufficient to describe the system dynamics,
and does it provide new mechanistic insights that would be
unavailable or unclear without the modeling approach? Each
framework has its limitations. For example, a Boolean model
typically uses some universal parameters and only provides
qualitative or at most semiquantitative information. It can be
a good starting point to analyze how multiple regulatory factors interact to generate different EMT cell types as demonstrated by Steinway et al. [11]. The model has limited capacity
to describe how different time scales of the signal transduction
pathways involved in EMT contribute to quantitative detection
and encoding of the dose and duration information of the
stimulating signals. For the latter purpose, an ODE-based
model is a more appropriate choice, as demonstrated by
Zhang et al. [26] to show how pathway cross talk leads to a
temporal checkpoint mechanism for detecting TGF-β duration
information.
As a rule of thumb, one chooses a modeling framework that is
simple and sufficient to address the underlying problem. The widely
regarded criterion suggested by Einstein for evaluating physics
theories also applies here: “Everything should be made as simple
as possible, but not simpler.” It is possible that for a given problem,
initially a coarse-grained framework is appropriate, and as more and
more quantitative data becomes available, a different framework
becomes necessary to incorporate the new information.
Unfortunately, a commonly held misconception emphasizes that
it is always desirable to incorporate additional biological details
Mathematical Modelling of EMT
387
can be deterministic (meaning that one can precisely predict the
temporal evolution of the variables from a set of initial conditions),
or stochastic (meaning that the prediction is only probabilistic).
There is no best modeling framework for all cases, and one needs to
determine what is appropriate and justified for the biological system
and process under study. Some general aspects that may be considered include:
1. What is the qualitative and quantitative information available?
Compared to a Boolean model, an ODE model typically has
more parameters and requires more quantitative data to constrain these model parameters. Therefore, for a large regulatory
network without much quantitative data such as the one studied by Steinway et al. [11], the Boolean framework is appropriate. It would be questionable whether an alternative
ODE-based model with dozens or even hundreds of free parameters can provide further additional information (but see
systematic statistical analyses of model ensembles discussed
below).
2. Is the framework sufficient to describe the system dynamics,
and does it provide new mechanistic insights that would be
unavailable or unclear without the modeling approach? Each
framework has its limitations. For example, a Boolean model
typically uses some universal parameters and only provides
qualitative or at most semiquantitative information. It can be
a good starting point to analyze how multiple regulatory factors interact to generate different EMT cell types as demonstrated by Steinway et al. [11]. The model has limited capacity
to describe how different time scales of the signal transduction
pathways involved in EMT contribute to quantitative detection
and encoding of the dose and duration information of the
stimulating signals. For the latter purpose, an ODE-based
model is a more appropriate choice, as demonstrated by
Zhang et al. [26] to show how pathway cross talk leads to a
temporal checkpoint mechanism for detecting TGF-β duration
information.
As a rule of thumb, one chooses a modeling framework that is
simple and sufficient to address the underlying problem. The widely
regarded criterion suggested by Einstein for evaluating physics
theories also applies here: “Everything should be made as simple
as possible, but not simpler.” It is possible that for a given problem,
initially a coarse-grained framework is appropriate, and as more and
more quantitative data becomes available, a different framework
becomes necessary to incorporate the new information.
Unfortunately, a commonly held misconception emphasizes that
it is always desirable to incorporate additional biological details
Mathematical Modelling of EMT
387