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Geometric evolution towards the understanding of biomembranes

理解生物膜的几何进化

基本信息

批准号：
32787769
负责人：
Professor Dr. Axel Voigt
金额：
--
依托单位：
Professur für Wissenschaftliches Rechnen und Angewandte Mathematik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2006
资助国家：
德国
起止时间：
2005-12-31 至 2012-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/32787769?language=en
关键词：
Geometric evolution towards understanding biomembranes

项目摘要

Biological membranes are a mixture of many different types of lipids and protein components, and their relative amount and composition differ between functionally distinct domains. The strongly increasing interest in lipid membranes results from the hypothesized coupling of lipid phase segregation in the membrane to fundamental cell biological processes, such as membrane signaling and trafficing [1]. Sub-domains of distinct curvature may have precise biological properties [2], thus an understanding how lipid components can dynamically influence to membrane morphology is of utmost importance. Changes in lipid composition are assumed to assist or antagonize the membrane curvature on one side, but also might respond to the curvature by concentrating in domains of curvature that they prefer on the other side. Strong curvature variations have recently been observed experimentally in giant liposomes, where different lipids segregate according to their chemical properties and lead to the formation of buds [3, 4]. The strong coupling of phase separation and shape dynamics in lipid membranes has also been shown numerically by molecular dynamics [5] and Monte Carlo simulations [6]. Such atomistic simulations however are limited in the accessible length and time scales. With the curvature as one of the crucial ingredients to determine properties of membranes it seems natural to model the evolution within a continuum framework. This is further justified by the different length scales which come into play. The thickness of the membrane is in the nm-range, while a typical size of a biomembrane is in the µm-range. This length scale separation allows the biomembrane to be described as an elastic surface [7], which is the basis for our treatment. Within such a continuum description the observed budding in multicomponent lipid bilayers can be understood, by the possibility to reduce the line energy associated with the domain boundaries by budding these domains [8], an additional degree of freedom which is not present for phase separation processes in the bulk. A dynamic simulation of multicomponent biomembranes on a continuum level however is until now limited to small deformations or special shapes [9, 10, 11], which is due to the high-order nonlinear terms in the governing equations to describe the phase separation and domain formation on evolving surfaces. We propose to study the dynamics of the interactions between membrane structure, domain formation and shape deformation within a mathematical model for lipid bilayer biomembranes which will overcome this limitations. A thermodynamically consistent model will be derived, which mathematically leads to a higher order evolution equation on an evolving surface. We will consider various numerical approaches for such problems, including combined front-tracking and phase-field models, combined level-set and phasefield models and fully phase-field model to consider the evolution of the surface combined with the phase-separation on the surface. All approaches will use adaptive finite elements and multilevel techniques. Parallelization furthermore will allow to solve the highly nonlinear system in 3d in a reasonable amount of time and to answer questions concerning the long time behavior.

生物膜是许多不同类型的脂质和蛋白质组分的混合物，并且它们的相对量和组成在功能不同的结构域之间不同。对脂质膜的兴趣日益增加，这是由于膜中脂质相分离与基本细胞生物学过程（如膜信号传导和运输）的假设偶联[1]。不同曲率的子域可能具有精确的生物学特性[2]，因此了解脂质组分如何动态影响膜形态至关重要。脂质组成的变化被认为是帮助或拮抗一侧的膜曲率，但也可能通过集中在他们喜欢的另一侧的曲率域来响应曲率。最近在实验中观察到巨大脂质体中的强曲率变化，其中不同的脂质根据其化学性质分离并导致芽的形成[3，4]。脂膜中相分离和形状动力学的强耦合也已通过分子动力学[5]和Monte Carlo模拟[6]数值显示。然而，这种原子模拟在可访问的长度和时间尺度上是有限的。由于曲率是决定膜性质的关键因素之一，因此在连续体框架内模拟进化似乎是很自然的。这是进一步证明了不同的长度尺度发挥作用。膜的厚度在nm范围内，而生物膜的典型尺寸在μ m范围内。这种长度尺度的分离允许将生物膜描述为弹性表面[7]，这是我们处理的基础。在这样的连续描述中，可以通过使这些结构域出芽来降低与结构域边界相关的线能量的可能性来理解在多组分脂质双层中观察到的出芽[8]，这是本体中的相分离过程不存在的额外自由度。然而，到目前为止，在连续体水平上对多组分生物膜的动态模拟仅限于小变形或特殊形状[9，10，11]，这是由于控制方程中的高阶非线性项描述了演化表面上的相分离和域形成。我们建议研究膜结构，域形成和形状变形之间的相互作用的动力学在一个数学模型的脂质双层生物膜，这将克服这种局限性。将导出一个物理上一致的模型，该模型在数学上导致在演化表面上的高阶演化方程。我们将考虑这些问题的各种数值方法，包括结合前沿跟踪和相场模型，结合水平集和相场模型和完全相场模型，以考虑表面的演变与表面上的相分离。所有的方法将使用自适应有限元和多级技术。此外，网格化将允许在合理的时间内解决3D中的高度非线性系统，并回答有关长期行为的问题。