Biomedical Engineering Reference
In-Depth Information
have constraints on the cell volume and surface. Indeed, assuming that cells
do not significantly grow during migration, the fluctuations of their volumes
are kept negligible with high constant values volume
;N
;C 1, for
any individual and for such that ( ) 2 fN;Cg (respectively, in 2D
surface
;N
= volume
= surface
;C 1).
On the other hand, when moving in matrix environments, cells are typ-
ically deformable, while their nuclei show a rigidity higher than the cyto-
plasm region: therefore, for any and for such that ( ) = C, we set
surface
;C
1, while and for such that ( ) = N, we set surface
1
;N
(respectively, in 2D perimeter
;C
1 and perimeter
;N 1). The extracellular
environment is instead assumed to have homogeneous mechanical and mi-
crostructural properties: in particular, the matrix fibers are assumed to be
rigid by setting surface
F = perimete F 1 when ( ) = F in both two and
in three dimensions. However, it is useful to emphasize that in the following
we will analyze how the explicit variation of fiber and nucleus stiffness will
affect cell migratory phenotypes within three-dimensional matrices.
H adhesion is, as usual, differentiated in the contributions due to either the
generalized contact tension between the nucleus and the cytoplasm within the
same cell, or the effective adhesion between a cell and both the medium and
the fibrillar matrix component, and, in the case of collision, between cells.
In particular, J int
N;C 0 implicitly models the forces exerted by intermediate
actin filaments and microtubules to anchor the nucleus to the cell cytoskeleton,
preventing cells from fragmenting.
J ext
E;M and J ext
E;F evaluate instead the heterophilic contact interactions be-
tween cells and matrix components: specifically, they are a measure of the
anity between cell surface adhesion complexes (i.e., sugar-binding receptors
or integrins) to either nonsolid (i.e., glycosaminoglycans in medium) or solid
(i.e., fibrillar collagen) extracellular ligands, respectively [348]. In particular,
we assume J ext
E;F < J ext
E;M since, as widely demonstrated in the literature, most
cell lines in standard conditions adhere more strongly with the fibrous part
of the extracellular matrix rather than with its soluble component (see [382]
and the references therein).
J ext
E;E represents the local adhesive strength between neighboring cells, a
measure of the local quantity of active and exposed cadherin molecules. It is
kept high to avoid cell{cell adhesive interactions upon accidental cell collisions
that may affect cell movement.
Setting in general constant and homogeneous values for the bond energies
Js corresponds to assuming a uniform distribution of adhesion molecules on
cell surfaces and of ligands in the external environment, without any change
during the observation time. A summary of values of all the model parameters
used in the simulations is given in Table C.10 in Appendix C.
Given the Hamiltonian, the transition probability of a spin flip has the form
of Equation (4.24). In particular, we use p(T (t)) = tanh(T (t)). Indeed,
for each cell and for ( ) = N, T ; = T ;N gives the agitation rate of
 
Search WWH ::




Custom Search