Theoretical Problems in Soft Matter and Quantitative Biology

该奖项支持理论研究和教育，以利用统计物理学的力量来洞察位于生物学，物理学和材料科学界面的复杂系统。该方法将对材料和材料相关现象的理解跨越学科界限，应用于具有潜在应用意义的生物学启发问题。该项目包含三个主要的调查目的：1)空间障碍如何改变入侵生物染色体种群中出现在特定位置的基因分布。特别感兴趣的是深入了解环境的不同质性不仅可以塑造入侵细菌种群的边界，还可以塑造细菌的遗传结构。这项研究有可能有助于理解细菌对抗生素耐药性的演变，当机会性病原体如铜绿假单胞菌侵入与住院患者连接的导管时。极薄外壳的机械性能是如何受温度影响的。这是建立在观察的基础上的，即随着温度升高而产生的波动会导致不寻常的机械特性，这些特性描述了板材在长距离上的扭曲。PI的目的是了解当薄片卷成一个薄的球形壳时会发生什么。这项研究有可能有助于开发将药物输送到身体受影响部位的策略，同时也对在比人类头发直径小1000倍左右的尺度上组装机械系统有影响。描述动物和人类神经发育的网络，特别是神经元之间连接的丧失以及神经连接的增强和减弱如何导致神经回路学习各种功能。该项目将有助于培养学生和博士后对跨学科影响问题的现代理论方法。该奖项将支持统计物理方法在材料科学和生物物理学中各种问题的发展和应用方面的理论研究和教育。PI将解决挑战理论的问题，并与实验进行有趣的对抗。所涉及的问题包括障碍和狭窄附近的空间群体遗传学，薄热化壳的软凝聚态物理以及控制具有空间随机性的稀疏网络中定向局部化非线性动力学的特征函数和特征值理论。包括遗传漂变、突变、迁移、竞争和合作在内的非平衡统计动力学和群体遗传学在许多物种的进化史中发挥了至关重要的作用，特别是在固体表面上。例子包括入侵物种的迁移，或细菌对动物组织的入侵。利用非平衡统计动力学和群体遗传学的工具，PI将研究这些现象如何影响包含障碍的空间介质中的遗传谱系。由于生物有机体通常不会在混合良好的试管或无特征的培养皿中生长，因此了解它们在环境不均匀性存在下的行为是很重要的。PI对热化壳的研究建立在薄板和壳的“极限力学”上，其特点是高度非线性的Foeppl - von Karman方程。相对于平板，热激发球壳的背景曲率提出了新的挑战，这将通过推广图形求和和重整化群方法来解决，这些方法已被证明对片状聚合物很有用。最后，该项目将研究在相互作用的生态系统和稀疏神经网络的简单模型中自然产生的强非厄米矩阵（包括兴奋性和抑制性连接）中的定向定位和相关的非平衡动力学。PI的理论研究将确定控制自发活动和诱导反应的复杂分形特征值谱是如何随着抑制性连接与兴奋性连接的比例增加以及信息在特定方向上传递的可变偏差而变化的。该研究具有很强的跨学科性质，可以为控制人类病原体入侵、开发药物递送策略以及人类和动物神经发育提供见解。此外，该项目将有助于培养具有广泛适用性的现代理论方法的学生和博士后。

NONTECHNICAL SUMMARYThis award supports theoretical research and education to exploit the power of statistical physics to gain insight into complex systems that lie at the interface of biology, physics, and materials science. The approach applies understanding of materials and materials-related phenomena across disciplinary boundaries into biologically inspired problems with potential implications for applications. The project contains three major aims to investigate:1.) How spatial obstacles change the distribution of genes that appear at a particular place on a chromosome populations of invading organisms. Of particular interest is gaining insight into how environmental inhomogeneities can shape not only the boundaries at front of a population of invading bacteria but also the genetic structure of the bacteria. This research has potential to contribute to understanding the evolution of resistance of bacteria to antibiotics, as when opportunistic pathogens such as Pseudomonas aeruginosa invade catheters connected to hospitalized patients.2.) How mechanical properties of very thin shells are affected by temperature. This builds on the observation that fluctuations that arise with increasing temperature lead to unusual mechanical properties that describe distortions of a sheet over long distances. The PI aims to understand what happens when the sheet is rolled in to a thin spherical shell. This research has potential to contribute to developing strategies for the delivery of drugs to affected areas of the body, as well as having implications for mechanical systems assembled on scales 1000 times or so smaller than the diameter of a human hair.3.) Networks that describe neural development in animals and humans, and in particular how loss of connections among neurons and the strengthening and weakening of neural connections lead to neural circuits learning various functions.The project will contribute to the training of students and postodocs in modern theoretical methods on problems with impact across disciplinary boundaries.TECHNICAL SUMMARYThis award will support theoretical research and education in the development and application of statistical physics methods to diverse problems in materials science and biophysics. The PI will tackle problems that challenge theory and lead to intriguing confrontations with experiments. The issues addressed include spatial population genetics near obstacles and constrictions, the soft condensed matter physics of thin thermalized shells and the theory of the eigenfunctions and eigenvalues that control the nonlinear dynamics of directed localization in sparse networks with spatial randomness. Nonequilibrium statistical dynamics and population genetics that incorporate genetic drift, mutations, migrations, and competition and cooperation have played a crucial role in the evolutionary history of many species, in particular on solid surfaces. Examples include the migrations of invasive species, or bacterial invasions of animal tissue. Using the tools of nonequilibrium statistical dynamics and population genetics the PI will examine how these phenomena affect genetic lineages in spatial media containing obstacles. Because biological organisms do not typically grow up in well-mixed test tubes or featureless Petri dishes, it is important to understand how they behave in the presence of environmental inhomogeneities. The PI's research on thermalized shells builds on the "extreme mechanics" of thin plates and shells, characterized by the highly nonlinear Foeppl - von Karman equations. The background curvature of thermally excited spherical shells presents new challenges relative to flat plates, which will be addressed by generalizing graphical summation and renormalization group methods that have proven useful for sheet polymers. Finally, the project will investigate directed localization and the associated nonequilibrium dynamics in strongly non-Hermitian matrices (involving both excitatory and inhibitory connections) that arise naturally in simple models of interacting ecosystems and in sparse neural networks. The PI's theoretical research will determine how the intricate fractal eigenvalue spectrum that controls the spontaneous activity and induced response changes with an increasing ratio of inhibitory to excitatory connections and with a variable bias for the transfer of information in a particular direction. Strongly interdisciplinary by nature, the research could provide insights into controlling human pathogen invasions, the development of drug delivery strategies, and human and animal neural development. In addition, the project will contribute to the training of students and postodocs in modern theoretical methods with a wide area of applicability.