Biomedical Engineering Reference
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indeed adapt their shape and squeeze through rigid matrix arrangements by
concomitant elongation of their body. Cells cultured in progressively soft ma-
trices show instead decreasing elongation, and cells within complete compli-
ant ECMs remain uniformly rounded, as they easily deform the collagen-like
threads and lack cytoskeletal traction [397]. In summary, cells migrate in a
biphasic manner at theoretical conditions of either increasing density or in-
creasing stiffness alone, but, however, also at experimental conditions, upon
the combined increase of density and stiffness together (imagine a decreasing
curve in the plots of Figure 9.10 from left top to right bottom).
Bimodal relationships between cell migratory ability and the deformabil-
ity of matrix scaffolds have been observed in experimental models of smooth
muscle cells [310] and mouse fibroblasts, cultured in EDAC-cross-linked colla-
genglycosaminoglycan (CG) matrices with constant pore size [177]. A biphasic
dependence on matrix rigidity has been previously reported in isotropic ho-
mogeneous networks, as in the case of prostate cancer cells coated in Matrigels
with a fixed fibronectin level and variables stiffness [422]. Finally, the inhibi-
tion of cell motility in rigid ECMs has been also demonstrated in [397] for
glioma cell lines.
Indeed, our results may be of particular relevance for the design of ecient
synthetic biomaterials, used in tissue engineering applications and physiology.
Matrix scaffolds with optimal values of pore size and stiffness may in fact
accelerate cell in-growth into an initially acellular structure, which is a criti-
cal requirement for the development of implants for regenerative biomedical
therapies.
9.8 Effect of Varying Nucleus Compressibility in 3D
Analysis of the results provided in the previous sections suggests that cells
fail to neck down to micrometer dimensions and to migrate through steric
barriers posed by matrix scaffolds in which the pore size is smaller than nuclear
diameters and the component fibers are too rigid to be deformed. However,
migration over significant distances in such highly constrained environments
may be achieved with drastic deformations of their nucleus (whose rigidity is,
as seen, the main reason of the halt in cell locomotion due to steric obstacles).
Therefore, the degree of nuclear deformability may contribute to the migration
eciency of a cell. The nucleus elasticity is mainly regulated by both the
chromatin structure and the lamin intermediate filaments that form a part of
the nuclear envelope [144, 160]. The softness of a nucleus can be modeled by
lowering the values of the nuclear rigidity
surface
;N
from 8.5 (see Table C.10)
to 0.5 (compare Figure 9.10(A) and (B)).
At high pore sizes of 10 m or higher and lower ber rigidity (i.e., at
left{upper corner), migration remains unaltered regardless of nuclear elastic-
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