Biomedical Engineering Reference
In-Depth Information
steps: (1)
rolling
along the vasculature (mediated through transient interactions
between selectin proteins and their carbohydrate ligands), (2)
activation
of both
neutrophils and endothelial cells and a high affinity interaction between integrins
and glycoproteins of immunoglobulin superfamily, and (3)
extravasation
(crawl-
ing along the endothelium, diapedesis, and migration into tissue) in response to a
chemoattractant gradient. Somatic cells migrating in vivo show large single protru-
sions and highly directed migration, in contrast to the multiple small protrusions
they display on planar substrates, and cancer cells can modify their morphology
and nature of migration in response to environmental changes.
7.3.1.1 Measuring Cell Migration
Migratory behavior of all cells depends on their microenvironment.
Chemokinesis
is the induction of random, nondirectional migration in response to a ligand with-
out any oriented cues. To describe the random motility of a cell in the
x
-direction, a
flux of the form similar to Fick's first law (Chapter 2) is assumed, that is,
dn
(7.17)
J
=−
D
random
n
dx
where
D
n
is the cell random-motility coefficient and
n
is the cell density (similar to
concentration of a chemical). Random motility in 3D can be obtained by
⎛
dn
dn
dn
⎞
J
=−
D
+
+
=−
D
∇
n
(7.18)
⎜
⎟
random
n
n
⎝
dx
dy
dz
⎠
where
is the gradient operator. However, cell migration primarily occurs due to
the presence of ligands secreted by certain cell types in addition to the concentration
of binding domains in the extracellular matrix. Chemotaxis (from the Greek
taxis
“to arrange”) describes the directed migration of cells towards a positive gradient
of soluble chemoattractant, whereas haptotaxis is the directed migration of cells
along a gradient of anchored substrate (laminin and fibronectin). Analogous to
random motility, chemotactic flux can also be written as
∇
J
=
χ
()
c n
∇
c
chemo
where
(
c
) is a chemotactic function and
c
is the concentration of the soluble che-
moattractant. Chemotactic function is dependent on the receptor-ligand interac-
tions. Similarly, the influence of haptotaxis is modeled as
χ
J
ρ=∇
n
f
hapto
0
where
0 is the (constant) haptotactic coefficient and
f
is the concentration
of the substrate-bound haptotactic factor. When all three factors (chemokinesis,
chemotaxis, and haptotaxis) are considered to assess the migratory pattern, the
ρ
0
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