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Quantifying zebrafish pattern variability and model robustness

Banff International Research Station for Mathematical Innovation and Discovery

Wild-type zebrafish feature black and yellow stripes across their body and fins, but mutants display a range of altered patterns, including spots and labyrinth curves. All these patterns form due to the interactions of pigment cells, which sort out through movement, birth, competition, and transitions in cellular shape during early development. The diversity of patterns on zebrafish makes it a useful organism for helping elucidate how genes, cell behavior, and visible animal characteristics are related, and the goal of our work is to help link genetic mutations to altered cell behaviors. Using an agent-based approach, we couple deterministic cell migration by ODEs with stochastic rules for updating population size to reproduce a range of fish patterns. Within a single zebrafish mutation, however, there is a lot of variability, and this makes it challenging to first identify the features of a pattern that we are trying to reproduce and then judge model success. Moreover, cells interact in a noisy environment on the fish skin, and model results need to be robust to realistic biological stochasticity. To help address these challenges, here we present a study of pattern variability and model robustness using topological tools to quantify zebrafish pattern features. This is joint work with Melissa McGuirl and Bjorn Sandstede.

Mathematics; Biology and other natural sciences; Partial differential equations; Mathematical biology

video/mp4

Author affiliation: Ohio State University

2019-12-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72803

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/