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Fluctuation tension and shape transition of vesicles: renormalisation calculations and Monte Carlo simulations
Soft Matter ( IF 2.9 ) Pub Date : 2017-09-04 00:00:00 , DOI: 10.1039/c7sm01272a Guillaume Gueguen 1, 2, 3, 4, 5 , Nicolas Destainville 1, 2, 3, 4, 5 , Manoel Manghi 1, 2, 3, 4, 5
Soft Matter ( IF 2.9 ) Pub Date : 2017-09-04 00:00:00 , DOI: 10.1039/c7sm01272a Guillaume Gueguen 1, 2, 3, 4, 5 , Nicolas Destainville 1, 2, 3, 4, 5 , Manoel Manghi 1, 2, 3, 4, 5
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It has been known for long that the fluctuation surface tension of membranes r, computed from the height fluctuation spectrum, is not equal to the bare surface tension σ, which is introduced in the theory either as a Lagrange multiplier to conserve the total membrane area or as an external constraint. In this work we relate these two surface tensions both analytically and numerically. They are also compared to the Laplace tension γ, and the mechanical frame tension τ. Using the Helfrich model and one-loop renormalisation calculations, we obtain, in addition to the effective bending modulus κeff, a new expression for the effective surface tension σeff = σ − εkBT/(2ap) where kBT is the thermal energy, ap the projected cut-off area, and ε = 3 or 1 according to the allowed configurations that keep either the projected area or the total area constant. Moreover we show that the crumpling transition for an infinite planar membrane occurs for σeff = 0, and also that it coincides with vanishing Laplace and frame tensions. Using extensive Monte Carlo (MC) simulations, triangulated membranes of vesicles made of N = 100–2500 vertices are simulated within the Helfrich theory. As compared to alternative numerical models, no local constraint is applied and the shape is only controlled by the constant volume, the spontaneous curvature and σ. It is shown that the numerical fluctuation surface tension r is equal to σeff both with radial MC moves (ε = 3) and with corrected MC moves locally normal to the fluctuating membrane (ε = 1). For finite vesicles of typical size R, two different regimes are defined: a tension regime for ![[small sigma, Greek, circumflex]](http://www.rsc.org/images/entities/i_char_e111.gif)
eff = σeffR2/κeff > 0 and a bending one for −1 < eff < 0. A shape transition from a quasi-spherical shape imposed by the large surface energy, to more deformed shapes only controlled by the bending energy, is observed numerically at eff ≃ 0. We propose that the buckling transition, observed for planar supported membranes in the literature, occurs for eff ≃ −1, the associated negative frame tension playing the role of a compressive force. Hence, a precise control of the value of σeff in simulations cannot but enhance our understanding of shape transitions of vesicles and cells.
中文翻译：
囊泡的波动张力和形状转变：重新归一化计算和蒙特卡洛模拟
长期以来人们已经知道，由高度波动谱计算出的膜的波动表面张力r不等于裸露表面张力σ，在理论上，它作为拉格朗日乘数被引入以节省总膜面积，或者被称为拉格朗日乘数。作为外部约束。在这项工作中，我们在分析和数值上都将这两个表面张力相关联。还将它们与拉普拉斯张力γ和机械框架张力τ进行比较。使用赫尔弗里希模型和一个回路再归一化的计算，我们得到，除了有效弯曲模量κ EFF，对于有效表面张力的新的表达σ EFF =σ - εK乙Ť /（2一p）其中ķ乙Ť是热能，一个p投影截止区，和ε =根据所允许的配置，保持任一的投影面积或总面积3或1持续的。此外，我们显示，对于一个无限平面膜起皱转变发生于σ EFF = 0，并且还使得它与消失拉普拉斯和帧张力一致。使用广泛的蒙特卡洛（MC）模拟，由N制成的囊泡的三角膜=在Helfrich理论中模拟了100–2500个顶点。与替代的数值模型相比，没有施加局部约束，并且形状仅由恒定体积，自发曲率和σ控制。它被示出的数值波动表面张力- [R等于σ EFF都与径向MC移动（ε = 3），并用校正MC移动局部垂直于所述波动的膜（ε = 1）。对于典型尺寸的有限囊泡- [R ，两个不同的机制被定义：用于张力政权EFF = σ EFF - [R 2 / κ EFF> 0和弯曲一个用于-1 < EFF <0.形状过渡从由大表面能施加的准球形的形状，仅通过弯曲能控制多个变形的形状，在数值上观察到EFF ≃0。我们建议在文献中观察到的对于平面支撑膜的屈曲转变发生在eff -1，相关的负框架张力起着压缩力的作用。因此，的值的精确控制σ EFF在模拟不能不提高我们的囊泡和细胞的形状转变的理解。
更新日期：2017-09-08
eff = σeffR2/κeff > 0 and a bending one for −1 < eff < 0. A shape transition from a quasi-spherical shape imposed by the large surface energy, to more deformed shapes only controlled by the bending energy, is observed numerically at eff ≃ 0. We propose that the buckling transition, observed for planar supported membranes in the literature, occurs for eff ≃ −1, the associated negative frame tension playing the role of a compressive force. Hence, a precise control of the value of σeff in simulations cannot but enhance our understanding of shape transitions of vesicles and cells.
中文翻译：
囊泡的波动张力和形状转变：重新归一化计算和蒙特卡洛模拟
长期以来人们已经知道，由高度波动谱计算出的膜的波动表面张力r不等于裸露表面张力σ，在理论上，它作为拉格朗日乘数被引入以节省总膜面积，或者被称为拉格朗日乘数。作为外部约束。在这项工作中，我们在分析和数值上都将这两个表面张力相关联。还将它们与拉普拉斯张力γ和机械框架张力τ进行比较。使用赫尔弗里希模型和一个回路再归一化的计算，我们得到，除了有效弯曲模量κ EFF，对于有效表面张力的新的表达σ EFF =σ - εK乙Ť /（2一p）其中ķ乙Ť是热能，一个p投影截止区，和ε =根据所允许的配置，保持任一的投影面积或总面积3或1持续的。此外，我们显示，对于一个无限平面膜起皱转变发生于σ EFF = 0，并且还使得它与消失拉普拉斯和帧张力一致。使用广泛的蒙特卡洛（MC）模拟，由N制成的囊泡的三角膜=在Helfrich理论中模拟了100–2500个顶点。与替代的数值模型相比，没有施加局部约束，并且形状仅由恒定体积，自发曲率和σ控制。它被示出的数值波动表面张力- [R等于σ EFF都与径向MC移动（ε = 3），并用校正MC移动局部垂直于所述波动的膜（ε = 1）。对于典型尺寸的有限囊泡- [R ，两个不同的机制被定义：用于张力政权
EFF = σ EFF - [R 2 / κ EFF> 0和弯曲一个用于-1 < EFF <0.形状过渡从由大表面能施加的准球形的形状，仅通过弯曲能控制多个变形的形状，在数值上观察到EFF ≃0。我们建议在文献中观察到的对于平面支撑膜的屈曲转变发生在eff -1，相关的负框架张力起着压缩力的作用。因此，的值的精确控制σ EFF在模拟不能不提高我们的囊泡和细胞的形状转变的理解。
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