The human brain is poorly understood. Although insufficient, investigating its structure is necessary to discern how it operates. This structure on a microscale can vary wildly between individuals. Understanding how these networks form would help in explaining this variability. To do so, we need to develop computational models that simulate the processes involved. With a relatively small and (near) completely reconstructed connectome, C. elegans is an ideal subject for this research. A previous attempt at this used stochastic methods, where connections are assigned randomly and weighted by the distance between soma. While useful, this model failed to predict particular network attributes of the C. elegans connectome. We aimed to develop a minimal model that incorporates the spatial embedding of neurites to approximate the process of neurite growth and synapse formation in Euclidean space, examining the impact of neurites on network structure. We found that networks that incorporate the spatial embedding of neurites resulted in particular attributes consistent with connectomes of C. elegans .

In their most abstract form, we can understand tissues as being composed of three general cell types: stem cells, transit-amplifying cells, and differentiated cells. Additionally, we know that these cell types can secrete molecules or regulatory factors that can exert control over other cell populations. Recent work in theoretical biology examined several cell lineage control networks that result in tissue homeostasis. We develop an alternative mass action model that views developmental cell lineages as biological pathways. We demonstrate that three cell lineages are homeostatic irrespective of the implementation and that their control structures exhibit a degeneracy, containing solely negative feedback or negative resistance. We replicate and extend the homeostatic control architectures previously outlined and report on the relevant bifurcations and dynamics of these pathways.