Fluid lipid membranes: From differential geometry to curvature stresses
Fluid lipid membranes: From differential geometry to curvature stresses
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DOI：
10.1016/j.chemphyslip.2014.05.001
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发表时间：
2015-01-01
影响因子：
3.4
通讯作者：
Deserno, Markus
中科院分区：
文献类型：
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作者：
Deserno, Markus
流体脂质膜传递的应力和扭矩完全由其几何形状决定。它们可以分别用应力张量和扭矩张量来描述，它们通过在膜表面上绘制的任何曲线产生单位长度的力或扭矩。在没有外力或扭矩的情况下，这些张量的表面发散消失，揭示了它们作为膜形状的基本欧拉-拉格朗日方程的守恒量。这篇评论提供了对这些概念的全面介绍，而不假设读者熟悉微分几何，而是根据需要开发，依赖于向量微积分。Helfrich哈密顿量，然后介绍和讨论在一定程度上深入。如Guven（2004）所提出的，通过将对能量最小化形状的追求表达为受几何约束的函数变分问题，应力张量和扭矩张量自然出现，它们与形状方程的联系变得明显。如何与张量的原因，然后说明了一些简单的例子，在此之后，这篇评论的结论与四个更复杂的应用：粘附膜的边界条件，校正经典的微量吸管抽吸方程，膜屈曲，膜介导的相互作用。(C)2014爱思唯尔爱尔兰有限公司版权所有。
A fluid lipid membrane transmits stresses and torques that are fully determined by its geometry. They can be described by a stress- and torque-tensor, respectively, which yield the force or torque per length through any curve drawn on the membrane's surface. In the absence of external forces or torques the surface divergence of these tensors vanishes, revealing them as conserved quantities of the underlying Euler-Lagrange equation for the membrane's shape. This review provides a comprehensive introduction into these concepts without assuming the reader's familiarity with differential geometry, which instead will be developed as needed, relying on little more than vector calculus. The Helfrich Hamiltonian is then introduced and discussed in some depth. By expressing the quest for the energy-minimizing shape as a functional variation problem subject to geometric constraints, as proposed by Guven (2004), stress- and torque-tensors naturally emerge, and their connection to the shape equation becomes evident. How to reason with both tensors is then illustrated with a number of simple examples, after which this review concludes with four more sophisticated applications: boundary conditions for adhering membranes, corrections to the classical micropipette aspiration equation, membrane buckling, and membrane mediated interactions. (C) 2014 Elsevier Ireland Ltd. All rights reserved.