含刚性平面内含物的囊泡形状平衡
Shape equilibria of vesicles with rigid planar inclusions
AI总结：
该研究针对含单个平面圆形刚性内含物的闭合囊泡，结合解析与计算方法分析Helfrich模型的弹性基态，揭示了内含物占比对囊泡形状从长椭球向扁椭球转变及对称性破缺的调控规律，为复合囊泡的形状与力学特性提供理论解释。
摘要：
受近期对在流体双分子层相内整合有二维固态结构域的两相脂质囊泡研究的启发，我们研究了含有单个平面圆形内含物的闭合囊泡的形状平衡。尽管二维固态弹性倾向于排斥高斯曲率，但拓扑结构要求闭合囊泡维持非零的平均高斯曲率，这导致了一种随内含物尺寸增大而加剧的基本形状失稳机制。我们通过解析与计算相结合的方式，研究了平面-流体复合囊泡Helfrich模型的弹性基态，将其作为平面占比和约化体积的函数。值得注意的是，我们发现仅引入占比百分之几的平面内含物，就会使囊泡的基态形状从以长椭球为主急剧转变为扁椭球，此外还会使最优表面积与体积比大幅偏离球形的对应比值。我们表明，对于尺寸足够小的平面内含物，弹性基态会通过多种复杂的不对称扁椭球、长椭球和三轴形状发生对称性破缺；而当内含物尺寸超过约8%时，复合囊泡会采取轴对称扁椭球形状。这些预测为流-固复合囊泡的涌现形状和力学响应提供了有用的阐释。
英文摘要：
Motivated by recent studies of two-phase lipid vesicles possessing 2D solid domains integrated within a fluid bilayer phase, we study the shape equilibria of closed vesicles possessing a single planar, circular inclusion. While 2D solid elasticity tends to expel Gaussian curvature, topology requires closed vesicles to maintain an average, non-zero Gaussian curvature leading to an elementary mechanism of shape frustration that increases with inclusion size. We study elastic ground states of the Helfrich model of the planar-fluid composite vesicles, analytically and computationally, as a function of planar fraction and reduced volume. Notably, we show that incorporation of a planar inclusion of only a few percent dramatically shifts the ground state shapes of vesicles from predominantly {\it prolate} to {\it oblate}, and moreover, shifts the optimal surface to volume ratio far from spherical shapes. We show that for sufficiently small planar inclusions, the elastic ground states break symmetry via a complex variety of asymmetric oblate, prolate, and triaxial shapes, while inclusion sizes above about $8\%$ drive composite vesicles to adopt axisymmetric oblate shapes. These predictions cast useful light on the emergent shape and mechanical responses of fluid-solid composite vesicles.
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