Biomedical Engineering Reference
In-Depth Information
Chapter 4
4.1 Advantages and Limitations of the Basic CPM
Basic CPM approaches work surprisingly well in modeling a wide range of bi-
ological processes. In particular, they can provide important new insights into
the principles of multicellular (tissutal) patterning in a number of phenom-
ena, as they are able to analyze their driving mechanisms; see, for example,
[183, 252, 314]. Moreover, CPM applications are a way of comparing the out-
comes of different and equally plausible scenarios, providing a predictive value
as well. It is possible in fact to analyze the system's response to a range of
experimental perturbations, as shown in [246, 262, 351, 365].
The first advantage of the CPM compared to alternative cell-based mod-
eling approaches that represent biological individuals as point particles or
fixed-sized spheres or ellipsoids (for examples, see [11]) is that it differen-
tiates between bound and unbound regions of their membranes. Moreover,
morphologies and changes of shape of discrete elements are easily and real-
istically implemented. The key benefits of the CPM energetic formalism are
its simplicity and extensibility. Almost any biological mechanism can, in fact,
be included in the model, simply by adding an appropriate generalized po-
tential term in the Hamiltonian H, as suggested in the main reviews of the
method [20, 165]. It is therefore possible to easily comprehend the importance
of each mechanism involved in the simulated phenomenon by only altering the
relative Potts parameter, so that the other terms in the Hamiltonian scale ac-
cordingly. In particular, by equating all the other terms to zero, it is possible
to understand whether such a mechanism is individually capable of producing
the process of interest, or whether it requires cooperative processes.
However, most CPM approaches suffer from some limitations. First, the
reproduction of biological entities is improbable, since they are usually repre-
sented by single discrete objects, which are isotropic and formed by equivalent
and undifferentiated sites. This representation provides a useful level of ab-
straction, but also hides relevant inhomogeneous properties that characterize
all biological individuals and become essential in several natural phenomena.
For example, in the case of simulated cells reproduced by a single functional
unit, on one hand the cytoskeleton and the plasmamembrane do not have
an independent existence, while on the other, the nuclear envelope is not
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