CAREER: Multi-Scale Modeling of Biological Gels by Coupling Langevin Equations and Fractional Viscoelastic Constitutive Models

这项研究将确定重要生物流体的数学特性，这些流体影响各种过程，如从呼吸道清除粘液和在细胞分裂期间DNA在细胞核中的组织。日常生活中遇到的许多流体，如水、汽油和蜂蜜，都是人们熟知的(牛顿)流体，但许多与工业和生物应用相关的流体却不是。非牛顿流体的常见例子包括油漆、多级发动机油、洗衣清洁剂、儿科液体药物、肺粘液和细胞膜。非牛顿流体的一个显著特征是微观结构，这些结构可以在流动过程中显著地重新排列，从而随着时间的推移和环境之间的变化而改变行为。本研究的目的是建立生物软物质微观结构过程与流动特性之间的数学关系。目前在显微镜、流动测量、理论和计算方面的进展将导致新的模型，使科学家能够设计和测试下一代生物材料，并研究生物流动。本科生和研究生不仅能够学习如何设计和执行湿实验室实验，建立数学模型和执行高性能的计算模拟，而且还有机会与来自数学、生物、物理和生物医学科学的研究人员密切互动。南卡罗来纳州少数族裔参与联盟计划的STEM学生将被招募为新生，参加该项目支持的各种研究和教育活动。第二个项目是SC女性科学午餐会，将把女本科生和研究生聚集在一起，进行垂直整合的研究陈述、讨论和指导。这些教育努力将对培养下一代STEM科学家产生广泛影响，为他们跨越不同领域的职业生涯做好准备。许多非牛顿流体的一个显著特征是，它们具有微观或分子级结构，可以在流动中显著重新排列，从而改变材料的宏观行为或性能。本项目将重点研究在许多生物和工业领域普遍存在的幂定律流变学。新的数学关系将通过研究平衡软物质和远离平衡反应的软物质来建立，其中热涨落占主导地位。这些关系将受到实验结果的密切影响，并基于随机、积分-微分方程式和确定性、分数分式偏微分方程式的耦合。这些项目的成果包括对幂定律材料中宏观和微观动力学之间关系的新理解，新型线性和非线性本构方程，使用分数阶微积分描述非局域量的分析结果，生理条件下分数模型的数值模拟，以及对软物质微观结构的新实验见解。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。

This research will determine the mathematical properties of important biological fluids which influence processes as diverse as clearance of mucus from airways and the organization of DNA in the nucleus of cells during cell division. Many of the fluids encountered in everyday life, such as water, gasoline, and honey, are well-understood (Newtonian) fluids, but many of the fluids related to industrial and biological applications are not. Common examples of non-Newtonian fluids include paint, multi-grade engine oils, laundry detergent, pediatric liquid medicines, pulmonary mucus, and cell membranes. A distinguishing feature of non-Newtonian fluids is microscopic structures that can be rearranged significantly during flow and consequently alter behavior over time and between circumstances. The goal of this research is to establish mathematical relationships between microstructural processes and flow properties in soft biological matter. Current advances in microscopy, flow measurement, theory and computation will lead to new models, allowing scientists to design and test next-generation biomaterials and investigate biological flows. Undergraduate and graduate students will not only be able to learn how to design and perform wet-lab experiments, formulate mathematical models and perform high-performance computational simulations, but also have opportunities to closely interact with researchers from mathematics, biology, physics and biomedical sciences. STEM students from the South Carolina Alliance for Minority Participation program will be recruited as incoming freshmen to participate in a variety of research and educational activities supported by this project. A second program, the SC Women in Science Luncheon, will bring together female undergraduate and graduate students for vertically-integrated research presentation, discussion and mentoring. These educational efforts will have a broad impact on educating the next generation of STEM scientists, preparing them for careers that span the boundaries between different fields. A distinguishing feature of many non-Newtonian fluids is that they have microscopic or molecular-level structures that can be rearranged significantly in flow and as a consequence alter the macroscopic behavior or performance of the material. This project will focus on power-law rheology, which is ubiquitous in many biological and industrial fields. New mathematical relationships will be established by investigating soft matter both in equilibrium, where thermal fluctuations dominate, and for far-from-equilibrium responses. These relationships will be closely informed by experimental findings and are based on the coupling of stochastic, integro-differential equations and deterministic, fractional partial differential equations. The outcomes of these projects include a new understanding of the relation between macro- and micro-scale dynamics in power-law materials, new classes of linear and nonlinear constitutive equations, analytical results describing non-local quantities using fractional calculus, numerical simulations of fractional models under physiological conditions, and new experimental insights into the microstructure of soft matter.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.