Biomechanical and Biochemical Mechanisms for Patterns on Plants

生物系统中的形态发生涉及在一系列时间和空间尺度上运作的相互作用的生化和生物物理机制。特别是，最近的实验表明，叶序模式(植物顶端叶芽的排列和形状)是由多种机制控制的非均匀生长引起的。这项工作基于对植物形态发生中生物化学和生物力学之间相互作用的实验洞察力，建立了叶系模式的模型，并推导出控制叶系模式缺陷的方程。将收集有关叶芽形状、应用小波方法分析图案、用模拟生物生长的凝胶进行实验测试的模型以及所研究图案的包装特性的数据。单个植物细胞的生长模型也将扩展到组织中的细胞生长模型。所涉及的数学技术包括多尺度分析和动力系统理论的工具。合作者包括艾萨克·陈奇亚、托德·库克和艾伦·纽尔。生物学家们越来越意识到，机械刺激与植物和动物的生化途径相互作用。阐明这些错综复杂的相互作用的机制和性质，虽然在实验上非常具有挑战性，但有可能影响我们对许多生理过程的理解。这个项目的重点是对植物顶端叶芽形成模式所涉及的生化和生物力学过程进行建模，这是一个几个世纪以来一直吸引科学家的话题，目前也是许多实验工作的主题。在植物上观察到的图案呈现出在许多实验室和自然系统中观察到的波纹、六边形或正方形平面形状的独特变化，如云形成、动物皮毛和流体对流实验。这些变化为我们提供了关于机制之间竞争与合作的潜在线索。除了建模和数学分析，还开发了简单的实验系统，其中模型可以在实验室的凝胶上进行测试，比在生物系统中对参数有更多的控制。本科生和研究生的参与是该项目理论和实验组成部分的一个组成部分。

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.