Computational Mechanobiology in Cartilage and Bone Tissue Engineering: From Cell Phenotype to Tissue Structure - Computational Modeling in Tissue Engineering - page 334

of the cellular forces with the substrate stiffness, the development of structural
anisotropy dependent on cell shape and boundary conditions and the co-localisa-
tion of high concentrations of stress-fibres with focal adhesion sites or externally
induced local stress concentrations. From a modelling perspective it is noteworthy
that this type of model allows a representation of the cytoskeleton in some ways
similar to that in tensegrity models [ 48 ] and not usually captured in continuum
models. Additionally, the continuum approach offers the advantage that the
cytoskeletal arrangement does not have to be pre-defined and is dynamic in nature,
i.e. the cytoskeleton can remodel, which is a non-trivial task for tensegrity models.
Cells are attached to the ECM through discrete multi-protein complexes called
focal adhesions. These focal adhesions assemble and disassemble depending on
the forces exerted upon them and are linked to the formation and dissociation of
stress-fibres in the cytoskeleton. The adhesion sites undergo maturation from
dynamic to fully reinforced static adhesion sites, passing the stages of initial
adhesions, adhesion complexes and focal adhesions. Based on continuum
mechanics arguments it has been suggested that with maturation into the static
state the adhesion sites loose their sensitivity to substrate stiffness; for more details
on adhesion sites in relation to mechanosensitivity see the articles by Fereol et al.
[ 32 ], Nicolas et al. [ 85 ], and Nicolas and Safran [ 84 ]. The cell contractility model
[ 27 ] described previously has been extended and applied to the investigation of
focal adhesion dynamics using a thermodynamical approach and uniaxial example
problems [ 28 ]. The authors of this study stated that: ''The fact that many proteins
perform both structural and signaling functions hinders the ability of traditional
genetic approaches to parse the mechanisms that regulate [focal adhesion]
dynamics, since knocking out a protein by genetic manipulation may also elimi-
nate an essential structural component. Consequently, to understand how specific
molecular features give rise to the observed behavior it is essential to combine
experimental studies of adherent cells—including the use of microscopy to
observe the structure and dynamics of the cytokskeleton and [focal adhesions]—
with computational models that include the salient mechanics'' [ 28 ]. Among the
successful predictions made by the model was the focal adhesion concentration
around the cell periphery as well as the dependence of focal adhesion intensity on
cell size and contractility.
The coupled mechanosensitive focal adhesion/stress-fibre model was extended
to two dimensions and applied to simulate the effect that a micro-patterned shape
of ligands would have on cytoskeletal remodelling and focal adhesion distributions
[ 88 ]. Both convex ligand patterns where the entire cell periphery adheres to the
substrate and various concave patterns with free non-adhered edges were inves-
tigated. The model's predictions in terms of stress-fibre alignment and concen-
tration were regarded as satisfactory while some discrepancies in the vinculin 1
distribution were observed.
1 A protein in the membrane that correlates with the concentration of high-affinity integrins and
is involved in their binding to cytoskeletal components.