Brown University. Department of Applied Mathematics (sponsor)
The zebrafish (Danio rerio), a widely-studied model organism, is a small fish with distinctive black and yellow stripes on its body and fins. Numerous experimental studies have shown that these stripes, which form as the fish develops from a larva to an adult, emerge due to the interactions of pigment cells. Notably, many zebrafish mutations that disrupt cell interactions display altered patterns, including spots, widened stripes, or labyrinth curves. In this thesis, we work closely with the biological data to develop agent-based models of pattern formation on zebrafish, with the goal of helping to identify wild-type cell interactions and link genes to their functions by suggesting cell behaviors that are impacted in mutations. We model pigment cells as individual agents that interact through migration (coupled differential equations) and experience changes in population size based on a series of short- and long-range interactions (stochastic rules) on growing domains. In a first model, we consider two types of cells, black melanophores and yellow xanthophores, interacting through cell birth, death, and movement. Motivated by new experimental results, our next model incorporates five types of cell agents, and represents a predictive, current system consistent with a range of zebrafish dynamics, including wild-type, early-stage mutations, ablation experiments, and quantitative measurements. It suggests a candidate network of interactions governing cell behavior and proposes, among other findings, what interactions are altered in the spotted leopard zebrafish. Finally, our third model reconciles differences in the number of cells involved in body and fin patterning by showing that two types of cells are sufficient to create stripes on the caudal fin under certain conditions on growth and bone rays.