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Monolayerwise application of linear elasticity theory well describes strongly deformed lipid membranes and the effect of solvent.
Soft Matter ( IF 2.9 ) Pub Date : 2020-01-14 , DOI: 10.1039/c9sm02079a Timur R Galimzyanov 1 , Pavel V Bashkirov , Paul S Blank , Joshua Zimmerberg , Oleg V Batishchev , Sergey A Akimov
Soft Matter ( IF 2.9 ) Pub Date : 2020-01-14 , DOI: 10.1039/c9sm02079a Timur R Galimzyanov 1 , Pavel V Bashkirov , Paul S Blank , Joshua Zimmerberg , Oleg V Batishchev , Sergey A Akimov
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The theory of elasticity of lipid membranes is used widely to describe processes of cell membrane remodeling. Classically, the functional of a membrane's elastic energy is derived under assumption of small deformations; the membrane is considered as an infinitely thin film. This functional is quadratic on membrane surface curvature, with half of the splay modulus as its proportionality coefficient; it is generally applicable for small deformations only. Any validity of this functional for the regime of strong deformations should be verified experimentally. Recently, research using molecular dynamics simulations challenged the validity of this classic, linear model, i.e. the constancy of the splay modulus for strongly bent membranes. Here we demonstrate that the quadratic energy functional still can be applied for calculation of the elastic energy of strongly deformed membranes without introducing higher order terms with additional elastic moduli, but only if applied separately for each lipid monolayer. For cylindrical membranes, both classic and monolayerwise models yield equally accurate results. For cylindrical deformations we experimentally show that the elastic energy of lipid monolayers is additive: a low molecular weight solvent leads to an approximately twofold decrease in the membrane bending stiffness. Accumulation of solvent molecules in the inner monolayer of a membrane cylinder can explain these results, as the solvent partially prevents lipid molecules from splaying there. Thus, the linear theory of elasticity can be expanded through the range from weak to strong deformations-its simplicity and physical transparency describe various membrane phenomena.
中文翻译：
线性弹性理论的单层应用很好地描述了严重变形的脂质膜和溶剂的作用。
脂质膜的弹性理论被广泛用于描述细胞膜重塑的过程。传统上，膜的弹性能量的功能是在假设较小变形的情况下得出的；这是因为膜的弹性能是由膜的弹性所决定的。该膜被认为是无限薄的薄膜。该函数在膜表面曲率上为平方，展开系数的一半为比例系数。它通常仅适用于小变形。此功能对于强变形状态的任何有效性都应通过实验验证。最近，使用分子动力学模拟进行的研究挑战了这种经典的线性模型的有效性，即强弯曲膜的张量模量的恒定性。在这里，我们证明二次能函数仍然可以用于计算强烈变形的膜的弹性能，而无需引入具有附加弹性模量的高阶项，但前提是分别应用于每个脂质单层。对于圆柱形膜，经典模型和单层模型都可得出同样准确的结果。对于圆柱变形，我们实验表明脂质单层的弹性能是可加的：低分子量溶剂会导致膜的弯曲刚度降低大约两倍。膜圆筒内部单层中溶剂分子的积累可以解释这些结果，因为溶剂部分阻止了脂质分子在此处展开。因此，
更新日期：2020-02-13
中文翻译：
线性弹性理论的单层应用很好地描述了严重变形的脂质膜和溶剂的作用。
脂质膜的弹性理论被广泛用于描述细胞膜重塑的过程。传统上，膜的弹性能量的功能是在假设较小变形的情况下得出的；这是因为膜的弹性能是由膜的弹性所决定的。该膜被认为是无限薄的薄膜。该函数在膜表面曲率上为平方，展开系数的一半为比例系数。它通常仅适用于小变形。此功能对于强变形状态的任何有效性都应通过实验验证。最近，使用分子动力学模拟进行的研究挑战了这种经典的线性模型的有效性，即强弯曲膜的张量模量的恒定性。在这里，我们证明二次能函数仍然可以用于计算强烈变形的膜的弹性能，而无需引入具有附加弹性模量的高阶项，但前提是分别应用于每个脂质单层。对于圆柱形膜，经典模型和单层模型都可得出同样准确的结果。对于圆柱变形，我们实验表明脂质单层的弹性能是可加的：低分子量溶剂会导致膜的弯曲刚度降低大约两倍。膜圆筒内部单层中溶剂分子的积累可以解释这些结果，因为溶剂部分阻止了脂质分子在此处展开。因此，
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