Biomedical Engineering Reference
In-Depth Information
tor occupancy on any given cell, a fact that is very useful in solving the problem
numerically.
This biophysical framework can be used to predict the possible effects of
localized perturbations of epithelial layers. For example, Peri et al. (35) constitu-
tively activated Rhomboid in a small group of cells within the follicular epithe-
lium. The effect of this perturbation was localized to its neighborhood: the
EGFR-target genes were affected a few cell diameters from the cluster with the
constitutively active ligand release. What is the outcome of such perturbations in
general? Under what conditions will they remain localized or, alternatively, gen-
erate a propagating wave where secreted Spitz will be inducing Rhomboid ex-
pression and further Spitz release from the neighboring cells? This question can
be easily addressed with the described model. For example, Figure 7C shows
how the transition between the stationary and propagating patterns is affected by
the size of the perturbation and the rate of ligand release. Clearly, a high rate of
ligand release and a large size of perturbation promote generation of traveling
waves. Because of its potential for "runaway" behavior, a positive feedback is
tightly regulated. Genetic studies in the ovary indicate that the domain of the
positive feedback is restricted in space, presumably to prevent propagation of
traveling waves (24).
3.3. Pattern Formation by Interacting Feedback Loops
Dorsal appendage morphogenesis provides a genetically tractable system
for studying the mechanisms by which simple inductive cues are converted into
more elaborate spatial patterns. The components of the mechanism proposed by
Wasserman and Freeman are well established. But, is the proposed mechanism
actually correct? Specifically, does it account for the phenotypes that are in-
duced by various genetic manipulations of the DER network and can it make
testable predictions? These questions led us to develop our initial phenomenol-
ogical model of EGFR-mediated patterning in
Drosophila
oogenesis (26,30).
The model accounts for the interactions between the spatially nonuniform input
by Gurken and the feedback loops by Spitz and Argos (Figure 8A). We formu-
lated the model in one spatial dimension and assumed that the characteristic size
of the pattern greatly exceeds the size of a single cell. This led to a system of
nonlinear reaction-diffusion equations that was analyzed by time integration and
numerical bifurcation analysis.
Our main goal was to test whether the mechanism could account for the
various eggshell morphology phenotypes. We were particularly interested in the
phenotypes generated by manipulations of the dose and the spatial distribution
of the oocyte-derived signal (see Nilson and Schupbach (20) for a comprehen-
sive review). It is known that a systematic decrease in the level of Gurken signal
