Deformation, Phase Segregation and Adhesion of Lipid-Bilayer Vesicles

BhattacharyaDMS-0606667 研究者试图研究描述脂质双层膜的形状、相分布和粘附的平衡和演变的偏微分方程。 形状、成分分布和压力之间的复杂相互作用使这些膜能够经历各种成分和有序相关的相变，从而导致复杂的微观结构。 这些反过来又影响膜的功能。 双层膜的力学、相分离和粘附的实验研究是一个非常活跃和迷人的领域。 一些考虑不同方面和不同近似的理论模型和研究开始出现。这是一个系统的数学分析的阶段，它可以确定不同模型之间的关系，了解各种近似的状态，并绘制不同参数和行为状态的地图。这种数学分析是这个项目的目的。 调查人员不仅寻求编目和协调可用的实验观察，但希望通过指出潜在的有趣区域来激励新的实验和新现象的发现。 该项目建立在并扩展了一类数学问题，涉及扩散，相变和图案的形成，已被研究在平坦的空间，在材料科学问题的动机，到一类新的问题，涉及这些现象的变形流形。 调查员开始与一个充满活力的formulationof单相膜，并得出限制理论usingformal（匹配渐近）和严格（伽玛收敛）的方法。 然后，他认为多物种膜和识别的情况下，当有强烈的相分离，研究成核稳定性的考虑，并derivessharp界面模型。 演化问题被视为适当能量的梯度流. 最后，他研究了这种分析对细胞粘附的影响。 脂双层膜在生物体中普遍存在，如细胞壁、线粒体、高尔基体和许多其他重要的细胞器。 它们在生物学中起着至关重要的作用，因为它们通过形成各种复杂的形状和结构来保护，调节流动和主持许多代谢功能。 该项目旨在促进我们对这些膜的形状和成分分布的因素的理解。它通过建立基于现有观测的数学模型并使用数学分析来探索这些模型的完整性来实现。 该项目提供了一个博士生在这个关键的和新兴的跨学科领域的培训。 学生接受训练，并使用现代数学分析方法，但也接触到生物学实验和力学与材料科学理论。 该项目还培训了三名暑期本科研究生。

BhattacharyaDMS-0606667 The investigator seeks to study partial differentialequations that describe the equilibrium and evolution of theshape, phase distribution, and adhesion of lipid bilayermembranes. An intricate interaction between the shape, thecomposition distribution, and pressure enable these membranes toundergo a variety of composition- and ordering-related phasetransformations resulting in complex microstructure. These inturn affect the function of the membrane. The experimental studyof the mechanics, phase segregation, and adhesion of bilayermembranes is an extremely active and fascinating field. A numberof theoretical models and studies that consider different aspectsand different approximations are beginning to emerge. This hasset the stage for a systematic mathematical analysis thatexamines the relationship between the different models,understands the status of the various approximations, and yieldsa mapping of the different parameter and behavioral regimes. This mathematical analysis is the aim of this project. Theinvestigator seeks not only to catalog and reconcile availableexperimental observations but hopes to motivate new experimentsand the discovery of new phenomena by pointing out potentiallyinteresting regions. The project builds on and extends the classof mathematical problems involving diffusion, phasetransformation, and pattern formation that has been studied inflat spaces, motivated by issues in materials science, to a newclass of problems that involve these phenomena on deformablemanifolds. The investigator starts with an energetic formulationof the single phase membrane and derives limiting theories usingboth formal (matched asymptotic) and rigorous (Gamma convergence)methods. He then considers multi-species membranes andidentifies circumstances when there is strong phase separation,studies nucleation from stability considerations, and derivessharp interface models. Evolutionary problems are treated asgradient flows of appropriate energy. Finally, he studies theimplications of this analysis for cell adhesion. Lipid bilayer membranes are ubiquitous in living organismsas cell walls, mitochondria, golgi apparatus, and numerous otherimportant organelles. They play a critical role in biology asthey protect, regulate flow, and host many metabolic functions byforming a variety of complicated shapes and structures. Thisproject seeks to advance our understanding of the factors thatgovern the shape and composition distribution of these membranes. It does so by building mathematical models based on existingobservations and using mathematical analysis to explore the fullimplications of these models. The project provides for thetraining of a doctoral student in this critical and emerginginterdisciplinary area. The student is trained in and usescontemporary methods of mathematical analysis, but also isexposed to experiments in biology and theories in mechanics andmaterials science. The project also trains three summerundergraduate research students.