CAREER: Probing Multiscale Growth Dynamics in Filamentous Cell Walls

各种植物和真菌依靠丝状生长在环境压力下发育、繁殖或生存。例如，一细胞宽度的根毛的生长有效地增加了植物根的表面积，以吸收水分和养分。尽管一个多世纪以来，实验方法已经能够跟踪扩张的细胞壁表面的细胞壁形态和运动学，但细胞壁生长的调节需要进一步阐明。该项目将开发数学模型和计算方法来模拟由于新的细胞壁材料的空间图案以及与细胞内部的机械相互作用而导致的细胞壁扩张。此外，还将设计推断方法，从细胞壁几何形状预测壁-材料运输的空间模式，并量化细胞壁内的体积增长是如何分布和重新排列的，以维持在膨胀和机械约束下的细胞壁几何形状。本研究开发的方法可应用于花粉管、根毛、菌丝等丝状生长系统，对促进农业发展和改善公众健康具有重要意义。作为这项研究的补充，研究人员将邀请包括K-12、本科生和研究生在内的学生参加研究指导、期刊俱乐部和一个新的互动学习平台“Filaform”，通过结合现代和新兴的实验技术，利用几何和其他数学促进对这一生物过程的兴趣和跨学科理解。为了达到研究和教育目标，将开发两个不同尺度的互补数学模型。第一种是薄壳模型，将细胞壁表面近似为一个不断增长的弹性边界，由细胞内部的膨胀压力膨胀。三次样条解将被用来模拟在膨胀压力和胞吐作用分布的影响下表面生长的演变，胞吐作用是一种沿着细胞壁内表面分布新的细胞壁材料的过程。此外，还将提出一个与模型方程的子集相结合的反问题，以推断给定稳态细胞形状时胞吐的分布。将胞吐作用分布作为输入，第二个模型将是一个三维模型，它描述了细胞壁厚度上的生长分布和方向性(各向异性)。发展了一种基于能量的物质点方法来模拟移动胞壁区域的动力学。研究人员将通过建立受三维模型约束的最优化问题来推断细胞壁域中体积增长和各向异性的空间图。这两个模型的理论预测将通过跟踪细胞壁形态、参与胞吐作用的蛋白质复合体的信号以及细胞壁中的新聚合物的实验来验证。研究人员将基于薄壳模型及其模拟，创建一个面向K-12教育工作者和学生的开源互动教学平台。该项目由数学科学部的数学生物学计划和土木工程、机械和制造创新部的生物力学和机械生物学(BMMB)计划共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Various plants and fungi rely on filamentous growth to develop, reproduce, or survive under environmental stress. For example, the growth of root hairs with one-cell width effectively increases the surface area of the plant roots to absorb water and nutrients. Although experimental approaches have been able to track cell wall morphology and kinematics on the expanding cell wall surface for more than a century, the regulation of cell wall growth needs further elucidation. This project will develop mathematical models and computational methods to simulate the cell wall expansion due to the spatial patterning of new cell wall materials and mechanical interaction with the cell interior. Further, inference methods will be devised to predict the spatial patterning of wall-material trafficking from the cell wall geometry and quantify how volume growth inside the cell wall is distributed and rearranged to sustain the cell wall geometry during expansion and under mechanical constraints. The methods developed in this research can be applied to filamentous growth systems such as pollen tubes, root hairs, fungus hyphae, thus having significant implications in advancing agriculture and improving public health. Complementary to the research, the investigator will engage students, including K-12, undergraduate, and graduate students, in research mentorship, journal clubs, and a new interactive learning platform "Filaform”, to promote interest and transdisciplinary understanding of this biological process by leveraging geometry and other mathematics in conjunction with modern and emerging experimental techniques. To reach the research and education goals, two complementary mathematical models at different scales will be developed. The first will be a thin-shell model approximating the cell wall surface as a growing elastic boundary inflated by turgor pressure from the cell interior. Cubic-spline solutions will be developed to simulate the evolution of surface growth under the influence of turgor pressure and the distribution of exocytosis, a process that distributes new cell wall material along the cell wall interior surface. In addition, an inverse problem coupled with a subset of the model equations will be formulated to infer the distribution of exocytosis given the steady-state cell shape. Taking the exocytosis distribution as an input, the second model will be a three-dimensional model that describes the growth distribution and directionality (anisotropy) across the cell wall thickness. An energy-based material-point method will be developed to simulate the dynamics of the moving cell-wall domain. The investigator will infer the spatial map of the volume growth and anisotropy in the cell-wall domain by formulating optimization problems constrained by the three-dimensional model. Theoretical predictions from both models will be validated by experiments tracking the cell wall morphology, signals of protein complexes involved in exocytosis, and new polymers in the cell wall. The investigator will create an open-source interactive teaching and learning platform for outreach to K-12 educators and students based on the thin-shell model and its simulation. This project is jointly funded by the Mathematical Biology program of the Division of Mathematical Science and by the Biomechanics and Mechanobiology (BMMB) program in the Division of Civil, Mechanical, and Manufacturing Innovation.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.