SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2448-2471, January 2020.
Biological cells and membranes need to be properly shaped to fulfill many fundamental functions. This shaping is often aided by the aggregation of membrane-bound proteins that both sense the membrane curvature and shape it. Therefore, these protein inclusions interact with each other through the deformation of the membrane that they influence, and a key question is to understand the law that governs their interaction. Whereas the theoretical case of isotropic proteins is well understood, an important feature of many such proteins is their anisotropic interaction with the membrane. Here, we derive an interaction law for rigid circular membrane inclusions which impose an anisotropic contact angle on the surrounding membrane. We include the effects of both membrane bending and tension. Using asymptotic analysis, we identify two distinguished limits corresponding to weak anisotropy/weak tension and strong anisotropy/strong tension, respectively. The resulting laws exhibit a bistability in the equilibrium separation of inclusions. Inclusions with very weak anisotropy equilibrate with large separation, those with very strong anisotropy equilibrate with small separation, while there is a range of anisotropies for which both equilibria are stable. Our results provide a theoretical mechanism for the global aggregation of inclusions seen both in experiments and simulations.

中文翻译：

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流体膜上各向异性包裹体的相互作用

SIAM应用数学杂志，第80卷，第6期，第2448-2471页，2020年1月。
需要适当调整生物细胞和膜的形状，以实现许多基本功能。通常通过膜结合蛋白的聚集来辅助这种塑形，该蛋白既可以感知膜的曲率，也可以使膜变形。因此，这些蛋白质内含物通过它们影响的膜的变形而彼此相互作用，一个关键问题是理解控制它们相互作用的规律。尽管各向同性蛋白质的理论情况是众所周知的，但许多这类蛋白质的重要​​特征是它们与膜的各向异性相互作用。在这里，我们得出了硬质圆形膜夹杂物的相互作用定律，它在周围的膜上施加了各向异性的接触角。我们包括膜弯曲和拉伸的影响。使用渐近分析，我们确定了分别对应于弱各向异性/弱张力和强各向异性/强张力的两个显着极限。所得定律在夹杂物的平​​衡分离中表现出双稳态。各向异性很弱的夹杂物在大分离时会达到平衡，各向异性很强的夹杂物在小的分离时会达到平衡，而在一定范围内，两种平衡都是稳定的。我们的结果为实验和模拟中看到的夹杂物的整体聚集提供了一种理论机制。那些具有非常强的各向异性的平衡点之间的间隔很小，而在一定范围的各向异性下，两种平衡点都是稳定的。我们的结果为实验和模拟中看到的夹杂物的整体聚集提供了一种理论机制。那些具有非常强的各向异性的平衡点之间的间隔很小，而在一定范围的各向异性下，两种平衡点都是稳定的。我们的结果为实验和模拟中看到的夹杂物的整体聚集提供了一种理论机制。