胶原纤维径向结构的平衡双捻模型
An equilibrium double-twist model for the radial structure of collagen fibrils
摘要：
哺乳动物组织含有胶原纤维的网络和有序阵列，胶原纤维来源于螺旋状300 nm长的原胶原复合物的周期性自组装。原纤维半径通常在25至250 nm之间，并且表面处的原胶原似乎表现出相对于原纤维轴的特征性扭转角。在体外观察到类似的原纤维半径和扭转角的表面，这表明这些功能是由一个类似的自组装过程控制。在这项工作中，我们提出了一个物理机制的平衡半径控制胶原纤维的基础上径向变化的双扭曲排列的原胶原内的胶原纤维。取向的自由能类似于液晶蓝相的自由能，并且我们采用解析欧拉-拉格朗日和数值自由能最小化来确定分子轴和原纤维轴之间沿径向方向的扭转角。不同弹性能组分之间的竞争，连同表面能，决定了原纤维表面的平衡半径和扭转角。一个简化的模型与扭转角是线性的半径是一个合理的近似在某些参数制度，并解释了幂律依赖的半径和扭转角在表面的参数是变化的。原纤维半径和扭转角在表面上对应于一个平衡的自由能最小值是一致的，与现有的实验测量的胶原纤维。值得注意的是，在实验制度中，我们所有的模型参数是重要的控制胶原纤维的平衡结构参数。
英文摘要：
Mammalian tissues contain networks and ordered arrays of collagen fibrils originating from the periodic self-assembly of helical 300 nm long tropocollagen complexes. The fibril radius is typically between 25 to 250 nm, and tropocollagen at the surface appears to exhibit a characteristic twist-angle with respect to the fibril axis. Similar fibril radii and twist-angles at the surface are observed in vitro, suggesting that these features are controlled by a similar self-assembly process. In this work, we propose a physical mechanism of equilibrium radius control for collagen fibrils based on a radially varying double-twist alignment of tropocollagen within a collagen fibril. The free-energy of alignment is similar to that of liquid crystalline blue phases, and we employ an analytic Euler-Lagrange and numerical free energy minimization to determine the twist-angle between the molecular axis and the fibril axis along the radial direction. Competition between the different elastic energy components, together with a surface energy, determines the equilibrium radius and twist-angle at the fibril surface. A simplified model with a twist-angle that is linear with radius is a reasonable approximation in some parameter regimes, and explains a power-law dependence of radius and twist-angle at the surface as parameters are varied. Fibril radius and twist-angle at the surface corresponding to an equilibrium free-energy minimum are consistent with existing experimental measurements of collagen fibrils. Remarkably, in the experimental regime, all of our model parameters are important for controlling equilibrium structural parameters of collagen fibrils.
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