Modeling, Simulation and Validation of Transport at Interfaces in Lipid Membranes and Enantiomer Separation

脂质膜界面传输和对映体分离的建模、模拟和验证

• 批准号: 166954264
• 负责人: Professor Dr. Thomas Franke
• 金额: --
• 依托单位: Lehrstuhl für Angewandte Analysis mit Schwerpunkt Numerische Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/166954264?language=en
• 关键词: Modeling; Simulation; Validation; Transport; Interfaces

This project is about the dynamics and formation of differently ordered phases in lipid layers and the separation of chiral objects (so-called enantiomers) in such layers. Under natural conditions, cell membranes, which are made up of a lipid bilayer, can be thought of as a binary fluid. The two phases arise as saturated and unsaturated lipids and tend to organize in domains in the presence of cholesterol. In fact, the phase diagram for ternary systems exhibits different phases such as homogeneous liquid and gel phases as well as liquid-liquid and liquid-gel coexistence. These phase separation phenomena are not restricted to bilayer systems but also occur in lipid monolayers, which are easily accessible to experimental observations and control. Several different types of patterns have been observed, such as hexagonal structures and domains formed in the separation process that are chiral, i.e, domains which only differ by their handedness. The dynamics and the separation of the phases depends on various mechanisms such as temperature, viscosities, line tension, curvature and the presence of charged lipids. The first central aim of this project is to systematically study the impact of these mechanisms by providing appropriate mathematical models that will be validated through extensive numerical simulations and experimental measurements. The experimental setup allows to investigate the separation process in flat or almost flat monolayers as well as in curved lipid bilayers. Both setups will be considered in a unified modeling approach using the framework of Allen-Cahn/Cahn-Hilliard type equations. Numerical simulations will be done based on finite element methods and on level set methods for the evolution of geometric flows. The separation of enantiomers by their chirality is an important process in many industries such as pharmaceutical, food, flavor, and fragrance. Most of the currently available separation techniques are costly and do not provide information about the dynamics of the separation process. However, it has recently been suggested to separate chiral objects by exposing them to specific flow fields created by piezoelectrically agitated surface acoustic waves (SAW). This technique, which already has been successfully used for generating flow fields in microfluidic biochips, is not only cost-effective but also has the potential for an extremely high time resolution of the dynamics of the separation process. The second central aim of this project is to model, simulate, and validate models of a setup, in which enantiomers are separated in lipid membranes by creating a flow field in the fluid below the membrane using SAW. This is supposed to be considered for several lithographically produced rigid chiral objects floating on the membrane as well as for elastic domains within the membrane which have been formed in the separation process. These investigations eventually result in the realization and understanding of molecular enantiomer separation. We can rely on a profound experience in the experimental investigation, the mathematical modeling, and numerical simulation of SAW driven microfluidic biochips and in the motion and deformation of viscoelastic objects under the influence of fluid flows in microchannels. In particular, for enantiomer separation and the motion/deformation of elastic domains in the membrane we will use fictitious domain/Lagrange multiplier techniques and finite element immersed boundary methods.

这个项目是关于脂层中不同有序相的动力学和形成，以及在这样的层中手性物体(所谓的对映体)的分离。在自然条件下，由脂质双层组成的细胞膜可以被认为是一种二元流体。这两个阶段以饱和和不饱和脂质的形式出现，在胆固醇存在的情况下倾向于在区域中组织。事实上，三元体系的相图显示出不同的相，如均相液体和凝胶相，以及液-液和液-凝胶共存。这些相分离现象不仅限于双层体系，而且也发生在脂类单层中，这很容易被实验观察和控制。已经观察到了几种不同类型的图案，例如在分离过程中形成的六方结构和结构域是手性的，也就是说，结构域只是因为它们的左手不同而不同。相的动力学和分离取决于不同的机制，如温度、粘度、线张力、曲率和带电类脂的存在。该项目的第一个中心目标是通过提供适当的数学模型来系统地研究这些机制的影响，这些模型将通过广泛的数值模拟和实验测量得到验证。该实验装置允许研究在平坦或几乎平坦的单层膜以及弯曲的脂类双层中的分离过程。将在使用Allen-Cahn/Cahn-Hilliard类型方程框架的统一建模方法中考虑这两种设置。将基于有限元方法和水平集方法对几何流动的演化进行数值模拟。手性拆分对映体在医药、食品、香料、香料等行业中具有重要的应用价值。目前可用的大多数分离技术都很昂贵，并且不能提供有关分离过程动态的信息。然而，最近有人建议通过将手性对象暴露在由压电搅拌表面声波(SAW)产生的特定流场中来分离手性对象。这项技术已经成功地用于在微流控生物芯片中产生流场，不仅具有成本效益，而且有可能对分离过程的动力学进行极高的时间分辨率。这个项目的第二个中心目标是模拟、模拟和验证装置的模型，在该装置中，通过使用SAW在膜下的流体中创建流场来在脂膜中分离对映体。这应该被考虑到漂浮在膜上的几个光刻产生的刚性手性物体，以及在分离过程中形成的膜内的弹性域。这些研究最终导致了人们对分子对映体分离的认识和理解。在声表面波驱动的微流控生物芯片的实验研究、数学建模和数值模拟方面，以及在流体在微通道中流动的影响下，粘弹性物体的运动和变形方面，我们可以依靠丰富的经验。特别是，对于膜中对映体的分离和弹性域的运动/变形，我们将使用虚拟域/拉格朗日乘子技术和有限元浸没边界方法。