$α$ -辅肌动蛋白交联F-肌动蛋白网络循环硬化的微观结构模型
Microstructural model for cyclic hardening in F-actin networks crosslinked by $α$-actinin
摘要：
近年来，肌动蛋白网络的流变性引起了人们的广泛关注。为了全面了解这些新型材料的流变特性，有必要在大变形状态下对其内部结构进行研究。从这个意义上说，Schmoller等人（2010）表明，与$α$ -辅肌动蛋白交联的F-肌动蛋白重构网络在受到循环剪切时意外硬化。这一观察结果与在大多数软材料（如橡胶和活组织）中观察到的预期Mullins效应相矛盾，其中当它们循环变形时观察到明显的软化。我们认为理解这种惊人效果的关键是凝胶化过程。为了定义它，最相关的成分是化学交联- $α$ -辅肌动蛋白-，物理交联-由半柔性网络的纠缠引入-以及它们之间的相互作用。作为这种相互作用的结果，预应力网络出现并引入反馈效应，其中预应力还调节$α$ -辅肌动蛋白的粘附能，将结构设置为亚稳态参考构型。因此，在循环加载过程中，外部载荷和陷阱应力的演变驱动了微观结构的变化。在这项工作中，我们提出了一个微观力学模型的框架内的非线性连续介质力学。采用半柔性纤维的蠕虫状链模型模拟F-肌动蛋白纤维的力学行为，采用$α$ -肌动蛋白和物理交联的介观动力学模型模拟F-肌动蛋白纤维的凝胶化过程，并与实验结果进行了比较。
英文摘要：
The rheology of F-actin networks has attracted a great attention during the last years. In order to gain a complete understanding of the rheological properties of these novel materials, it is necessary the study in a large deformations regime to alter their internal structure. In this sense, Schmoller et al. 2010 showed that the reconstituted networks of F-actin crosslinked with $α$-actinin unexpectedly harden when they are subjected to a cyclical shear. This observation contradicts the expected Mullins effect observed in most soft materials, such as rubber and living tissues, where a pronounced softening is observed when they are cyclically deformed. We think that the key to understand this stunning effect is the gelation process. To define it, the most relevant constituents are the chemical crosslinks -$α$-actinin-, the physical crosslinks -introduced by the entanglement of the semiflexible network- and the interaction between them. As a consequence of this interaction, a pre-stressed network emerges and introduces a feedback effect, where the pre-stress also regulates the adhesion energy of the $α$-actinin, setting the structure in a metastable reference configuration. Therefore, the external loads and the evolvement of the trapped stress drive the microstructural changes during the cyclic loading protocol. In this work, we propose a micromechanical model into the framework of nonlinear continuum mechanics. The mechanics of the F-actin filaments is modeled using the wormlike chain model for semiflexible filaments and the gelation process is modeled as mesoscale dynamics for the $α$-actinin and physical crosslink.The model has been validated with reported experimental results.
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