Constitutive Model of Erythrocyte Membranes with Distributions of Spectrin Orientations and Lengths
Constitutive Model of Erythrocyte Membranes with Distributions of Spectrin Orientations and Lengths
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DOI：
10.1016/j.bpj.2020.10.025
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发表时间：
2020-12-01
影响因子：
3.4
通讯作者：
Peng, Zhangli
中科院分区：
文献类型：
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作者：
Feng, Zhe;Waugh, Richard E.;Peng, Zhangli
我们提出了一个分析超弹性本构模型的红细胞（红细胞）膜的基础上最近改进的表征密度和微观结构的血影蛋白网络蛋白质组学和冷冻电子断层扫描。该模型包括分布的方向和自然长度的血影蛋白和更新的拷贝数的蛋白质。通过对谱网络施加有限变形，我们得到了总的自由能和应力的剪切和面积变形的不变量。我们推广的初始剪切模量，这是独立的网络内的分子取向的数量的表达式，并推导出一个简化版本的模型。我们应用该模型及其简化版本来分析微管抽吸计算和分析，并探讨局部细胞骨架密度变化的影响。我们还探讨了文献中报道的使用不同的实验技术测量的剪切模量值之间的差异。我们发现，该模型具有硬化行为，可以解释许多这些差异。此外，我们发现，当使用正确的蛋白质拷贝数时，自然长度的分布在硬化行为中起着至关重要的作用。我们使用我们目前的模型获得的初始剪切模量值（5.9-15.6 pN/μ m）接近早期的估计（6-9 pN/μ m）。据我们所知，这种新的本构模型建立了血影蛋白网络的分子结构和本构律之间的直接联系，也定义了一个新的图片比在以前的研究中假设的更密集的血影蛋白网络。
We present an analytical hyperelastic constitutive model of the red blood cell (erythrocyte) membrane based on recently improved characterizations of density and microscopic structure of its spectrin network from proteomics and cryo-electron tomography. The model includes distributions of both orientations and natural lengths of spectrin and updated copy numbers of proteins. By applying finite deformation to the spectrin network, we obtain the total free energy and stresses in terms of invariants of shear and area deformation. We generalize an expression of the initial shear modulus, which is independent of the number of molecular orientations within the network and also derive a simplified version of the model. We apply the model and its simplified version to analyze micropipette aspiration computationally and analytically and explore the effect of local cytoskeletal density change. We also explore the discrepancies among shear modulus values measured using different experimental techniques reported in the literature. We find that the model exhibits hardening behavior and can explain many of these discrepancies. Moreover, we find that the distribution of natural lengths plays a crucial role in the hardening behavior when the correct copy numbers of proteins are used. The initial shear modulus values we obtain using our current model (5.9-15.6 pN/mu n) are close to the early estimates (6-9 pN/mu m). This new, to our knowledge, constitutive model establishes a direct connection between the molecular structure of spectrin networks and constitutive laws and also defines a new picture of a much denser spectrin network than assumed in prior studies.