Kinematics, material symmetry, and energy densities for lipid bilayers with spontaneous curvature.
Kinematics, material symmetry, and energy densities for lipid bilayers with spontaneous curvature.
复制标题
具有自发曲率的脂质双层的运动学、材料对称性和能量密度。
DOI：
10.1007/s10237-012-0459-7
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发表时间：
2013
影响因子：
3.5
通讯作者：
Fried,Eliot
中科院分区：
文献类型：
--
作者：
Maleki,Mohsen;Seguin,Brian;Fried,Eliot
连续介质力学工具被用来描述具有自发曲率的脂双层的变形、能量密度和材料对称性。在传统的方法中，脂质双分子层的材料表面建模相反，在这里，我们依赖于一个三维的方法，其中的脂质双分子层是由一个壳状体与有限的厚度建模。在这种情况下，脂质双层的小叶之间的界面被假定为与相应的壳状体的中间表面重合。三维变形梯度被发现涉及的曲率张量的中间表面的自发和变形状态，中间表面的变形梯度，和横向变形。还注意小叶的连贯性和封闭脂质双层的区域相容性（即，囊泡）。本文发展了液相中脂双层的超弹性本构理论。结合起来，框架无差异性和材料对称性的要求产生了脂双层能量密度的表示。这种表示表明，三个标量不变量足以描述的本构响应的脂双层表现出面内流动性和横向各向同性。除了探索这些不变量的几何和物理性质，基本组成相关联的运动学量强调。在此基础上，考虑了假定脂双层不可压缩对能量密度的影响。最后，使用降维变元从三维能量密度中提取每单位面积的面积能量密度。这一步解释了面能量密度中自发曲率的起源。重要的是，沿着与脂质双层的自然曲率相关的标准贡献，我们的分析表明，脂质双层的小叶之间的组成不对称性引起自发曲率的二次贡献。
Continuum mechanical tools are used to describe the deformation, energy density, and material symmetry of a lipid bilayer with spontaneous curvature. In contrast to conventional approaches in which lipid bilayers are modeled by material surfaces, here we rely on a three-dimensional approach in which a lipid bilayer is modeling by a shell-like body with finite thickness. In this setting, the interface between the leaflets of a lipid bilayer is assumed to coincide with the mid-surface of the corresponding shell-like body. The three-dimensional deformation gradient is found to involve the curvature tensors of the mid-surface in the spontaneous and the deformed states, the deformation gradient of the mid-surface, and the transverse deformation. Attention is also given to the coherency of the leaflets and to the area compatibility of the closed lipid bilayers (i.e., vesicles). A hyperelastic constitutive theory for lipid bilayers in the liquid phase is developed. In combination, the requirements of frame indifference and material symmetry yield a representation for the energy density of a lipid bilayer. This representation shows that three scalar invariants suffice to describe the constitutive response of a lipid bilayer exhibiting in-plane fluidity and transverse isotropy. In addition to exploring the geometrical and physical properties of these invariants, fundamental constitutively associated kinematical quantities are emphasized. On this basis, the effect on the energy density of assuming that the lipid bilayer is incompressible is considered. Lastly, a dimension reduction argument is used to extract an areal energy density per unit area from the three-dimensional energy density. This step explains the origin of spontaneous curvature in the areal energy density. Importantly, along with a standard contribution associated with the natural curvature of the lipid bilayer, our analysis indicates that constitutive asymmetry between the leaflets of the lipid bilayer gives rise to a secondary contribution to the spontaneous curvature.