Valdman David, Lopez Benjamin J, Valentine Megan T, Atzberger Paul J
Department of Mathematics, University of California, Santa Barbara, USA.
Soft Matter. 2013 Jan 21;9(3):772-778. doi: 10.1039/C2SM27218K.
Cellular biopolymers can exhibit significant compositional heterogeneities as a result of the non-uniform binding of associated proteins, the formation of microstructural defects during filament assembly, or the imperfect bundling of filaments into composite structures of variable diameter. These can lead to significant variations in the local mechanical properties of biopolymers along their length. Existing spectral analysis methods assume filament homogeneity and therefore report only a single average stiffness for the entire filament. However, understanding how local effects modulate biopolymer mechanics in a spatially resolved manner is essential to understanding how binding and bundling proteins regulate biopolymer stiffness and function in cellular contexts. Here, we present a new method to determine the spatially varying material properties of individual complex biopolymers from the observation of passive thermal fluctuations of the filament conformation. We develop new statistical mechanics-based approaches for heterogeneous filaments that estimate local bending elasticities as a function of the filament arc-length. We validate this methodology using simulated polymers with known stiffness distributions, and find excellent agreement between derived and expected values. We then determine the bending elasticity of microtubule filaments of variable composition generated by repeated rounds of tubulin polymerization using either GTP or GMPCPP, a nonhydrolyzable GTP analog. Again, we find excellent agreement between mechanical and compositional heterogeneities.
由于相关蛋白质的非均匀结合、细丝组装过程中微观结构缺陷的形成，或者细丝不完全捆绑成直径可变的复合结构，细胞生物聚合物可能会表现出显著的组成异质性。这些会导致生物聚合物沿其长度方向的局部力学性能出现显著变化。现有的光谱分析方法假定细丝是均匀的，因此只报告整个细丝的单一平均刚度。然而，以空间分辨的方式理解局部效应如何调节生物聚合物力学对于理解结合蛋白和捆绑蛋白如何在细胞环境中调节生物聚合物刚度和功能至关重要。在这里，我们提出了一种新方法，通过观察细丝构象的被动热涨落来确定单个复杂生物聚合物的空间变化材料特性。我们为异质细丝开发了基于统计力学的新方法，该方法可将局部弯曲弹性估计为细丝弧长的函数。我们使用具有已知刚度分布的模拟聚合物验证了该方法，并发现推导值与预期值之间具有极好的一致性。然后，我们确定了通过使用GTP或GMPCPP（一种不可水解的GTP类似物）进行多轮微管蛋白聚合生成的可变组成微管细丝的弯曲弹性。同样，我们发现力学异质性和组成异质性之间具有极好的一致性。
