Extended Cellular Potts Model - Cellular Potts Models: Multiscale Extensions and Biological Applications - page 60

it is always possible to set a suitable model whose outcome is is ;l itself. For
the sake of simplicity, it is not restrictive to combine groups of reactions in
(4.11) whose results have the same effect on the final result of the network.
Biochemical kinetics can be accurately described by reaction-diffusion (RD)
systems, which usually specialize in several coupled differential equations. As
an example of the potentials of the proposed model development, the Boltz-
mann temperature T in Equation (1.2) is no longer a biologically meaningless
agitation rate but becomes a variable property of each moving cell, assuming a
well-defined value of cell intrinsic motility, which can be realistically mediated
by a wide range of intracellular substances (i.e., calcium ions, fatty acids, . . . ).
For instance, in the limit of very low levels of such chemicals, cells actually
freeze, a behavior that can now be correctly modeled by a Potts parameter
T 0.
Microscopic models of intracellular dynamics can be used together with the
compartmentalized approach described in the previous section (if repre-
sents a subregion of compartmentalized individual , the internal state vector
is is ; ), to further increase the realism of the model. In fact, if represents
a cell subunit, the biochemical processes defined in Equation (4.11) are accu-
rately localized within a well-defined subcellular compartment, as occurs in
reality. Such an integration between the two proposed extensions of the CPM
therefore allows one to handle several biological mechanisms, that are dicult
to reproduce with the basic CPM. For example, the explicit representation of
the cell plasmamembrane permits one to straightforwardly model a wide range
of surface-receptor-activated intracellular pathways, as well as specific protein
cascades that mediate the activity of the cell adhesion molecules. Moreover,
the geometrical properties of the cell cytosolic compartment, such as its elas-
ticity, can now evolve according to a model of the active reorganization of the
actin filaments, which is powered, for example, by ATP hydrolysis.
A more realistic representation of the mitotic process is also possible. In
most existing CPMs, the cell cycle is not modeled explicitly, since cells usually
undergo duplication when they reach a fixed volume [25, 334, 365]. With the
presented CPM improvements, it is instead possible to incorporate appropriate
intracellular signaling cascades regulating cell-cycle-dependent events.
The proposed method to interface the basic mesoscopic CPM with models
of microscopic dynamics can be considered a general guide to reproduce com-
plex interactions between the different levels of organization that are typical
of biological phenomena. In fact, it can be applied to a number of situations,
given the knowledge of
The pathways of interest.
The specific functional laws that describe their influence on the biophys-
ical properties of individuals, i.e., the functions f and g.
Indeed, all these components are integrated and interfaced together, constitut-
ing a hybrid-nested simulation environment characterized by a constant flux