Biomedical Engineering Reference
In-Depth Information
decision. Once the single-cell aspects of the motion are in place, we must still
figure out the nature of the collectively-produced streaming pattern that has
already been mentioned.
Each of these topics could serve as the focus of a long, comprehensive
review covering all the relevant data and all the different models. This is not
the purpose here. Instead, we will focus on one representative model for each
aspect as a way of showing what types of dynamical mechanisms are necessary
to produce the observed behavior. None of these models are perfect, and the
shortcomings will be used as a way to motivate alternatives (also not perfect)
in the literature. By this strategy, we can illustrate the types of questions that
can be answered with the help of models and, perhaps more importantly, how
to use models to figure out what key experiments still need to be done.
3.3 Signaling Models
We have just seen why Dicty is such a rich system for modelers. It is thus not
surprising that the modeling of the cAMP signaling machinery has attracted
considerable attention from the physics and mathematics communities. Here
we will mostly focus on one of the earliest models, due to Martiel and Gold-
beter [3]. Afterwards, we will talk about shortcomings, other approaches, and
needed research.
The basic step underlying cAMP waves is the detection by the cell and the
resultant signal relay. This means that an initially small (but not infinitesimal)
stimulus will be amplified and give rise to a propagating disturbance; looked
at over the millimeter scales, these disturbances become organized in wave
patterns. The waves can be visualized by the technique of darkfield microscopy
in which changes in cell shape (sometimes called cringing) as the wave passes
by are detected via changes in light scattering. Note that the cells do not need
to be physically translocating to be imaged in this manner - all that is needed
is a shape alteration.
Goldbeter and colleagues realized that the experimentally observed am-
plification of a cAMP stimulus must originate from a positive feedback loop.
They also realized that a mechanism that eventually shuts off the positive feed-
back was needed. After all, without such a mechanism, the positive feedback
loop would continue indefinitely, leading to a singularity. In early attempts,
they proposed that such a mechanism could be offered by the depletion of one
of the ingredients involved in the machinery [4]. They postulated that this in-
gredient was ATP, the substrate of the enzyme adenylate cyclase (ACA) that
generates cAMP production, and that feedback would terminate once ATP
was used up. However, subsequent experimental data ruled out this possibil-
ity because it demonstrated that the internal ATP level does not significantly
alter during an oscillation cycle [5, 6].
In an updated version of the model, Martiel and Goldbeter (hereafter
denoted by MG) removed this depletion step and assumed that the cAMP
