College of Engineering, University of Georgia, Athens, Georgia.
Department of Mechanical Engineering, Binghamton University, Binghamton, New York.
Biophys J. 2021 Sep 7;120(17):3697-3708. doi: 10.1016/j.bpj.2021.07.019. Epub 2021 Jul 24.
Axon bundles cross-linked by microtubule (MT) associate proteins and bounded by a shell skeleton are critical for normal function of neurons. Understanding effects of the complexly geometrical parameters on their mechanical properties can help gain a biomechanical perspective on the neurological functions of axons and thus brain disorders caused by the structural failure of axons. Here, the tensile mechanical properties of MT bundles cross-linked by tau proteins are investigated by systematically tuning MT length, axonal cross-section radius, and tau protein spacing in a bead-spring coarse-grained model. Our results indicate that the stress-strain curves of axons can be divided into two regimes, a nonlinear elastic regime dominated by rigid-body like inter-MT sliding, and a linear elastic regime dominated by affine deformation of both tau proteins and MTs. From the energetic analyses, first, the tau proteins dominate the mechanical performance of axons under tension. In the nonlinear regime, tau proteins undergo a rigid-body like rotating motion rather than elongating, whereas in the nonlinear elastic regime, tau proteins undergo a flexible elongating deformation along the MT axis. Second, as the average spacing between adjacent tau proteins along the MT axial direction increases from 25 to 125 nm, the Young's modulus of axon experiences a linear decrease whereas with the average space varying from 125 to 175 nm, and later reaches a plateau value with a stable fluctuation. Third, the increment of the cross-section radius of the MT bundle leads to a decrease in Young's modulus of axon, which is possibly attributed to the decrease in MT numbers per cross section. Overall, our research findings offer a new perspective into understanding the effects of geometrical parameters on the mechanics of MT bundles as well as serving as a theoretical basis for the development of artificial MT complexes potentially toward medical applications.
轴突束由微管（MT）结合蛋白交联，并被壳状骨架束缚，这对于神经元的正常功能至关重要。了解复杂几何参数对其力学性能的影响，可以帮助我们从生物力学的角度理解轴突的神经功能，以及轴突结构破坏引起的脑疾病。在这里，我们通过系统地调整 MT 长度、轴突横截面半径和 tau 蛋白间距，在珠子-弹簧粗粒化模型中研究了由 tau 蛋白交联的 MT 束的拉伸力学性能。我们的结果表明，轴突的应力-应变曲线可以分为两个区域，一个是非线性弹性区，主要由刚性的 MT 之间的滑动主导，另一个是线性弹性区，主要由 tau 蛋白和 MT 的仿射变形主导。从能量分析的角度来看，首先，tau 蛋白在拉伸下主导轴突的力学性能。在非线性区，tau 蛋白经历刚体样的旋转运动，而不是伸长，而在非线性弹性区，tau 蛋白沿 MT 轴经历柔性伸长变形。其次，随着 MT 轴向相邻 tau 蛋白平均间距从 25nm 增加到 125nm，轴突的杨氏模量线性减小，而当平均间距从 125nm 增加到 175nm 时，杨氏模量先减小后达到一个平台值，并伴随着稳定的波动。第三，MT 束横截面半径的增加导致轴突杨氏模量的降低，这可能是由于每横截面上 MT 数量的减少。总的来说，我们的研究结果为理解几何参数对 MT 束力学性能的影响提供了新的视角，并为人工 MT 复合物的开发提供了理论基础，可能为医学应用提供潜在的帮助。
