Biomedical Engineering Reference
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outcome is given by the fact that if the number of threads is above a certain
threshold, moving individuals, in their search of cell-fiber adhesive interac-
tions, do not need to spread in the surroundings. This explanation can be
interpreted as the model counterpart of the so-called integrin receptor sat-
uration, originally proposed and thermodynamically analyzed in [102], and
observed in the phagocytosis of latex beads [171] and in the immune synapse
between the antigen presenting cell and the T cell [168].
Finally, when the matrix is formed by a continuous carpet of fibers (i.e., >
6 10
7
, corresponding to more than 5 10
5
collagen-like molecules/m
2
), the
cells' migratory capacity is clearly comparable to the case of the unpercolated
substrate.
In the three-dimensional case, the abundance of matrix threads results in
the formation of a scaffold characterized by small pores (i.e., half of a cell
diameter or less), which prohibit any cell migration over long distances. An
even complete stretch of cell cytosol, captured in the insets of the bottom{
right panel of Figure 9.6, is in fact not sucient to pass through such steric
hindrances, as the nucleus cannot significantly deform (
surface
;N
is high), caus-
ing the overall individual to be confined in a small area. In this regard, in the
following we will examine how the migration ability of cells depends on the
deformability of their nucleus.
The outcomes of the models are then consistent with the relative observa-
tions provided in the experimental literature. Different studies have, in fact,
coherently shown that migration on planar substrates is limited for low fiber
densities by the inability of the cells to form sucient attachments to generate
traction and to move forward [167, 228]. Optimal ligand densities, in contrast,
preclude the formation of stable focal adhesions [17, 70, 224, 302] and re-
quire rapid focal adhesion turnovers, which result in maximal cell movements
characterized by frequent membrane protrusions. Eventually, at high densities
migration is blocked because integrin receptors engage into stable focal ad-
hesions that exclude coordinated attachment-detachment for cell movement
[123, 156]. Blocked migration due to stable focal contact formation is usually
accompanied by an increased spreaded area (again, refer to [70]), which we,
however, did not capture with our approach.
In 3D environments, neutrophil migration (both velocity and directional
coecient) has been reported to vary in a biphasic manner with the gel pore
size [219], while mouse fibroblasts have been observed to migrate more signifi-
cantly in collagenglycosaminoglycan (CG) scaffolds featuring small pore sizes,
whereas they have exhibited less dispersion in matrices with larger pores [177].
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