巨大的脂质囊泡形成不寻常的多球形或“多气球”形状,由几个通过膜颈连接的球体组成。当膜的两侧暴露于不同的糖溶液时,最近观察到这种多球形形状。这种糖不对称引起了自发弯曲,可以通过将内部与外部解决方案交换来反转其标志。这里,回顾和扩展了以前对多球形形状的研究,以发展这些形状的综合理论。每个多球由大球体和小球体组成,以两个半径为特征,大球体半径,Rl,和小球体半径,RS.对于正的自发曲率,多球体可以由大球体和小球体的可变数量Nl和Ns构成。此外,由N*=Nl+Ns等尺寸的球体组成的多球体也是可能的,并且提供恒定平均曲率表面的示例。对于负的自发曲率,所有多球体由一个大球体组成,该球体包围可变数量Ns的小球体。多重球体的这些一般特征源于曲率弹性的两个基本特性:球形膜段的局部形状方程和封闭膜颈的稳定性条件。此外,(Nl+Ns)-多重球可以形成几个方式不同的(Nl+Ns)-模式,其中球体是相互连接的。这些图案可能涉及由连接到两个以上相邻球体的单个球体组成的多球体结。多重球体的几何形状由两个多项式方程控制,这意味着(NlNs)-多重球体只能在一定的有限范围的囊泡体积内形成。每个(Nl+Ns)-模式的特征可以在于取决于闭合颈部的稳定性和多球形几何形状的某一稳定性状态。未来研究的有趣和具有挑战性的主题包括多领域对局部施加的外力的反应,球体之间的膜融合,以创建更高属拓扑的多球形形状,以及由于脂质相分离和膜内结构域而引起的多球体的形态复杂性扩大。
Giant lipid vesicles form unusual multispherical or \"multi-balloon\" shapes consisting of several spheres that are connected by membrane necks. Such multispherical shapes have been recently observed when the two sides of the membranes were exposed to different sugar solutions. This sugar asymmetry induced a spontaneous curvature, the sign of which could be reversed by swapping the interior with the exterior solution. Here, previous studies of multispherical shapes are reviewed and extended to develop a comprehensive theory for these shapes. Each multisphere consists of large and small spheres, characterized by two radii, the large-sphere radius, Rl, and the small-sphere radius, Rs. For positive spontaneous curvature, the multisphere can be built up from variable numbers Nl and Ns of large and small spheres. In addition, multispheres consisting of N*=Nl+Ns equally sized spheres are also possible and provide examples for constant-mean-curvature surfaces. For negative spontaneous curvature, all multispheres consist of one large sphere that encloses a variable number Ns of small spheres. These general features of multispheres arise from two basic properties of curvature elasticity: the local shape equation for spherical membrane segments and the stability conditions for closed membrane necks. In addition, the (Nl+Ns)-multispheres can form several (Nl+Ns)-patterns that differ in the way, in which the spheres are mutually connected. These patterns may involve multispherical junctions consisting of individual spheres that are connected to more than two neighboring spheres. The geometry of the multispheres is governed by two polynomial equations which imply that (Nl+Ns)-multispheres can only be formed within a certain restricted range of vesicle volumes. Each (Nl+Ns)-pattern can be characterized by a certain stability regime that depends both on the stability of the closed necks and on the multispherical geometry. Interesting and challenging topics for future studies include the response of multispheres to locally applied external forces, membrane fusion between spheres to create multispherical shapes of higher-genus topology, and the enlarged morphological complexity of multispheres arising from lipid phase separation and intramembrane domains.