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Browsing Department of Mathematics by Subject "absorbance spectra"

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    Nonlinear dynamics of plant pigmentation
    (Colorado State University. Libraries, 2022) Hsu, Wei-Yu, author; Shipman, Patrick, advisor; Mueller, Jennifer, committee member; Bradley, Richard, committee member; Finke, Richard, committee member
    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 self association and intermolecular association of the colored forms of anthocyanins. We develop a series of models for the interconversion of the colorless and colored forms of anthocyanins, including zwitterionic species and extend these models to include association of the colored species. 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 a system of partial differential equations for in vivo anthocyanin synthesis (a modification of the Gierer-Meinhardt activator-inhibitor model), we simulate and analyze a variety of colorful spotted patterns in plant flowers. These studies are aided by a linear stability analysis and nonlinear analysis of the modified Gierer-Meinhardt model. The extended model that we propose is a first model to analyze the effects of association in pattern formation. Association may occur with various geometries which have an effect on the absorbance spectrum. Based on the Beer–Lambert law and our evaporative experiments, we develop methods of deconvoluting absorbance spectra of anthocyanin solutions into absorbance spectra of monomers, dimers and trimers, thus providing clues into the geometry of the smallest associated particles. Finally, 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.