Biomedical Engineering Reference
In-Depth Information
Table 1
. Parameters in the model (25-30,39,40)*
Param. Description Value
D
Ligand diffusion coefficient
10
-10
-10
-6
cm
2
/s (37,38)
R
tot
Number of receptors per cell
10
3
-10
5
rec/cell
k
on
Receptor-ligand forward binding rate constant
1.667 x 10
9
cm
3
/mole-s
0.02 s
-1
k
off
Complex dissociation rate constant
0.02 s
-1
k
e
Complex endocytosis rate constant
R
cell
Receptor cell surface density (cell area ~25
m
2
)
40-4000 rec/
m
2
0.5
m
h
Height of the extracellular medium
C
T
Threshold complex concentration for Rho
induction
U
Time scale for Rho degradation
~20 min (49)
I
|i-m|,|j-n|
Cell-cell coupling coefficient
*Unless indicated otherwise, the references for the parameters can be found in these papers
and the references therein.
3.1. Models of Ligand Transport and Binding
The mechanisms of EGFR-mediated patterning in
Drosophila
development
depend on the spatial ranges of EGFR ligands. Spitz was identified as a short-
ranged ligand acting over 3-4 cell diameters (31-33), while Gurken was pro-
posed to act as a long-range morphogen that can act over more than 10 cell di-
ameters (34-36). The spatial ranges of Gurken and Spitz were derived from
observing their effects on the expression of EGFR-target genes. At this time, the
mechanisms governing the differences in the apparent ranges of the ligand are
not well understood. Since both molecules are secreted, their spatial range can
be tuned by the rates of extracellular transport and ligand-receptor interaction.
Given a large and rapidly growing amount of information about each of these
processes in the EGFR system, it is reasonable to ask if the experimentally de-
rived estimates of ligand range can be interpreted in terms of the elementary
processes, such as binding and receptor-mediated endocytosis. The ability to
predict and manipulate the spatial ranges of secreted growth factors can be used
to develop computational models of patterning networks and design new ex-
periments for evaluating proposed mechanisms. In the following, we use a sim-
plified geometry of cell-cell communication to illustrate a mechanistic model of
ligand transport (Figure 6A).
In the model, the ligand diffuses between the receptor-covered and reflect-
ing surfaces. This geometry approximates the one in egg development where
EGFR ligands diffuse in the thin gap between the oocyte and the follicular epi-
thelium. The motion of the secreted ligand is modeled by free diffusion with an
