Collaborative Research: Modeling and Computation of Three-Dimensional Multicomponent Vesicles in Complex Flow Domains

长期以来，囊泡一直被认为是研究细胞和微胶囊等复杂生物系统基础物理的模型系统。 此外，囊泡越来越多地被用作药物递送的载体或在生理环境中运行的生化微反应器。 该项目旨在开发有效的计算模型和数值工具来模拟囊泡动力学，其中涉及相分离、区室的形成以及囊泡与其水环境之间的相互作用。 研究结果预计将有助于设计囊泡表面的相域，以便特定的蛋白质可以锚定在膜上以启动后续的生物反应。 该项目旨在为构建具有多个隔室的人造细胞的前沿研究做出贡献。该研究还推进了生物膜力学和颗粒流背景下的数值方法开发、分析理论和积分方程公式。该项目将为学生创造接受数学、生物和物理科学跨学科培训的机会。该项目解决了使用锐接口方法对复杂流域中的三维多组分和多室囊泡进行数学建模和数值模拟的挑战。在连续体水平上，囊泡动力学的数学描述是一个高度非线性、非局部的移动边界问题，其中双层膜充当移动边界。基本的数学特征是，该系统有效地耦合了表面相动力学、形态演化和隔室形成以及流体运动，使得该模型描述了比先前文献中开发的更真实的物理系统。研究人员开发并应用最先进的自适应数值方法，对重要的组成过程进行分析、数值和建模研究，并与实验人员合作测试模型预测并帮助阐明潜在的物理过程。该项目将研究表面相和多个隔室的存在如何改变经典运动和流体动力学相互作用，并可能导致新的动力学机制。该项目还将研究多室囊泡在应用流动中的形态稳定性，以及使用多个表面相来优化复杂流动域中的稳定性的可能控制策略。

Vesicles have long been considered as model systems for studying fundamental physics underlying complicated biological systems such as cells and microcapsules. Additionally, vesicles are increasingly being used as carriers for drug delivery or as biochemical micro-reactors operating in physiological environments. This project aims to develop efficient computational models and numerical tools for modeling of vesicle dynamics, which involves phase separation, formation of compartments, and interactions among vesicles and their aqueous environment. The results are expected to aid in the design of phase domains on the surface of a vesicle such that specific proteins can anchor on the membrane to initiate subsequent biological reactions. The project aims to contribute to the forefront of research on constructing artificial cells with multiple compartments. The research also advances numerical method development, analytical theory, and integral equation formulations in the context of bio-membrane mechanics and particulate flows. The project will create opportunities for students to receive interdisciplinary training crossing the mathematical, biological, and physical sciences.This project addresses the challenges of mathematically modeling and numerically simulating three-dimensional multi-component and multi-compartment vesicles in complex flow domains using sharp interface methods. At the continuum level, the mathematical description of vesicle dynamics is a highly nonlinear, nonlocal moving boundary problem where the bilayer membrane serves as the moving boundary. The fundamental mathematical feature is that this system effectively couples surface phase dynamics, morphological evolution and compartment formation, and fluid motion so that the model describes a more realistic physical system than has been developed previously in the literature. The investigators develop and apply state-of-the-art adaptive numerical methods, perform analytical, numerical and modeling studies of important constituent processes, and work with experimentalists to test the model predictions and to help elucidate the underlying physical processes. The project will investigate how the presence of surface phases and multiple compartments modifies the classical motions and hydrodynamic interactions and may lead to novel dynamical regimes. The project will also investigate the morphological stability of multi-compartment vesicles in applied flows, and possible control strategies using multiple surface phases for optimizing stability in complex flow domains.