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复杂生物系统（如细胞和微胶囊）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操作的生化微反应器。本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，包括相分离、室的形成以及囊泡与水环境之间的相互作用。这些结果有望帮助设计囊泡表面的相域，使特定的蛋白质可以锚定在膜上，以启动随后的生物反应。该项目旨在为构建具有多个隔间的人造细胞的研究做出贡献。该研究还推进了生物膜力学和颗粒流动背景下的数值方法发展，分析理论和积分方程公式。该项目将为学生创造机会，让他们接受数学、生物和物理科学的跨学科训练。该项目利用锐界面方法解决了复杂流域中三维多组分和多室囊泡的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以双层膜为运动边界的高度非线性、非局部运动边界问题。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，因此该模型描述了比以前文献中开发的更真实的物理系统。研究人员开发和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，并与实验人员一起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隔室的存在如何改变经典运动和流体动力相互作用，并可能导致新的动力机制。该项目还将研究应用流中多室囊泡的形态稳定性，以及使用多表面相优化复杂流域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.