Biomechanical and Biochemical Mechanisms for Patterns on Plants

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Morphogenesis in biological systems involves interacting biochemical and biophysical mechanisms that operate at a range of temporal and spatial scales. In particular, recent experiments indicate that phyllotactic patterns (the arrangement and shapes of leaf buds at plant apices) arise from nonhomogeneous growth controlled by multiple mechanisms. This work develops models for phyllotactic patterning based on experimental insights on the interaction between biochemistry and biomechanics in plant morphogenesis, and derives equations governing defects in phyllotactic patterns. Data will be gathered on the shape of leaf buds, wavelet methods applied to analyze the patterns, the model tested experimentally with gels that mimic biological growth, and the packing properties of the patterns studied. Models for the growth of individual plant cells will also be extended to models for the growth of cells in tissue. Mathematical techniques involved include multiple scales analysis and tools from dynamical systems theory. Collaborators include Isaac Chenchiah, Todd Cooke, and Alan Newell.Biologists are becoming increasingly aware that mechanical stimuli interact with biochemical pathways in plants as well as animals. Clarifying the mechanisms and properties of these intricate interactions, while experimentally very challenging, has the potential to impact our understanding of many physiological processes. This project focuses on modeling the biochemical and biomechanical processes involved in the patterning of leaf buds at plant apices, a topic that has intrigued scientists for centuries and that is currently the subject of much experimental work. Patterns observed on plants present unique variations on planforms of ripples, hexagons, or squares observed in many laboratory and natural systems such as cloud formations, animal coats, and fluid convection experiments. These variations provide us with potential clues on the competition and cooperation between mechanisms. The modeling and mathematical analysis is complemented by the development of simple experimental systems in which the models can be tested on gels in a laboratory, with more control over parameters than in biological systems. The involvement of undergraduate and graduate students is an integral part of both the theoretical and experimental components of the project.