1. Understanding zebrafish pigment pattern formation using mathematical modelling
- Author
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Owen, Jennifer, Kelsh, Robert, and Yates, Christian
- Abstract
Animal pigment patterns are as diverse as they are beautiful. Characterised by their striking blue and golden stripes along the body tails and fins, the adult Danio rerio (zebrafish) has become a major model organism for the study of pigment patterns. The stripes are comprised of three different pigment producing cell types which selforganise over a period of three weeks into the adult stripe pattern. Over the past two decades, a multitude of observational, cell and genetic studies have determined numerous mechanisms involved in this self-organisation, yet, it has still been unclear whether or not these rules were sufficient to generate the pattern. To aid analysis of complex systems such as this, mathematical modelling has become a powerful assistive tool. By providing a theoretical framework, a mathematical model allows us to clearly articulate our hypotheses in a quantitative manner and then test these hypotheses. The goal of this thesis is to develop a mathematical model of zebrafish stripe formation which will be used both within this thesis and in the future, in conjunction with biological experimentation to elucidate the key mechanisms underlying zebrafish stripe formation. We will start by introducing the known mechanisms as determined from biological experiments, as well as introducing the findings and limitations of previous mathematical models of zebrafish stripe formation. Based on this knowledge, we will build our own comprehensive mathematical model of zebrafish stripe formation incorporating all the up-to-date biological information. As we will demonstrate, not only does this model quantitatively and qualitatively reproduce the wild-type striped pattern, but it can also reproduce many of the mutant patterns. Thus we show that the rules determined from the biology are, to at least a good approximation, sufficient for producing the striped patterns. Having validated our approach, we next use the model as a predictive tool to guide further investigation. For example, in the last chapter of the thesis, we will use the model alongside biological experimentation to explore the importance of growth during pattern metamorphosis in the context of both Danio rerio and its close relatives. Along the journey of this interdisciplinary study, we will develop new techniques across mathematics and biology that will aid this investigation. For example, in order to validate our mathematical models ability to generate wild-type zebrafish stripes, as well as other mutant patterns, we will develop a pair correlation function: a statistical tool used for quantifying spatial correlation. In order to compare our theoretical model with the biology, we will refine a method for anaesthetising and subsequently imaging juvenile fish during pattern development that minimises suffering. Therefore the outcomes of this thesis not only aids our understanding of pattern formation, but provides a framework for future investigations of its kind.
- Published
- 2021