Dynamical Rigidity Percolation in Microtubule Bundles

技术总结该奖项支持数学科学和生物学相结合的理论和计算研究和教育。神经元轴突的微管-tau束是一种显著的活性物质，即使组成蛋白不断更新，其功能在几十年内也是稳定的。利用在阿尔茨海默病晚期阶段被提出的由a-β肽齐聚启动的tau去除机制，PI将发展一个粗粒度的理论，说明当tau蛋白被耗尽时，该系统的机械故障通过：(I)由a-β寡聚体引发的蛋白酶产生引起的tau碎裂；(Ii)通过a-β触发的激酶产生的tau充电(磷酸化)；(Iii)从束中夺走tau单体的聚集。这些过程的动力学过程应该产生不同的去除tau的时间进程，因此可以深入了解机械故障机制。牛头将被建模为弹簧。PI将对可能的tau齐聚物结构进行显式分子动力学模拟，以确定相关的弹力。被压缩的tau弹簧阻止了至少两个来源引起的机械崩溃：(I)插入分子引起的微管之间的衰减力，当微管一起崩溃时，微管具有更高的平移熵；(Ii)来自外膜/肌动蛋白细丝细胞骨架的表面张力。PI将为taus和微管耗尽力建立力模型，并将它们输入到机械刚性的二维渗流模型中。连续的“弹簧去除”可以映射到tau降解的动力学，以预测在暴露于a-β寡聚体下进行的细胞力学实验的时间进程。PI还将探索一种全三维模型，该模型允许微管倾斜，这可能是允许微管经历耗尽吸引的重要因素。最后，PI将尝试开发算法，将阿尔茨海默病的破坏性A-β寡聚体在实验室高浓度下的时间行为调整到生理相关浓度。使用力学方法来研究细胞内的性质是相对较新的，因为实验方法只是最近才赶上理论潜力。PIS将支持研究生和高级本科生解决这些问题；他们将接受物理和生物科学方面的跨学科教育，并将获得通过该奖项增强的最先进的基于GPU的计算设施。非技术性总结该奖项支持数学科学和生物学交界处的理论和计算研究和教育。PI将为神经细胞的长轴或轴突内的蛋白质的机械性质开发基于计算机的模型。具体地说，他们将模拟被称为微管的长蛋白质细丝，这些微管由蛋白质弹簧和tau蛋白质相互连接，以找出当tau蛋白质被移除时，系统的刚性是如何退化的。这发生在阿尔茨海默病的时间进程中，但tau去除的确切方式仍在进行中的研究中。通过对这些蛋白束的机械性能进行模拟，包括tau蛋白和微管的动态行为，PI可以解释在阿尔茨海默病中tau蛋白降解的不同途径。包括由于神经细胞内的其他分子和神经细胞外膜的“气球皮肤”而推动微管聚集在一起的力量，PI希望提供可实验验证的预测，以确定阿尔茨海默病神经细胞退化和死亡的关键过程。Tau蛋白本身就是一个有趣的系统：与血红蛋白等在人体中采用独特形状的蛋白质不同，tau蛋白本质上是无结构的，但显然对神经细胞功能很重要。作为更大规模力学模型的输入，PI将模拟单个和成对tau蛋白的力学性质。所获得的洞察力可能会为生命系统以外的活性、自我修复复合材料的新方法提供灵感。由于微管/tau束在健康、无疾病的个体中数十年来保持机械稳定和功能，它们是此类智能、活性材料的非凡模型系统。

TECHNICAL SUMMARYThis award supports theoretical and computational research and education at the interface of the mathematical sciences and biology. The coupled microtubule-tau bundles of the neuronal axon are a remarkable active material, functionally stable over decades even as the component proteins are constantly renewed. Using mechanisms proposed for tau removal in late stages of Alzheimer's Disease, which are initiated by oligomerization of the a-beta peptide, the PIs will develop a coarse grained theory of the mechanical failure of this system as the tau proteins are depleted via: (i) tau fragmentation induced by a-beta oligomer triggered protease production; (ii) tau charging (phosphorylation) through a-beta triggered kinase production; (iii) aggregation which robs tau monomers from the bundles. The kinetics of these processes should produce different time courses for tau removal and hence allow insight into mechanical failure mechanisms. The taus will be modeled as springs. The PIs will carry out explicit molecular dynamics simulations on likely tau oligomer structures to determine the relevant spring forces. The compressed tau springs hold off mechanical collapse induced by at least two sources: (i) depletion forces between microtubules induced by intercalating molecules, which have a higher translational entropy when the microtubules collapse together; (ii) surface tension from the outer membrane/actin filament cytoskeleton. The PIs will develop force models for the taus and microtubule depletion forces, and input them to a 2-dimensional percolation model for the mechanical rigidity. The sequential "spring removal" can be mapped to the kinetics of the tau degradation to predict time courses for cell mechanics experiments conducted under exposure to a-beta oligomers. The PIs will also explore a fully three-dimensional model, which allows for tilting of the microtubules, which might be important for allowing the microtubules to experience the depletion attraction. Finally, the PIs will attempt to develop algorithms to scale the time behavior at high laboratory concentrations for the damaging A-beta oligomers of Alzheimer's disease to physiologically relevant concentrations. The use of mechanical approaches to the study of intracellular properties is relatively new, as experimental approaches are only recently catching up to theoretical potential. The PIs will support both graduate students and advanced undergraduates to work on these problems; they will receive interdisciplinary education in the physical and biological sciences, and will have access to state of the art GPU based computing facilities augmented by this award. NON-TECHNICAL SUMMARYThis award supports theoretical and computational research and education at the interface of the mathematical sciences and biology. The PIs will develop computer-based models for the mechanical properties of the proteins inside the long shafts, or axons, of nerve cells. Specifically, they will simulate the long protein filaments, known as microtubules, which are interlinked by protein springs, tau proteins, to find how the stiffness of the system is degraded when the tau proteins are removed. This happens in the time course of Alzheimer's disease, but the precise manner in which the tau removal occurs is a matter of ongoing investigation. By developing simulations of the mechanical properties of these protein bundles, which include the dynamical behavior of the tau proteins and the microtubules, the PIs can account for the different paths by which tau proteins can be degraded in Alzheimer's disease. Including forces driving microtubules together due to other molecules inside the nerve cells and the "balloon skin" of the nerve cell external membrane, the PIs hope to provide experimentally testable predictions to identify the key processes of nerve cell degradation and death in Alzheimer's disease. Tau proteins are interesting systems in their own right: unlike proteins such as hemoglobin which adopt unique shapes in the human body, tau proteins are intrinsically unstructured yet clearly important to nerve cell function. As an input to larger scale mechanical models, the PIs will simulate the mechanical properties of individual and paired tau proteins. The insights gained may provide inspiration for new approaches to active, self-healing composite materials outside of living systems. Since the microtubule/tau bundles remain mechanically stable and functional over decades of time in healthy, disease free individuals, they are remarkable model systems for such smart, active materials.