Theoretical Problems in Soft Matter and Quantitative Biology

软物质和定量生物学的理论问题

• 批准号: 1005289
• 负责人: David Nelson
• 金额: $ 40.5万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005289&HistoricalAwards=false
• 关键词: Theoretical; Problems; Soft; Matter; Quantitative

TECHNICAL SUMMARYThe Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and education on soft condensed matter and non-equilibrium statistical mechanics at the interface of materials research and mathematics with biology. The research includes the study of population dynamics and properties of pollen grains and polymersomes. In various ways, the research contributes to the advance of non-equilibrium statistical mechanics, and biologically inspired materials and nanostructures. The PI aims to use methods from theoretical physics to understand the population waves which have played a crucial role in the evolutionary history of many species, including humans. Neutral genetic markers can be used to infer information about growth, ancestral population size and colonization pathways. Such phenomena can be studied experimentally by tracking the genetic de-mixing of pioneer micro-organisms arising from razor blade inoculations in a Petri dish. Enhanced fluctuations due to small population sizes at a growing front can lead to remarkable effects, such as "gene surfing". The PI plans to study such phenomena through a combination of techniques from non-equilibrium statistical mechanics, probability theory, and population genetics, with particular emphasis understanding how "inflation" impedes de-mixing of radial expansions in two and three dimensions. The PI also plans to construct a detailed theory of sector numbers, fixation probabilities and genetic instabilities at moving population frontiers. Using analytical and numerical methods for solving the Foppl-von Karman equations for thin shells, the PI will explore folding strategies and shapes of pollen grains during dehydration as they migrate from flower to flower. The grain can be modeled as a pressurized high-Young-modulus sphere with a weak sector and a nonzero spontaneous curvature. In the absence of such a weak sector, these shells crumple irreversibly under pressure via a strong instability. The weak sectors of both one and three-sector pollen grains eliminate the hysteresis and allow easy rehydration at the pollination site, somewhat like the collapse and subsequent reassembly of a folding chair. The PI aims to determine the optimal shape and position of the weak sectors, and see if nature has indeed adopted such strategies in specific cases. In addition, the PI will study how thermal fluctuations affect thin-shelled polymersomes, a new kind of vesicle that resists shear and is made from diblock copolymers. This award also supports interdisciplinary training for graduate students through the opportunities provided by the research. NONTECHNICAL SUMMARY:The Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and education on soft condensed matter and non-equilibrium statistical mechanics at the interface of materials research and mathematics with biology. The research includes the study of population dynamics and properties of pollen grains and polymersomes. In various ways, the research contributes to the advance of non-equilibrium statistical mechanics, and biologically inspired materials and nanostructures. The PI will use techniques from non-equilibrium statistical mechanics and mathematics to understand migrations of biological organisms. Potential applications include impeding harmful bacteria, such as Pseudomonas aeruginosa, which can grow along the surfaces of medical tubing or prosthetic devices. In such bacterial infections and more generally some diseases, the rate at which the attacking genome at the frontier evolves to evade the immune system, can determine whether patients live or die. A second thrust of the research is to understand how a pollen grain folds onto itself when it is exposed to a dry environment and polymersomes crumple using the fundamental principles of materials and geometry. Polymersomes are vesicles that are made of long chain-like molecules and surround liquid. The investigation of polymersomes could lead to a better understanding of the strength of these drug encapsulation devices. A better understanding of how natural materials function contributes to efforts to discover new materials that mimic biology and exploit nature's design ideas.This research contributes to the intellectual foundations of the discovery of new materials, new technologies, and disease control through a better understanding of the design principles and forces of nature.This award also supports interdisciplinary training for graduate students through the opportunities provided by the research.

数学科学部和材料研究部为该奖项提供资金。它支持在材料研究和数学与生物学的界面上对软凝聚态和非平衡统计力学的理论研究和教育。 研究内容包括花粉粒和聚合体的种群动态和特性研究。该研究以各种方式促进了非平衡统计力学、生物材料和纳米结构的发展。PI的目标是使用理论物理学的方法来理解在包括人类在内的许多物种的进化历史中发挥关键作用的人口波动。中性遗传标记可用于推断有关生长、祖先种群大小和定殖途径的信息。这种现象可以通过在皮氏培养皿中跟踪由剃刀刀片接种产生的先驱微生物的遗传去混合来进行实验研究。 在增长前沿，由于人口规模小而引起的波动加剧，可能导致显著的影响，如“基因冲浪”。PI计划通过非平衡统计力学、概率论和群体遗传学的技术组合来研究这种现象，特别强调理解“膨胀”如何阻碍二维和三维径向扩张的去混合。PI还计划构建一个详细的理论，在移动人口边界的部门数量，固定概率和遗传不稳定性。使用解析和数值方法求解薄壳的Foppl-von Karman方程，PI将探索花粉粒在脱水过程中从一朵花迁移到另一朵花的折叠策略和形状。晶粒可以被建模为一个受压的高杨氏模量的球与弱扇区和非零的自发曲率。在没有这种薄弱环节的情况下，这些壳在压力下通过强烈的不稳定性不可逆地起皱。单扇形和三扇形花粉粒的弱扇形消除了滞后现象，并允许在授粉部位容易地再水化，有点像折叠椅的倒塌和随后的重新组装。PI旨在确定薄弱部门的最佳形状和位置，并查看大自然是否确实在特定情况下采取了这种策略。此外，PI将研究热波动如何影响薄壳聚合物囊泡，这是一种新型的囊泡，可抵抗剪切，由二嵌段共聚物制成。 该奖项还通过研究提供的机会支持研究生的跨学科培训。非技术摘要：数学科学部和材料研究部为该奖项提供资金。它支持在材料研究和数学与生物学的界面上对软凝聚态和非平衡统计力学的理论研究和教育。 研究内容包括花粉粒和聚合体的种群动态和特性研究。该研究以各种方式促进了非平衡统计力学、生物材料和纳米结构的发展。PI将使用非平衡统计力学和数学技术来理解生物有机体的迁移。 潜在的应用包括阻碍有害细菌，如绿脓杆菌，它可以沿着医疗管道或假体装置的表面生长。在这种细菌感染和更普遍的一些疾病中，处于前沿的攻击基因组进化以逃避免疫系统的速度可以决定患者的生存或死亡。 研究的第二个重点是了解花粉粒在暴露于干燥环境时如何折叠，以及聚合物囊泡如何使用材料和几何学的基本原理起皱。 聚合物囊泡是由长链状分子组成的囊泡，包围着液体。聚合物囊泡的研究可以更好地了解这些药物封装装置的强度。更好地了解自然材料的功能有助于发现模仿生物学和利用自然设计思想的新材料。这项研究有助于发现新材料，新技术，通过更好地理解设计原理和自然力量来控制疾病。该奖项还通过提供的机会支持研究生的跨学科培训通过研究。