propagate the ODEs for a sufficiently long time under the
condition of no TGF-β to reach a steady state, and use the
steady state values as the initial conditions at time 0.
5. Perform standard analyses such as bifurcation analysis, phase diagram, temporal trajectories, and robustness/sensitivity analysis.
One may either write custom computer code (e.g., in Matlab,
Python, etc.), or use available computer packages, e.g., XPP
(http://www.math.pitt.edu/~bard/xpp/xpp.html),
Oscill8
(http://oscill8.sourceforge.net/), and BioNetGen [32].
2.4 Explain Available
Experiments and Make
Testable Predictions
A unique advantage of computational modeling over experimental
studies is that, generally, it is much easier to perform a series of in
silico studies than their experimental counterparts, as the latter may
be either time and resource consuming, or may even not be feasible. Generally speaking, mathematical/computational modeling
can:
1. Provide mechanistic insights not evident from the data, and
sometimes resolve conflicting experimental results or distinguish competing mechanisms. For a given system, data are
typically collected from different sources and using different
techniques. Each experimental technique or approach can only
reveal partial information about the system, and modeling
integrates the discrete information. By placing all the experimental results on a common ground, a modeling study allows
one to check whether the data are consistent mutually, and with
the conceived mechanisms.
2. Make predictions leading to new experimental measurements
that might not have been considered otherwise. For example,
the modeling study by Tian et al. [13] inspired a subsequent
measurement of single cell SNAIL1 expression levels using flow
cytometry [28].
3. Identify essential ingredients or missing links necessary to
explain the observations. For a given system, there may be
too much information, and some of it may not be or may
only be marginally relevant to addressing a specific question.
By adding or removing individual components and examining
the effect on model behavior, one can identify the essential
ingredients of a model. In other cases, the available information
may be insufficient. In such a scenario, following a similar
procedure of systemically adding individual components, one
can predict the missing component(s) that are necessary to
explain the experimental results. The missing component may
then be identified in subsequent experimental studies. For
example, the study by Lu et al. [9] suggested the existence of
positive feedback in the regulation of ZEB in EMT regulation
(dashed line in Fig. 1).
390
Shubham Tripathi et al.
condition of no TGF-β to reach a steady state, and use the
steady state values as the initial conditions at time 0.
5. Perform standard analyses such as bifurcation analysis, phase diagram, temporal trajectories, and robustness/sensitivity analysis.
One may either write custom computer code (e.g., in Matlab,
Python, etc.), or use available computer packages, e.g., XPP
(http://www.math.pitt.edu/~bard/xpp/xpp.html),
Oscill8
(http://oscill8.sourceforge.net/), and BioNetGen [32].
2.4 Explain Available
Experiments and Make
Testable Predictions
A unique advantage of computational modeling over experimental
studies is that, generally, it is much easier to perform a series of in
silico studies than their experimental counterparts, as the latter may
be either time and resource consuming, or may even not be feasible. Generally speaking, mathematical/computational modeling
can:
1. Provide mechanistic insights not evident from the data, and
sometimes resolve conflicting experimental results or distinguish competing mechanisms. For a given system, data are
typically collected from different sources and using different
techniques. Each experimental technique or approach can only
reveal partial information about the system, and modeling
integrates the discrete information. By placing all the experimental results on a common ground, a modeling study allows
one to check whether the data are consistent mutually, and with
the conceived mechanisms.
2. Make predictions leading to new experimental measurements
that might not have been considered otherwise. For example,
the modeling study by Tian et al. [13] inspired a subsequent
measurement of single cell SNAIL1 expression levels using flow
cytometry [28].
3. Identify essential ingredients or missing links necessary to
explain the observations. For a given system, there may be
too much information, and some of it may not be or may
only be marginally relevant to addressing a specific question.
By adding or removing individual components and examining
the effect on model behavior, one can identify the essential
ingredients of a model. In other cases, the available information
may be insufficient. In such a scenario, following a similar
procedure of systemically adding individual components, one
can predict the missing component(s) that are necessary to
explain the experimental results. The missing component may
then be identified in subsequent experimental studies. For
example, the study by Lu et al. [9] suggested the existence of
positive feedback in the regulation of ZEB in EMT regulation
(dashed line in Fig. 1).
390
Shubham Tripathi et al.