Amphiphilic Morphology: Lipids, Proteins, and Entropy

该项目开发了多组分类脂膜与油和蛋白质相互作用的新数学模型。脂膜是构成许多蛋白质的隔离壁、管道和集合点的细胞结构的基本构件。这项工作将由一个由数学家和植物生物学家组成的跨学科团队进行，重点是根据多组分脂质模型的预测来验证对脂滴的实验观察。脂滴对公众健康具有重要意义，因为它们是代谢综合征发病的信号，代谢综合征与肝脏内小脂肪包裹体(脂滴)的发展有关。油籽和藻类中的脂滴被用作储能隔间，以提高生物质的能量含量。该提案的数学元素确定了脂类结构重排中的关键瓶颈，以及在更高维度系统内创建和破坏最低能量路径，这些路径对应于有助于观察到的自组装结构的脂类和油的最佳包装。该项目对自由能的结构进行了详细的分析，这些自由能支配着代表两亲性形态的低能连接和作为重组最低成本的高能垒。PI和他的合作者研究了一个中心论点，即两亲性分子堆积的熵的主要表现在于这个连接问题的结构。基于包装的能量景观是强非线性的，与建立在Cahn Hilliard框架上的更弱的非线性混合模型有根本的不同。基于堆积的能量将通过脂滴的体外实验进行验证，脂滴是由界面竞争驱动的双流体两亲性系统的典型例子，并与自洽平均场理论模型的短链极限得到的熵描述进行比较。具体地说，该方案使用空间动力学和奇异摄动技术来发展稳健的珍珠抑制，以稳定连接的珍珠模式，并通过分段定义和奇异摄动的动力系统方法来调节因式Melnikov结构中连接和势垒的存在和持久性。脂滴形成的双流体模型将用于研究夹断和合并事件，而一个流体模型将解决相分离(漂流)和局部珍珠现象。这些模型将通过比较从两亲性混合物的自洽平均场模型中提取的熵效应、脂滴的体外实验形态以及合成两亲性聚合物铸件的分叉图来验证。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project develops new mathematical models of the interactions of multicomponent lipid membranes with oils and proteins. Lipid membranes are fundamental building blocks of cellular structure forming the separating walls, the plumbing, and the assembly points for many proteins. The work will be conducted by an interdisciplinary team of mathematicians and plant biologists and will focus on validating experimental observations of lipid droplets against predictions of the multicomponent lipid models. Lipid droplets are of significance to public health for their role as a signal of the onset of metabolic syndrome, which has a correlation with the development of small fatty inclusions (lipid droplets) within the liver. Lipid droplets are being pursed in oil seeds and algae as energy storage compartments to improve the energy content of the biomass. The mathematical elements of the proposal identify key bottlenecks within the rearrangement of lipid structures with the creation and destruction of minimal energy pathways within a higher dimensional system, these pathways correspond to optimal packings of lipids and oil that contribute to the observed self-assembled structures. The project presents a detailed analysis of the structure of the free energy governing the low energy connections that represent amphiphilic morphologies and high energy barriers that are the minimal cost of reorganization. The PI and his collaborators investigate the central thesis that the dominant manifestation of the entropy of packing of amphiphilic molecules lies in the structure of this connection problem. Packing-based energy landscapes are strongly nonlinear, and fundamentally distinct from the more weakly nonlinear mixture-based models built upon the Cahn Hilliard framework. The packing-based energy will be validated against in-vitro experiments on lipid droplets, the prototypical example of a two-fluid amphiphilic system driven by interfacial competition, and are compared with entropic descriptions derived from short- chain limits of self-consistent mean field theory models. Specifically, the proposal uses spatial dynamics and singular perturbation techniques to develop robust pearling inhibition that stabilizes the pearling modes of connections, and tunes the existence and persistence of connections and barriers within factored Melnikov structure via piecewise defined and singularly perturbed dynamical system approaches. The two fluid model of lipid droplet formation will be used to investigate pinch-off and merging events while one fluid models address phase separation (rafting) and localized pearling. The models will be validated by comparison to entropic effects extracted from self-consistent mean field models of amphiphilic blends, to in-vitro experimental morphology of lipid droplets, and to the bifurcation diagram for castings of synthetic amphiphilic polymers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.