Abstract
Proposed almost 60 years ago, the Turing mechanism has been rigorously studied as a potential basis for morphogenesis and the driving force behind multiple patterning behaviors found in biology, ecology, behavioral science, mathematics, and chemistry. Growth, which is ubiquitous in biology, has been shown to impact Turing pattern formation in a variety of simple model systems. In this Dissertation, the influence of domain growth on Turing patterns is studied using both experimental and simulated systems. Domain growth significantly impacts pattern formation and morphology in all of these systems.
The first Turing pattern-generating system considered is the experimental chlorine dioxide - iodine - malonic acid (CDIMA) reaction. This reaction system has generated numerous previous insights into Turing-type morphogenesis. CDIMA's photosensitivity is harnessed to artificially ``grow" the patterned region, which causes a variety of pattern morphologies to occur \textit{via} multiple growth modes, all of which depend on the growth rate. This effect was qualitatively reproduced using a realistic chemical model (the Lengyel-Epstein model).
The second Turing pattern-generating system considered is a biologically-inspired model of the interactions between chromatophores (colored pigment cells) on the skin of a zebrafish. First, the patterning from this model (termed the ``Survival model") is shown to result from a Turing bifurcation, even in the absence of any cellular movement. Secondly, the Survival model and another related model are analyzed on a growing domain. Both models show that domain growth can orient the patterns perpendicularly to the growing boundary, albeit at different separations of length scales.
The third project presented here systematically considers the influence of domain growth on simulations of all possible two-node reaction networks. Using a recently published novel instability condition, simulations of each system are tested to see if they are sensitive to spatial perturbations while on a growing domain. All reaction networks show that domain growth can affect the region where the system is unstable to spatial perturbations; however, only a few generate Turing patterns.