Negative feedback loops are well known in physiology. Previous work at UCLA has iden-
tied a negative feedback pathway involving Bone Morphogenetic Protein 4 (BMP-4) and
an inhibitor of BMP-4 called Matrix Gla Protein (MGP) active in vascular development
and pathology. More recently, other inhibitors of BMP-4 have been identied in vascular
tissue, including Crossveinless 2 (CV-2). In addition, experimental works performed by our
collaborators at Dr. Bostrom's lab have identied oscillations in the concentrations of these
morphogens gene expressions.
We developed a mathematical model of the interactions among the new, larger set of
morphogens. In particular, there are at least 2 negative feedback loops, one acting with a
short time delay and the other acting with a longer time delay. In fact, there are 3 distinct
time delays in our mathematical model. The goal was to understand what conditions would give rise to sustained oscillations in this model. With a view to comparing these results to experimental observations in the lab of Dr. Kristina Bostrom at UCLA, we have attempted to draw general conclusions about the behavior of multiple loop feedback systems, a problem of general interest.