Biomedical Engineering Reference
In-Depth Information
subcellular, or global cell behavior. Therefore, choices have to be made clear at
the outset, ranging from distinguishing between prokaryotic and eukaryotic cells,
specificity within each of these types, whether the cell is “normal,” whether one
wants to model mitosis, blebs, migration, division, deformation due to confined flow
as with red blood cells, and the level of microscopic detail for any of these processes.
The review article by Hoffman and Crocker [
48
] is both an excellent overview
of cell mechanics and an inspiration for our approach. One might be interested,
for example, in duplicating the intricate experimental details reported in [
43
]:
“actin polymerization periodically builds a mechanical link, the lamellipodium,
connecting myosin motors with the initiation of adhesion sites, suggesting that the
major functions driving motility are coordinated by a biomechanical process,” or to
duplicate experimental evidence of traveling waves in cells recovering from actin
depolymerization [
35
,
42
]. Modeling studies of lamellipodial structure, protrusion,
and retraction behavior range from early mechanistic models [
84
] to more recent
deterministic [
97
,
112
] and stochastic [
51
] approaches with significant biochemical
and structural detail. Recent microscopic-macroscopic models and algorithms for
cell blebbing have been developed by Young and Mitran [
116
], which update
cytoskeletal microstructure via statistical sampling techniques together with fluid
variables. Alternatively, whole cell compartment models (without spatial details) of
oscillations in spreading cells have been proposed [
35
,
92
,
109
] which show positive
and negative feedback mechanisms between kinetics and mechanics, and which are
sufficient to describe a modality of sustained cell oscillations. The generalization
of such a nonlinear limit cycle mechanism to include 3D spatial substructures
consistent with cell mechanics, and biochemical kinetics and diffusion, charts a
path that our group has elected. Detailed microscopic features are resolved through
effective or collective properties of each substructure, which are dynamically
updated by chemical species and processes. This choice is guided by a series of
developments in the biophysics community on cell structure and rheology (cf. New
Journal of Physics, Vol. 9, 2007), together with recent progress on the biochemical
feedback mechanisms associated with cell morphological oscillations [
20
,
35
,
58
]as
well as other dynamic cell modes.
Our approach is likewise guided by multiphase (implying differentiated sub-
structures) modeling and computational tools developed for analogous applications
such as biofilms [
68
,
108
,
119
,
121
] and complex fluid mixtures (polymer dispersed
nematic rods [
37
,
66
], liquid crystal drops in viscous fluids [
36
,
115
]). We integrate
these approaches to propose a multiphase cell model with an energy-based phase
field formulation, which we then simulate to illustrate qualitative phenomena that
are possible with such a model. We conclude the chapter with a summary of
experimental information and model advances that will be necessary to make
the model biologically relevant and applicable to experiments. Our goal is a
modeling and numerical framework which captures sufficient biological structure
acceptable to cell biologists, which relies upon experimental data to parametrize
the model equations for the structure, and which can reproduce single cell dynamic
morphology behavior including blebbing, migration, contractile waves, oscillations,
membrane-cortex rupture, and division. An early two-phase model of cell motion is
developed by Alt and Dembo [
2
].
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