Biomedical Engineering Reference
In-Depth Information
defined. Moreover, while certain model quantities, such as energy or tempera-
ture, have unambiguous meanings, most Potts parameters do not have a direct
correspondence with biophysical measurable quantities, as also commented in
[262]. This is a crucial drawback for a good quantitative comparison between
in silico and in vitro results, and thus for a predictive value of CPM appli-
cations. Additionally, these constraint weights, which modulate the dynamic
behavior of the simulated individuals, are generally static over the whole simu-
lations, or have unrealistic variations. This situation in not plausible since real
biological elements continuously change their biophysical and biomechanical
properties as a consequence of continuous internal and external stimuli.
These considerations lead to one of the main criticisms of CPM approaches:
most simulated phenomena emerge from quite strong a priori assumptions
that are derived from experimental observations (see again [262]). In partic-
ular, the behavior of the simulated individuals is constrained by qualitative
rules (such as the energetic constraints regulated by fixed parameters) that
do not easily adapt during the evolution of the system. Furthermore, all the
objects belonging to a given type () are usually constrained to feature the
same biophysical properties, such as the target states of most attributes or
the adhesive strength, despite their individuality.
Finally, by treating simulated individuals with only a cell-level phenomeno-
logical approach, most CPM applications do not consider (or, in some cases,
only approximately describe) the molecular scale of the biological organisms,
as carefully explained in [165]. In fact, basic CPMs neglect the continuous flow
of information between the microscopic and the mesoscopic scales, which, as
seen in the introduction, is fundamental for developmental biology.
In the next sections, we propose some extensions for CPM applications in
order to overcome the above-cited limitations and to improve the biological
realism of the method. These developments are then applied in the following
chapters to several biological problems, which range from unicellular processes
to multicellular phenomena.
4.2 Compartmentalization Approach
As seen, most existing CPMs generally treat biological individuals as undif-
ferentiated discrete objects, i.e., single functional units
identified by a
common spin . Dierent spin states therefore represent dierent simulated
entities. However, biological elements are composed of different parts (such as
the nucleus or the cytosol in an eukaryotic cell, or the microcompartments in
bacteria), which play a fundamental and unique role in the development of
the organism. Moreover, each of these parts is characterized by particular and
well-defined biophysical, biochemical, and biomechanical properties.
The simplest and most realistic way of reproducing such complex mor-
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