Biomedical Engineering Reference
In-Depth Information
Migrating individuals in fact uctuate and \rebound" between channel inter-
nal walls, whose width does not represent a significant geometrical contact
guidance. Indeed, cells do not reach an appreciable directional velocity, re-
maining almost in the middle of the structure. Cell migration both in the
middle and in the small channel (whose widths are smaller than cellular di-
mensions) is instead characterized by a penetrative phenotype. Without the
possibility to deform in a substantial way, the individuals are in fact prohibited
from squeezing through the confined environments. Therefore, they continue
to isotropically wander in the close proximity of the channel entrances.
We then analyze how the motile behavior of cells is affected by the remod-
eling of their cytoskeleton. Indeed, the elasticity of the cell cytosolic region
is allowed by a lower value of
surface
;C
= 0:5, whereas the nuclear cluster is
maintained rigid by retaining the previous high value for
surface
;N
= 15. With
respect to the previous set of simulations, the initial nondirected movement of
cells on the planar substrate is accompanied by a significant spreading (i.e.,
until a 1.3{fold increase in surface area; see Figure 10.3(A, top panel)). As
reproduced in the same image, the cell migratory phenotype in the largest
channel remains unaltered, regardless of cytosolic deformation abilities. As al-
ready observed, moving individuals in fact do not experience significant steric
hindrances that require substantial morphological changes and almost display
the same invasive phenotype.
At the intermediate channel width (i.e., smaller than cellular dimensions
and bigger than nuclear dimensions), cells with a deformable cytoplasm are
instead able to squeeze into and move within the microstructure. In particular,
they remodel toward an elongated mesenchymal shape and typically migrate
to the other end of the device, displaying a common permeative phenotype;
see again Figure 10.3. The transition from a stationary cell morphology to a
polarized shape, which is completely self{generating and due to the geometry
of the matrix environment, is fundamental in determining the persistent com-
ponent in cell movement. From a modeling viewpoint, cell elongation in fact
increases the relative magnitude of the persistence term (10.2) in the overall
hamiltonian, given by coecient
pers
. Therefore, once a cell has established
the direction of movement within a channel, it is energetically disadvantageous
to change direction and is forced to maintain the direction of locomotion.
Finally, cells are still not able to enter the smallest channel. The front end
of their cytoplasm quickly extends into the structure, while the voluminous
nuclear region cannot deform and passes through a highly constrained space,
therefore inhibiting the individual from pulling inside its entire body, as clearly
reproduced in Figure 10.3(C).
Our results are consistent with the experimental observations provided in
[28], where the authors used a Boyden chamber assay to correlate an incre-
ment in the ability of pancreatic cancer cells (Panc-1) to squeeze and migrate
through microporous membranes to a drop in their elastic modulus, measured
by a micro-plate based single-cell stretcher.
We next address the question of to what extent a variation in cell nucleus
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