Biomedical Engineering Reference
In-Depth Information
FIGURE 2.11: Hepatocyte growth factor-mediated increase of motility as
shown by manual time lapse analysis. Single cell motion tracks obtained from
24-hour lapse simulations of MLP-29 cells culture in the absence (N.S.) and
in the presence of HGF. For reference, the oval positioned at the center of the
group of tracks represents the size of a single cell.
involution and the island becomes compact again, a biological behavior that it
is possible to see also experimentally (see [271]). This second phase is modeled
by imposing c = 0 in Equation (2.5), while the other parameters are kept
unchanged.
The evolution of the simulated colony agrees well with the experimental ev-
idence from a quantitative point of view, as shown by Figure 2.10, which plots
the time evolution of the scattering index of the island, defined in (2.3) in the
two cases. It is noteworthy also that the simulated branching develops through
the three temporal phases as pointed out by the experiments in the introduc-
tion of this chapter. The scattering index does not significantly increase after
2500 MCS since it is possible to hypothesize an equilibrium between the
different forces: the tendency of the cells to elongate and to respond to HGF
can no more overcome the adhesion with the rest of the colony and the area
constraint. A breakage of this equilibrium would create the scattered island
fragment. An analogous behavior is experimentally seen with the scattered
colonies that reach and keep a limit conformation before the detachment of
some branches.
From a mechanical viewpoint, the branching process is due to the fact that
the presence of the growth factor produces a continuous, inward, normal force
at the boundary of the cell island, creating a buckling-like instability, as the
chemotactic force compresses small initial bumps laterally, producing sprouts.
Indeed, MLP-29 cells in the bumps are more likely to extend pseudopods
than cells in the valley between the bumps, since filopodia at growing tips
are more frequent because they have a lower energy cost, making the rate
of pseudopod extension critical to pattern evolution. In particular, for the
instability to persist, it is required that the cells in the valley must retract
while the others protrude, leading to the development of the branch they
belong to. At equilibrium, the tracks of the zones of HGF-action have therefore
 
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