Dynamical Rigidity Percolation in Microtubule Bundles

该奖项支持数学科学和生物学接口的理论和计算研究和教育。神经元轴突的耦合微管-tau束是一种显着的活性物质，即使组分蛋白质不断更新，数十年来功能稳定。使用针对阿尔茨海默病晚期tau去除提出的机制（其由α-β肽的寡聚化引发），PI将开发该系统的机械故障的粗粒度理论，因为tau蛋白通过以下方式耗尽：（i）由α-β寡聚体引发的蛋白酶产生诱导的tau片段化;（ii）tau充电（iii）通过α-β触发的激酶产生的磷酸化;（iii）从束中抢夺tau单体的聚集。 这些过程的动力学应该产生不同的时间过程的tau去除，因此允许洞察机械故障机制。 Taus将被建模为弹簧。PI将对可能的tau寡聚体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，当微管塌陷在一起时，嵌入分子具有更高的平移熵;（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度的二维渗流模型中。 可以将顺序的“弹簧去除”映射到tau降解的动力学，以预测在暴露于α-β寡聚体下进行的细胞力学实验的时间过程。 PI还将探索一个完全三维的模型，该模型允许微管的倾斜，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，将阿尔茨海默病的破坏性A-β寡聚体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。 PI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的跨学科教育，并将获得最先进的基于GPU的计算设施。非技术总结该奖项支持数学科学和生物学接口的理论和计算研究和教育。PI将开发基于计算机的模型，用于神经细胞长轴或轴突内蛋白质的机械特性。具体来说，他们将模拟长的蛋白质细丝，称为微管，它们通过蛋白质弹簧，tau蛋白相互连接，以发现当tau蛋白被去除时，系统的刚度如何降低。 这发生在阿尔茨海默病的时间过程中，但tau蛋白去除发生的确切方式是一个正在进行的研究。 通过开发这些蛋白质束的机械特性的模拟，包括tau蛋白和微管的动力学行为，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“气球皮肤”而驱动微管在一起的力量，PI希望提供实验可检验的预测，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蛋白本质上是非结构化的，但对神经细胞功能非常重要。 作为更大规模力学模型的输入，PI将模拟单个和成对tau蛋白的力学特性。 所获得的见解可能会为在生命系统之外开发活性自修复复合材料的新方法提供灵感。 由于微管/tau束在健康、无疾病的个体中保持机械稳定和功能数十年，因此它们是这种智能活性材料的显着模型系统。

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.