Pinigin Konstantin V, Kuzmin Peter I, Akimov Sergey A, Galimzyanov Timur R
A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31/4 Leninskiy prospekt, Moscow 119071, Russia.
Phys Rev E. 2020 Oct;102(4-1):042406. doi: 10.1103/PhysRevE.102.042406.
Lipid bilayer membranes under biologically relevant conditions are flexible thin laterally fluid films consisting of two unimolecular layers (monolayers) each about 2 nm thick. On spatial scales much larger than the bilayer thickness, the membrane elasticity is well determined by its shape. The classical Helfrich theory considers the membrane as an elastic two-dimensional (2D) film, which has no particular internal structure. However, various local membrane heterogeneities can result in a lipids tilt relative to the membrane surface normal. On the basis of the classical elasticity theory of 3D bodies, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)10.1007/s101890070003] derived the most general energy functional, taking into account the tilt and lipid monolayer curvature. Recently, Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)10.1063/1.4990404] showed that Hamm and Kozlov's derivation was incomplete because the tilt-curvature coupling term had been missed. However, the energy functional derived by Terzi and Deserno appeared to be unstable, thereby being invalid for applications that require minimizations of the overall energy of deformations. Here, we derive a stable elastic energy functional, showing that the squared gradient of the curvature was missed in both of these works. This change in the energy functional arises from a more accurate consideration of the transverse shear deformation terms and their influence on the membrane stability. We also consider the influence of the prestress terms on the stability of the energy functional, and we show that it should be considered small and the effective Gaussian curvature should be neglected because of the stability requirements. We further generalize the theory, including the stretching-compressing deformation modes, and we provide the geometrical interpretation of the terms that were previously missed by Hamm and Kozlov. The physical consequences of the new terms are analyzed in the case of a membrane-mediated interaction of two amphipathic peptides located in the same monolayer. We also provide the expression for director fluctuations, comparing it with that obtained by Terzi and Deserno.
在生物相关条件下，脂质双分子层膜是由两个单分子层（单层）组成的柔性薄横向流体膜，每个单分子层厚度约为2纳米。在比双分子层厚度大得多的空间尺度上，膜的弹性由其形状很好地决定。经典的赫尔弗里希理论将膜视为一种弹性二维（2D）膜，它没有特定的内部结构。然而，各种局部膜不均匀性会导致脂质相对于膜表面法线倾斜。基于三维物体的经典弹性理论，哈姆和科兹洛夫[《欧洲物理杂志E》3，323（2000年）10.1007/s101890070003]推导了最一般的能量泛函，考虑了倾斜和脂质单层曲率。最近，特尔齐和德塞尔诺[《化学物理杂志》147，084702（2017年）10.1063/1.4990404]表明，哈姆和科兹洛夫的推导是不完整的，因为遗漏了倾斜 - 曲率耦合项。然而，特尔齐和德塞尔诺推导的能量泛函似乎是不稳定的，因此对于需要最小化变形总能量的应用是无效的。在这里，我们推导了一个稳定的弹性能量泛函，表明在这两项工作中都遗漏了曲率的平方梯度。能量泛函的这种变化源于对横向剪切变形项及其对膜稳定性影响的更精确考虑。我们还考虑了预应力项对能量泛函稳定性的影响，并表明由于稳定性要求，应将其视为小量且有效高斯曲率应被忽略。我们进一步推广了该理论，包括拉伸 - 压缩变形模式，并对哈姆和科兹洛夫之前遗漏的项进行了几何解释。在位于同一单层中的两个两亲性肽的膜介导相互作用的情况下，分析了新项的物理后果。我们还提供了指向矢涨落的表达式，并将其与特尔齐和德塞尔诺得到的表达式进行比较。
