蠕虫束模型的静动力学
Statics and Dynamics of the Wormlike Bundle Model
摘要：
丝状聚合物束是广泛的细胞骨架结构的主要结构组分，并且它们的机械性质在从运动到机械转导和受精的细胞功能中起关键作用。我们给出了一个详细的推导蠕虫状束模型作为一个通用的描述的静态和动态的聚合物束由交联剂互连的半柔性聚合物。弹性自由度包括长丝的弯曲变形和扭转变形以及交联的剪切变形。我们表明，竞争之间的弹性性能的长丝和交联导致重整化的有效弯曲和扭转刚度，成为模式数依赖。这种依赖性的强度和特征被发现随束结构而变化，如截面中长丝的排列和预捻。我们讨论了两个典型的情况下，束架构，一个均匀的安排，发现在F-肌动蛋白束和壳状结构的特点微管的细丝。每个架构被发现有自己的通用比例的最大到最小的弯曲刚度，独立的特定类型的交联诱导丝耦合;我们的预测是在合理的协议与现有的实验数据微管。此外，我们分析了蠕虫状束模型的预测的实验观测量，如切线-切线相关函数和动态响应和关联函数。最后，我们分析了预扭曲（螺旋度）对纤维束力学性质的影响。我们预测，具有不同数量的原丝的微管在其有效的弯曲刚度应该有明显的变化。
英文摘要：
Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F-actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity.
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