Dynamical Rigidity Percolation in Microtubule Bundles

该奖项支持数学科学和生物学界面的理论和计算研究和教育。神经轴突的偶联微管-tau束是一种显著的活性物质，即使其组成蛋白不断更新，其功能也可以稳定数十年。利用提出的阿尔茨海默病晚期tau蛋白去除机制（由a- β肽的寡聚化引发），pi将发展该系统机械故障的粗粒度理论，因为tau蛋白通过以下途径被耗尽：(i)由a- β寡聚物引发的蛋白酶产生诱导的tau碎片化；（ii）通过a- β触发的激酶产生的tau充电（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tau去除的不同时间过程，从而允许深入了解机械失效机制。陶土将被建模成弹簧。pi将对可能的tau低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蛋白弹簧可以阻止至少两种来源引起的机械坍塌：(i)嵌入分子引起的微管之间的耗尽力，当微管一起坍塌时，这些分子具有更高的平移熵；（ii）外膜/肌动蛋白丝细胞骨架的表面张力。pi将开发陶氏体和微管耗竭力的力模型，并将其输入到机械刚度的二维渗透模型中。连续的“弹簧去除”可以映射到tau降解的动力学，以预测暴露于a- β低聚物下进行的细胞力学实验的时间过程。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，将阿尔茨海默病的破坏性a - β低聚物在高实验室浓度下的时间行为缩放到生理相关浓度。使用机械方法来研究细胞内特性是相对较新的，因为实验方法最近才赶上理论潜力。pi将支持研究生和高级本科生研究这些问题；他们将接受物理和生物科学领域的跨学科教育，并将有机会使用基于GPU的最先进的计算设备。该奖项支持数学科学和生物学界面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，他们将模拟被称为微管的长蛋白细丝，它们由蛋白弹簧（tau蛋白）相互连接，以发现当tau蛋白被移除时，系统的刚度是如何降低的。这发生在阿尔茨海默病的时间过程中，但tau蛋白去除的确切方式仍在研究中。通过模拟这些蛋白束的机械特性，包括tau蛋白和微管的动态行为，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”而驱动微管聚集的力量，pi希望提供实验可测试的预测，以确定阿尔茨海默病神经细胞降解和死亡的关键过程。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将模拟单个和成对的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制造主动的、自我修复的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了几十年的机械稳定和功能，因此它们是这种智能、活性材料的卓越模型系统。

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.