RUI: Collaborative Research: DMS/NIGMS 1: The mathematical laws of morphology and biomechanics through ontogeny

RUI：合作研究：DMS/NIGMS 1：通过个体发育的形态学和生物力学的数学定律

• 批准号: 2152792
• 负责人: Kathleen Foster
• 金额: $ 38.49万
• 依托单位: Ball State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2152792&HistoricalAwards=false
• 关键词: RUI; Collaborative; Research; DMS; NIGMS

Although fruitful interactions between mathematical theory and scientific experimentation were plentiful in the 20th century, even now the integration of math into biology is still in its infancy and mostly limited to fine scales. Already 100 years ago, D’Arcy Thompson developed critical concepts and tools for the analysis of form and function as organisms develop, yet nevertheless, we continue to lack a solid, mathematical theory of how macroscopic, fully 3D shapes and functions evolve through growth in animals. To thoroughly understand the mechanisms of changes in form and function through growth, it is necessary to derive rigorous mathematical laws that govern both morphology and locomotion through development. This project will concentrate on arboreal lizards, a model system in many fields of biology, and will combine biomechanical experiments and morphological analysis, together with mathematical modeling and machine learning. By capitalizing on the rapid growth and extraordinary diversity of body forms and locomotor behaviors of arboreal lizards, this research will build an integrative picture of how their form and function transform through development with mathematical rigor. This will provide a tangible contribution to our understanding of the mechanisms underlying the flexibility and resilience of species that face an ever-changing environment, while at the same time stimulating new research in applied mathematics such as the modeling of increasingly complex, multi-scale, and nonlinear systems. This project will have broad community and societal impacts through the education and training of highly qualified personnel (undergraduate, graduate, and postdoctoral scholars), particularly those from underrepresented groups in STEM. Through outreach initiatives, this project will educate school children, especially those from disadvantaged populations, and the public on the ways that math and biology can work together to contribute to our understanding of animal form and movement, climate change, population aging, and conservation. This project will bring new theoretical and methodological foundations to the understanding of the biology of arboreal lizards via the data-driven discovery of the mathematical laws that govern 1) their biomechanical transformation through ontogeny, in the form of differential equations describing the coupled motion of joints/limbs; 2) their transformations in morphology through ontogeny, via smooth group transformations in the form of nonlinear maps between shapes; and 3) how their shape and mechanics are related to each other, via explainable statistical and machine learning models and low-dimensional transformations across age-groups. Experiments will be conducted to collect comprehensive biomechanical and morphological data that will empower mathematical and machine learning models and will occur in two phases. Phase 1 will capitalize on a parthenogenic arboreal lizard (mourning gecko) and a common garden design to construct models that will allow us to quantify the coordinated changes of form and function through growth; Phase 2 will test the generality of our models on three additional arboreal lizard species. The longitudinal data produced will be unparalleled in its scale and scope in functional morphology and comparative biomechanics, making it a benchmark dataset and enabling and stimulating the investigation of further questions related to developmental biology, animal behavior, and ecomorphology. This work will provide a unifying perspective to how ontogeny, morphology, behavior, locomotion, community ecology, and evolution interact and merge by producing a common mathematical and computational framework that will become of broad use at the intersection of these disciplines.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

尽管在20世纪，数学理论与科学实验之间的富有成果的相互作用很丰富，但即使现在，数学整合到生物学中仍处于起步阶段，并且大部分仅限于精细的规模。 D'Arcy Thompson早在100年前就已经开发了关键的概念和工具，以分析随着生物的发展而分析形式和功能，但尽管如此，我们仍然缺乏关于宏观，完全3D的形状和功能如何通过动物的生长而发展的坚实的数学理论。为了彻底理解形式和功能变化通过增长的机制，有必要得出严格的数学定律，以通过发展来控制形态和机车。该项目将集中于树木蜥蜴，这是许多生物学领域的模型系统，并将生物力学实验和形态分析与数学建模和机器学习结合在一起。通过利用树木蜥蜴的身体形式和运动行为的快速增长和非凡的多样性，这项研究将建立综合的图景，说明其形式和功能如何通过数学严格的发展来发展。这将为我们理解面临不断变化的环境的灵活性和弹性的理解提供明显的贡献，同时刺激应用数学的新研究，例如越来越复杂，多规模和非线性系统的建模。该项目将通过对高素质的人员（本科，研究生和博士后学者）的教育和培训，特别是STEM中代表性不足的人的教育和培训，从而产生广泛的社区和社会影响。通过外展计划，该项目将教育小学生，尤其是来自处境不利的人群的儿童，以及公众对数学和生物学可以共同努力的方式来促进我们对动物形态和运动，气候变化，人口老化和保护的理解。该项目将通过数据驱动的数学定律的发现，将新的理论和方法论基础带入对树木蜥蜴生物学的理解。 2）它们通过个体发育中的形态转化，通过形状之间的非线性图的平滑群体转换； 3）它们通过可解释的统计和机器学习模型以及跨年龄段的低维转换如何相互关联的形状和机械。将进行实验以收集综合的生物力学和形态学数据，以增强数学和机器学习模型，并将分为两个阶段。第1阶段将利用孤tenegin的树木生殖蜥蜴（哀悼壁虎）和常见的花园设计，以构建模型，使我们能够通过生长来量化形式和功能的协调变化；第2阶段将测试我们模型的一般性，对三种额外的树木蜥蜴物种。产生的纵向数据将在功能形态和比较生物力学方面的规模和范围中无与伦比，使其成为基准数据集，并促进并刺激与发展生物学，动物行为和生态形态学有关的其他问题的投资。这项工作将提供一个统一的观点，即通过产生共同的数学和计算框架，将在这些学科的交汇处广泛使用，这将在这些奖项的交汇处进行广泛使用。该奖项通过NSF的法定任务反映了通过评估的精力来评估，该奖项将在这些训练的交集中广泛使用。