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

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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.