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

这个项目是关于脂质层中不同有序相的动力学和形成，以及这些层中手性物体（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。这两个相以饱和脂质和不饱和脂质形式出现，并且在存在胆固醇的情况下倾向于在结构域内组织。事实上，三元体系的相图表现为均相液相和凝胶相以及液-液和液-凝胶共存。这些相分离现象不仅局限于双层系统，而且也发生在脂质单层中，这很容易获得实验观察和控制。已经观察到几种不同类型的模式，例如六角形结构和在分离过程中形成的手性结构域，即仅以手性不同的结构域。动力学和相的分离取决于各种机制，如温度、粘度、线张力、曲率和带电脂质的存在。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进行验证。实验装置允许研究在平坦或几乎平坦的单层以及弯曲的脂质双层中的分离过程。这两种设置将在使用Allen-Cahn/Cahn-Hilliard型方程框架的统一建模方法中进行考虑。数值模拟将基于有限元方法和水平集方法进行几何流动的演化。利用手性分离对映体在制药、食品、香精、香料等行业中具有重要的应用价值。目前大多数可用的分离技术都是昂贵的，并且不能提供有关分离过程动力学的信息。然而，最近有人建议通过将手性物体暴露在由压电振动表面声波（SAW）产生的特定流场中来分离它们。这项技术已经成功地用于在微流体生物芯片中产生流场，它不仅具有成本效益，而且具有分离过程动力学的极高时间分辨率的潜力。该项目的第二个中心目标是建模、模拟和验证一种装置的模型，在这种装置中，通过在膜下的流体中使用SAW创建流场，对映体在脂质膜中分离。对于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，应该考虑到这一点。这些研究最终导致了分子对映体分离的实现和理解。我们在SAW驱动的微流控生物芯片的实验研究、数学建模和数值模拟以及微通道中流体流动影响下粘弹性物体的运动和变形方面具有丰富的经验。特别是，对于对映体分离和膜中弹性域的运动/变形，我们将使用虚拟域/拉格朗日乘子技术和有限元浸入边界方法。

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.