Dynamical Rigidity Percolation in Microtubule Bundles

微管束中的动态刚性渗透

• 批准号: 1207624
• 负责人: Daniel Cox
• 金额: $ 51万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1207624&HistoricalAwards=false
• 关键词: Dynamical; Rigidity; Percolation; Microtubule; Bundles

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.

技术摘要该奖项支持数学科学和生物学交叉领域的理论和计算研究及教育。神经元轴突的耦合微管-tau 束是一种非凡的活性物质，即使其成分蛋白质不断更新，其功能也能稳定数十年。利用在阿尔茨海默氏病晚期阶段去除 tau 蛋白的机制（该机制是由 a-β 肽寡聚化引发的），PI 将开发出一种粗粒度理论，说明当 tau 蛋白通过以下方式耗尽时该系统的机械故障：（i ) 由 a-β 寡聚体引发的蛋白酶产生诱导 tau 片段化； (ii) 通过 a-β 触发激酶产生进行 tau 充电（磷酸化）； (iii) 聚集，从束中夺走 tau 单体。 这些过程的动力学应该产生不同的 tau 蛋白去除时间过程，从而可以深入了解机械故障机制。 taus 将被建模为弹簧。 PI 将对可能的 tau 寡聚物结构进行明确的分子动力学模拟，以确定相关的弹簧力。 压缩的 tau 弹簧可以阻止由至少两个来源引起的机械塌陷：（i）由嵌入分子引起的微管之间的耗尽力，当微管一起塌陷时，微管之间具有更高的平移熵； (ii)来自外膜/肌动蛋白丝细胞骨架的表面张力。 PI 将开发 taus 和微管耗尽力的力模型，并将其输入到机械刚性的二维渗透模型中。 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 α-β 寡聚物下进行的细胞力学实验的时间进程。 PI 还将探索一个完整的三维模型，该模型允许微管倾斜，这对于让微管体验耗尽吸引力可能很重要。最后，PI 将尝试开发算法，将阿尔茨海默氏病的破坏性 A-β 寡聚物在高实验室浓度下的时间行为扩展到生理相关浓度。使用机械方法来研究细胞内特性相对较新，因为实验方法最近才赶上理论潜力。 PI 将支持研究生和高年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，并将有机会使用由该奖项增强的最先进的基于 GPU 的计算设施。非技术摘要该奖项支持数学科学和生物学交叉领域的理论和计算研究及教育。 PI 将开发基于计算机的模型，用于研究神经细胞长轴或轴突内蛋白质的机械特性。具体来说，他们将模拟长蛋白质丝（称为微管），它们通过蛋白质弹簧（tau 蛋白）相互连接，以了解当 tau 蛋白被去除时系统的刚度如何降低。 这种情况发生在阿尔茨海默氏病的病程中，但 tau 蛋白去除发生的精确方式仍在研究中。 通过对这些蛋白束的机械特性（包括 tau 蛋白和微管的动态行为）进行模拟，PI 可以解释 tau 蛋白在阿尔茨海默病中降解的不同途径。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”而驱动微管在一起的力，PI希望提供可通过实验测试的预测，以确定阿尔茨海默病中神经细胞退化和死亡的关键过程。 Tau 蛋白本身就是有趣的系统：与血红蛋白等在人体内具有独特形状的蛋白质不同，tau 蛋白本质上是非结构化的，但对神经细胞功能显然很重要。 作为更大规模机械模型的输入，PI 将模拟单个和配对 tau 蛋白的机械特性。 所获得的见解可能会为生命系统之外活性、自修复复合材料的新方法提供灵感。 由于微管/tau 蛋白束在健康、无疾病的个体中数十年保持机械稳定性和功能，因此它们是此类智能活性材料的卓越模型系统。