Biomedical Engineering Reference
In-Depth Information
incubation of a cell population toward confluence and the subsequent creation
of an artificial scratch with a sharp object (for example, a pipette tip). The
removal of cells from the wounded area acts as a stimulus for the remaining
mass to invade and fill the open space, with a characteristic traveling-wave-like
behavior. The rate of advancement of the wound edge, i.e., the quantification
of the area recolonized, gives a measure of the migratory capacity of the pop-
ulation of interest. In particular, this technique is widely used to compare
the motility properties of a cell line either in \resting conditions" (i.e., in the
absence of external stimuli) or in response to specific chemical stimulations or
modifications of expressions of molecules putatively involved in the migratory
processes.
The wound healing experiment has been reproduced by several mathemati-
cal models, most of which are based on the Fisher equation. For instance, these
methods have described the cell population as a density, while its motility has
been prescribed by a diffusive flux, where the diffusivity has been considered
either a constant [248, 249, 344, 387] or a function of an external chemical
factor [98]. These authors, numerically calculating the traveling-wave solution
of the Fisher equation, have therefore provided a simple relation between the
speed of the moving front of the mass and both the diffusion constant and the
mitotic time of cells. However, Fisher-like models have not included the effects
of mutual interactions between cells and between cells and the extracellular
environment and they cannot characterize and differentiate the dynamics of
single individuals (i.e., cells at the front of the mass behave obviously differ-
ently from those at the center of the mass), assuming that all cells within the
culture have the same migratory capacity.
A discrete approach has the potential to overcome these issues by retain-
ing the identity of each cell. Indeed, we here simulate the healing process of
a culture of ARO cells in response to the hepatocyte growth factor (HGF).
The HGF is a potent growth factor that elicits multiple cellular responses,
including scattering, motility, and morphogenesis [45, 92, 389, 394]. Such a
combination of events, also known as invasive growth, is fundamental during
the embryonic development of most epithelial tissues. When inappropriately
activated, this genetic program confers an invasive ability on normal and neo-
plastic epithelial cells [101, 380, 407]. The high anity receptor for HGF is the
tyrosine kinase Met [233] . As explained in Section 2.1, Met activation causes
both the disruption of intercellular adhesion complexes (cadherin{cadherin
interactions) and the enhancement in cell motility. In particular, the latter
is driven by a number of intracellular signaling pathways, which could not
be reproduced in the standard model presented in Chapter 2, but which can
now be described in full detail. Among others, we focus on phosphatidylinosi-
tol 3-kinases (PI3K) and mitogen-activated protein kinase (MAPK) cascades
that have been intensively studied, and well characterized [91, 423]. Indeed,
the activity of the multi-docking sites of Met triggers the biosynthesis in the
cell sub-plasmamembrane regions of PI3K (via the production of Gab1) and
of MAPK (via the activity of adaptor proteins Grb2 and Ras). PI3K and
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