稳定胶原纤维的多态性
Polymorphism of stable collagen fibrils
摘要：
胶原原纤维是多功能的自组装结构，其在哺乳动物组织内提供机械完整性。胶原纤维的半径根据实验条件\textit{in vitro}或解剖位置\textit{in vivo}而变化很大。在这里，我们探讨了各种各样的热稳定的原纤维配置，是可用的。我们使用一个液晶模型的径向胶原纤维结构的双扭转指向矢场。使用数值松弛方法，我们表明，两个无量纲的参数，鞍展扭弹性常数$ k_{24}/K_{22}$和表面张力的手征强度$\hatγ \equiv γ/(K_{22}q)$的比率，在很大程度上指定缩放的原纤半径和相关的表面扭曲的平衡原纤。我们发现，胶原纤维是稳定的阶段，相对于双相只有当减少的表面张力是小的，$\hatγ \lesssim 0.2$。在这种稳定的状态下，胶原纤维可以获得广泛的半径和相关的表面扭曲。值得注意的是，我们发现一个最大的平衡表面扭曲$0.33$ rad（$19^{\text{o}}$）。我们的研究结果与角膜胶原纤维是兼容的，我们展示了如何大的表面扭曲是需要解释角膜纤维半径的狭窄分布。相反，我们展示了如何小的表面扭曲所需的肌腱原纤维的热力学稳定性，在面对相当多的半径的多分散性。
英文摘要：
Collagen fibrils are versatile self-assembled structures that provide mechanical integrity within mammalian tissues. The radius of collagen fibrils vary widely depending on experimental conditions \textit{in vitro} or anatomical location \textit{in vivo}. Here we explore the variety of thermodynamically stable fibril configurations that are available. We use a liquid crystal model of radial collagen fibril structure with a double-twist director field. Using a numerical relaxation method we show that two dimensionless parameters, the ratio of saddle-splay to twist elastic constants $ k_{24}/K_{22}$ and the ratio of surface tension to chiral strength $\hatγ \equiv γ/(K_{22}q)$, largely specify both the scaled fibril radius and the associated surface twist of equilibrium fibrils. We find that collagen fibrils are the stable phase with respect to the cholesteric phase only when the reduced surface tension is small, $\hatγ \lesssim 0.2$. Within this stable regime, collagen fibrils can access a wide range of radii and associated surface twists. Remarkably, we find a maximal equilibrium surface twist of $0.33$ rad ($19^{\text{o}}$). Our results are compatible with corneal collagen fibrils, and we show how the large surface twist is needed to explain the narrow distribution of corneal fibril radii. Conversely, we show how small surface twist is required for the thermodynamic stability of tendon fibrils in the face of considerable polydispersity of radius.
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