Title: Nonlinear dynamics of plant pigmentation

Advisor:  Dr. Patrick Shipman

Committee:  Dr. Jennifer Mueller, Dr. Mark Bradley, Dr. Richard Finke

Red, blue, and purple colors in plants are primarily due to plant pigments called anthocyanins. In a plant cell, an equilibrium is established between anionic and cationic forms of anthocyanins as well electrically neutral colorless forms called hemiketals. In typical cellular pH ranges, the colorless hemiketal would be expected to be the dominant form.   Why then, do plants, in fact, display colors?  We propose that this is part due to intermolecular and intramolecular association of the colored forms of anthocyanins.

In this dissertation, we develop a series of models for the interconversion of the colorless and colored forms of anthocyanins, including Zwitterionic species and excited states.   We extend these models to include intermolecular and intramolecular association.  Analysis of these models leads us to suggest and implement experiments in which the total concentration changes over time, either slowly or quickly compared to the kinetics.  Coupling these models to an activator-inhibitor partial differential equation system for \textit{in vivo} anthocyanin synthesis, we simulate and analyze a variety of colorful spotted patterns in plant flowers.  This is a first model to introduce the effects of association in pattern formation.  The absorbance spectrum of a solution gives the absorbance $Abs(\lambda)$ as a function of the wavelength $\lambda$.  Based on the Beer–Lambert law, we develop methods of deconvoluting absorbance spectra of anthocyanin solutions.  We combine the spectrum deconvolutions with the results of the pattern-forming systems to produce spatially varying absorbance spectra.  We propose a novel geometric method of probing association by observing the changing shape of evaporating solution droplets.  The associated mathematical model involves solving the highly nonlinear mean-curvature equation with nonconstant mean curvature (surface tension), and we present new solutions making use of the hodograph transform.

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