Mathematics of DevoWorm

Presented at "Find Your Inner Modeler V". 

Developmental Biology provides fertile ground for the application of graph, mathematical, and computational models. In this poster, we will explore a number of problem domains and their associated modeling representation utilized within the DevoWorm group over our eight year history. The multitude of interactions and state changes (cell identity) that occur across embryogenesis can be captured using discrete dynamical and categorical models. Cellular automata and spatial data structures allow us to capture pattern formation and cell migration dynamics as a computational process. The rate, recombination, and conservation of growth and form can be characterized through lineage and differentiation tree modeling. Finally, we can characterize the organization of developmental cells, expanding morphological structures, and emerging connectomes using graph models such as neural networks, complex networks,  and trees. Future work involves furthering the Computational Developmental Biology enterprise by applying the different classes of model presented here to the ever-burgeoning variety of publicly available datasets.