REACTION-DIFFUSION MODELLING WITHIN COMPLEX BIOLOGICAL DOMAINS

Abstract

Morphogenesis, the emergence of shape during development, is a highly robust and organised process. Chemical cues called morphogens provide positional information to each cell in a concentration-dependent manner. Morphogen pattern formation is usually formalised as a set of reaction-diffusion equations, but existing models of morphogen patterning often do not account for the spatial complexities present in vivo. In this thesis, we are particularly interested in understanding the effects of biologically relevant spatial complexities on reaction-diffusion patterning of morphogens. Working in close collaboration with experimental labs studying zebrafish development, we take a theoretical and computational approach to address how reaction-diffusion patterning might resolve in some of these complex environments.

We focus on the brain and the tail of the developing zebrafish in particular. Using the tail, we outline new strategies for quantifying growing systems, and model signalling in a system with domain growth and cellular movement. In particular, we develop a novel framework for understanding cell positioning within growing systems. We then study the zebrafish brain to explore methods for performing multiscale reaction-diffusion simulations and investigate morphogen transportation in tortuous environments. Lastly, we present preliminary results from novel and emerging methods that may accelerate future reaction-diffusion modelling in complex spaces.