Mathematical Models of Moving Boundary Problems in Developmental Biology and Cell Motility

首席研究员和他的同事们开发了数学模型和计算方法来分析真核生物纤毛和鞭毛的运动，脊椎动物肢芽的生长和发育以及肿瘤的生长。纤毛建模的目的是建立单个纤毛或鞭毛的三维模型以及纤毛的三维阵列。这些模型结合了轴突超微结构的离散表征，包括个体动力蛋白和微管，以及使用浸入式边界方法对流体力学的连续描述。脊椎动物肢体发育是一种被广泛应用于发育研究的模型系统。研究者和他的合作者开发了一个脊椎动物肢体发育的二维模型，该模型描述了肢体芽的生长，并预测了生长因子和形态因子的时空分布。肢体发育建模的主要目标是进一步验证二维模型，将其扩展到三维，以确定细胞将哪些信号视为其在三维肢体芽和发育历史中的位置的函数，并由此建议细胞如何整合信号以产生观察到的空间模式。肢体发育与肿瘤生长是一个涉及组织生长、生长因子转运和基因活性调控的移动边界问题。研究人员正在开发肿瘤生长的浸入边界模型和肢体发育模型。这些数学模型专注于涉及细胞运动、脊椎动物发育和肿瘤生长的复杂生物系统。一个重要的方面是研究这些过程的计算工具的发展。因此，纤毛模型用于纤毛和鞭毛动力学失活机制的计算研究，多纤毛模型用于研究黏毛相互作用。脊椎肢发育模型可以作为解释实验结果的辅助工具，帮助确定新的实验，并测试可能难以通过实验验证的假设。由于本提案中描述的每个模型都包括流体力学表示，因此在它们的数学描述中有一个统一的元素。计算方法部分基于浸入边界法，并且计算机代码共享许多主要子程序。这一建议的一个重要方面是发展解决这些问题的并行数值方法；这一领域的进展可用于计算生物流体领域的各种问题。

Dillon0109957 The principal investigator and his colleagues developmathematical models and computational methods for analyzing themotion of eucaryotic cilia and flagella, the growth anddevelopment of the vertebrate limb bud and tumor growth. Theobjective of the cilia modeling is to develop three-dimensionalmodels for an individual cilium or flagellum and forthree-dimensional arrays of cilia. These models incorporatediscrete representations of the axoneme's ultrastructureincluding the individual dyneins and microtubules, as well as acontinuous description of the fluid mechanics using the immersedboundary method. Vertebrate limb development is a widely-usedmodel system for the study of development. The investigator andhis collaborators have developed a 2D model for vertebrate limbdevelopment that describes limb bud outgrowth and predicts thespatio-temporal distribution of growth factors and morphogens.The major goals of the limb development modeling are to furthervalidate the 2D model, to extend it to three dimensions in orderto determine what signals cells see as a function of theirposition in the three-dimensional limb bud and developmentalhistory and, from this, to suggest how the signals can beintegrated by cells to produce the observed spatial patterning.Limb development and tumor growth are moving boundary problemsthat involve tissue growth, the transport of growth factors andcontrol of gene activity. The investigators are developing animmersed boundary model for tumor growth along with the limbdevelopment model. These mathematical models focus on the complex biologicalsystems involved in cell motility, vertebrate development, andtumor growth. An important aspect is the development ofcomputational tools for the study of these processes. Thus, theciliary model is used for the computational study of dyneinactivation mechanisms in cilia and flagella and the multiciliarymodel for the study of mucociliary interaction. The vertebratelimb development model may be used as an aid in interpretingexperimental results, to help identify new experiments, and totest hypotheses that may be difficult to test experimentally.Because each of the models described in this proposal includes afluid-mechanical representation, there is a unifying element intheir mathematical description. The computational methods arebased in part on the immersed boundary method, and the computercodes share many of the major subroutines. An important aspect ofthis proposal is the development of parallel numerical methodsfor the solution of these problems; advances in this area can beused in a variety of problems in the field of computationalbiofluids.