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操作的生化微反应器。 该项目旨在开发有效的计算模型和数值工具，用于模拟囊泡动力学，其中涉及相分离，隔室的形成以及囊泡与其水环境之间的相互作用。 预期该结果有助于囊泡表面上相域的设计，使得特定蛋白质可以锚在膜上以引发随后的生物反应。 该项目旨在为构建具有多个隔室的人工细胞的研究前沿做出贡献。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制剂。该项目将为学生创造机会，接受跨学科的培训，跨越数学，生物和物理科学。该项目解决了数学建模和数值模拟的挑战，三维多组分和多隔室囊泡在复杂的流动域使用尖锐的界面方法。在连续介质水平上，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，其中双层膜作为移动边界。基本的数学特征是，该系统有效地耦合表面相动力学，形态演变和车厢的形成，和流体运动，使该模型描述了一个更现实的物理系统比以前在文献中已经开发。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间的存在如何修改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。该项目还将研究应用流中多室囊泡的形态稳定性，以及使用多个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.