Mathematical Modeling of Robust Spatiotemporal Dynamics in Epidermal Development

表皮发育中鲁棒时空动力学的数学模型

• 批准号: 1853636
• 负责人: Huijing Du
• 金额: $ 17.92万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1853636&HistoricalAwards=false
• 关键词: Mathematical; Modeling; Robust; Spatiotemporal; Dynamics

The project will develop a new generation of multiscale and stochastic models capable of integrating experimental data to study mouse epidermal development that includes chemical regulation and mechanical aspects of the system in a mechanistic, data-informed manner. Epidermal morphogenesis, which occurs during the second half of embryogenesis, is the developmental process that generates a skin permeability barrier essential for terrestrial survival. Defects with this barrier are associated with common skin disorders such as atopic dermatitis. Study of mechanisms that control epidermal development and differentiation is therefore highly relevant to human health. Comprehensive knowledge about adult epidermal homeostasis and regeneration, as well as adult epidermal stem cell biology, has been accumulated for decades. However, embryonic development of the epidermis, especially in the early period, still needs exploration. The overall goal of this project is to help address this knowledge gap by developing mathematical results and tools to unravel critical mechanisms underlying epidermal development that are generally applicable to multiple organisms and differentiation/developmental processes. The project will involve close multi-disciplinary interactions among students and researchers in the fields of biology, mathematics, statistics, and engineering cross colleges and universities in Nebraska with a commitment to enhancing the recruitment and support of female and underrepresented minority students.The project will investigate mechanical, chemical, and gene regulatory processes in a comprehensive modeling platform to understand how these processes influence epidermal development and its defects that may lead to an improved understanding of skin and other epithelial systems such as the tongue, esophagus, stomach, and the olfactory epithelium. Interactions among three major biological scales will be investigated: transcription factors within a cell, individual cells of different fates (or different intracellular states), and the epidermis consisting of many cells and diffusive regulatory molecules secreted from the cells. In order to do this, the project will first develop a 3D spatial multiscale model based on a novel anisotropic subcellular element method to account for structural aspects of the epidermis for self-organization. The project will then use a hybrid model consisting of a non-spatial cell lineage model with several cell stages and the spatial model to investigate the coupling of the biochemical and dynamical mechanisms of the organization with stochasticity that accounts for stochastic gene regulation and the interplay between gene regulation and extracellular signaling profile of the epidermis. Existing data where available will be used to inform model development, and the results will identify experiments capable of probing the mechanism responsible for robust epidermal organization. The project will also develop a new unified computational toolkit for modeling and simulating the interplay between discrete cells, biochemical signaling, gene regulation, and continuum mechanics that will have broad applications. This project is jointly funded by the Math Biology Program of the Division of Mathematical Sciences (DMS) and the Established Program to Stimulate Competitive Research (EPSCoR).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.

该项目将开发新一代多尺度和随机模型，能够整合实验数据，以研究小鼠表皮发育，包括系统的化学调节和机械方面的机械，数据知情的方式。表皮形态发生在胚胎发生的后半期，是产生陆地生存所必需的皮肤渗透屏障的发育过程。这种屏障的缺陷与常见的皮肤病如特应性皮炎有关。因此，研究控制表皮发育和分化的机制与人类健康高度相关。关于成人表皮稳态和再生以及成人表皮干细胞生物学的全面知识已经积累了几十年。然而，表皮的胚胎发育，特别是早期，仍需要探索。该项目的总体目标是通过开发数学结果和工具来帮助解决这一知识差距，以揭示通常适用于多种生物体和分化/发育过程的表皮发育的关键机制。该项目将涉及内布拉斯加州跨学院和大学的生物学，数学，统计学和工程学领域的学生和研究人员之间的密切多学科互动，致力于加强女性和代表性不足的少数民族学生的招聘和支持。该项目将调查机械，化学，和基因调控过程，以了解这些过程如何影响表皮发育及其缺陷，这可能会导致对皮肤和其他上皮细胞的更好理解。系统，如舌、食道、胃和嗅觉上皮。将研究三个主要生物尺度之间的相互作用：细胞内的转录因子，不同命运（或不同细胞内状态）的单个细胞，以及由许多细胞和从细胞分泌的扩散调节分子组成的表皮。为了做到这一点，该项目将首先开发一个基于新的各向异性亚细胞单元方法的3D空间多尺度模型，以解释表皮自组织的结构方面。然后，该项目将使用由具有几个细胞阶段的非空间细胞谱系模型和空间模型组成的混合模型来研究组织的生化和动力学机制与随机性的耦合，该随机性解释了随机基因调控以及基因调控与表皮细胞外信号传导谱之间的相互作用。现有的数据将用于通知模型开发，结果将确定能够探测负责强大的表皮组织的机制的实验。该项目还将开发一个新的统一计算工具包，用于建模和模拟离散细胞，生化信号，基因调控和连续介质力学之间的相互作用，将具有广泛的应用。该项目由数学科学部（DMS）的数学生物学项目和刺激竞争性研究的既定项目（EPSCoR）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价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes

• DOI: 10.1007/s10915-019-01073-3
• 发表时间: 2019-11
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: H. Du;Yingjie Liu;Yuan Liu;Zhiliang Xu