  When a founder cell and its progeny divide with incomplete cytokinesis, a
network forms in which each intercellular bridge corresponds to a past mitotic
event. Networks built in this manner are required for gamete production in many
animals, and different species have evolved very different final network
topologies. While mechanisms regulating network assembly have been identified
in particular organisms, we lack a quantitative framework to understand network
assembly and inter-species variability. Motivated by cell networks responsible
for oocyte production in invertebrates, where the final topology is typically
invariant within each species, we devise a mathematical model for generating
cell networks: each node is an oscillator, and after a full cycle, the node
produces a daughter to which it remains connected. These cell cycle
oscillations on the nodes are transient and coupled via diffusion over the
network's edges. By variation of three biologically motivated parameters, our
model generates nearly all such networks currently reported across
invertebrates. Furthermore, small parameter variations can rationalize cases of
within-species variation. Because cell networks outside of the ovary often form
less deterministically, we propose generalizations of our model to account for
different sources of stochasticity.
