Amphiphilic Morphology: Lipids, Proteins, and Entropy

两亲形态：脂质、蛋白质和熵

• 批准号: 1813203
• 负责人: Keith Promislow
• 金额: $ 30.09万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1813203&HistoricalAwards=false
• 关键词: Amphiphilic; Morphology; Lipids; Proteins; Entropy

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.

该项目开发了多组分脂质膜与油和蛋白质相互作用的新数学模型。脂质膜是细胞结构的基本组成部分，形成了许多蛋白质的分离壁、管道和组装点。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，重点是验证脂滴的实验观察结果与多组分脂质模型的预测。脂滴作为代谢综合征发病的信号，对公共卫生具有重要意义，代谢综合征与肝脏内小脂肪内含物（脂滴）的发展相关。油籽和藻类中的脂滴被用作能量储存室，以提高生物质的能量含量。该提案的数学元素确定了脂质结构重排中的关键瓶颈，并在更高维度的系统中创建和破坏最小能量途径，这些途径对应于脂质和油的最佳包装，有助于观察到的自组装结构。 该项目详细分析了自由能的结构，这些自由能控制着代表两亲形态的低能连接和作为重组成本最低的高能势垒。PI和他的合作者研究的中心论点是，两亲分子堆积熵的主要表现形式在于这种连接问题的结构。包装为基础的能源景观是强非线性的，从根本上不同于更弱的非线性混合模型建立在Cahn Hilliard框架。包装为基础的能源将验证对脂滴的体外实验，由界面竞争驱动的两种流体的两亲性系统的典型例子，并与熵的描述来自自洽平均场理论模型的短链限制进行比较。具体而言，该建议使用空间动力学和奇异摄动技术来开发鲁棒的珍珠抑制，稳定珍珠模式的连接，并通过分段定义和奇异摄动动力系统方法调整因子化Melnikov结构内的连接和障碍的存在性和持久性。脂滴形成的两种流体模型将用于研究夹断和合并事件，而一种流体模型解决相分离（漂流）和局部珍珠化。该模型将通过比较两亲性共混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，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

项目成果

Weak solutions for the functionalized Cahn–Hilliard equation with degenerate mobility

• DOI: 10.1080/00036811.2019.1585536
• 发表时间: 2019-03
• 期刊: Applicable Analysis
• 影响因子: 1.1
• 作者: Shibin Dai;Qiang Liu;K. Promislow

Competition and complexity in amphiphilic polymer morphology

• DOI: 10.1016/j.physd.2019.06.010
• 发表时间: 2017-11
• 期刊: Physica D: Nonlinear Phenomena
• 作者: A. Christlieb;Noa Kraitzman;K. Promislow

Codimension one minimizers of highly amphiphilic mixtures

高两亲性混合物的余维一最小化剂

• DOI: 10.1016/j.cam.2020.113320
• 发表时间: 2021
• 期刊: Journal of Computational and Applied Mathematics
• 影响因子: 2.4
• 作者: Dai, Shibin;Promislow, Keith
• 通讯作者: Promislow, Keith

High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics

• DOI: 10.4208/cicp.oa-2019-0006
• 发表时间: 2019-06
• 期刊: Communications in Computational Physics
• 影响因子: 3.7
• 作者: J. M. Church;Zhenlin Guo;P. Jimack;A. Madzvamuse;K. Promislow;B. Wetton;Stephen M Wise;F. Yang

On nonnegative solutions for the Functionalized Cahn–Hilliard equation with degenerate mobility

具有简并迁移率的函数化 Cahn-Hilliard 方程的非负解

• DOI: 10.1016/j.rinam.2021.100195
• 发表时间: 2021
• 期刊: Results in Applied Mathematics
• 影响因子: 2
• 作者: Dai, Shibin;Liu, Qiang;Luong, Toai;Promislow, Keith
• 通讯作者: Promislow, Keith