Mathematical Problems at the Interface between Materials Science and Biology: Polyelectrolyte gels, Devices and Physiological Applications

该奖项将支持数学、凝聚态物理、连续介质力学和生物学的跨学科研究。这部作品的一个主要主题是研究生命系统中的力。PI将从材料科学的角度出发，首先分析半柔性生物聚合物系统。它们是各向异性聚电解质凝胶，由具有方向偏置和带电的弹性网络组成，使流体与离子保持在一起。该项目首先提出了这样一个问题：组合的弹性各向异性(模拟为液晶弹性体的情况)、静电和短程Van-der-Waals相互作用如何解释半柔性聚合物中的负Poynting效应等现象。下一阶段的研究包括对间质组织进行建模。这是一种聚电解质凝胶，支持大的杆状蛋白质结构，使网络具有各向异性。一个主要的目标是建立水肿的模型，以解释限制患者间质组织中多余液体的巨大力量。数学问题被表述为源于混合理论的偏微分方程组。具体地说，它们包括液晶弹性体的含时方程和流体的Stokes问题，以及离子的Nernst-Planck方程。这项新的研究将部分遵循PI和合著者之前关于各向同性聚电解质凝胶的工作，但必须开发新的数学和建模工具。这些新工具还将被用于模拟癌细胞在纤维组织上的动力学。这项研究将是合作的，包括PI和来自数学、物理、生物科学和工程的教职员工，以及工业合作伙伴，以及博士后、研究生和本科生。这个奖项将支持旨在研究维持生命结构的力量的研究。PI将专注于对连接器官、血管和骨骼的间质组织进行建模。特别是，这项研究将试图了解间质组织中异常大量液体滞留的物理原理，这种情况被称为浮肿。这项工作是与明尼苏达大学医学院肾脏研究所的研究人员以及明尼阿波利斯的一家生物科学公司联合开展的，可能有助于推动对新疗法的探索。这些模型还将支持对癌细胞动力学的研究，目标是对肿瘤成核开始的生物力学方面进行建模。该奖项将支持来自数学、物理、生物科学和工程的教职员工以及本科生(数学、物理和生物科学)、博士后和研究生参与的合作研究。

This award will support interdisciplinary research in mathematics, condensed matter physics, continuum mechanics and biology. A main theme of the work is the study of forces in living systems. The PI will take the point of view of materials science, and analyze, first, semi-flexible, biopolymer systems. These are anisotropic polyelectrolyte gels and consist of directionally biased and electrically charged elastic networks holding fluid with ions. The project starts out woith the question how the combined elastic anisotropy (modeled as in the case of liquid crystal elastomers), electrostatic and short range Van-der-Waals interactions may explain phenomena such as the negative Poynting effect in semi-flexible polymers. The next stage of the research consists in modeling the interstitial tissue. This is a polyelectrolyte gel sustaining large, rod-like protein structures that make the network anisotropic. One main goal is the modeling of edema, in order to explain the large forces that confine the excess fluid in the interstitial tissue of patients. The mathematical problems are formulated as systems of partial differential equations stemming from mixture theory. Specifically, these consist of the time-dependent equations of liquid crystal elastomers coupled with Stokes problems for fluids, and with the Nernst-Planck equations for ions. The new research will partially follow previous work on isotropic polyelectrolyte gels by the PI and coauthors, but new mathematical and modeling tools have to be developed. These new tools will also be applied to modeling the dynamics of cancer cells on fiber tissue. The research will be collaborative, involving the PI and faculty members from mathematics, physics, bioscience and engineering, as well as industrial partners, together with postdocs and graduate and undergraduate students.This award will support research aimed at the study of forces that hold living structures together. The PI will focus on modeling interstitial tissue that connects organs, vessels and bone. In particular, the research will try to understand the physical principles underlying the trapping of unusually large amounts of liquid in the interstitial tissue, a condition known as edema. The work, jointly carried out with researchers at the Kidney Institute of the Medical School of the University of Minnesota and with a Minneapolis biosciences company, may help motivate the search for new therapies. These models will also support research on cancer cell dynamics, with the goal of modeling biomechanical aspects of the onset of tumor nucleation. The award will support collaborative research involving faculty members from mathematics, physics, bioscience and engineering, together with undergraduate students (math, physics and biosciences), postdocs and graduate students.