Galatola P, Fournier J-B
Université Paris Cité, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris Cedex 13, France.
Soft Matter. 2023 Aug 16;19(32):6157-6167. doi: 10.1039/d3sm00851g.
By means of a multipolar expansion, we study analytically and numerically the interaction, in tensionless membranes, between multiple identical curvature-inducing membrane inclusions having arbitrary cross sections but uniform small detachment angles. In particular, for circular inclusions forming regular polygons, we obtain analytical expressions for the total asymptotic interaction, up to = 6, and we numerically compute the different multi-body contributions at arbitrary separations. We find that the latter are comparable to the sum of the two-body contributions. For = 5 inclusions, the analytical asymptotic interaction scales as the inverse sixth power of the nearest neighbors distance , weaker than the power for ≠ 5. The analytical interactions are always repulsive and in good agreement with the numerical results. In the case of noncircular cross sections, we consider the case of two identical inclusions having a given number of equally shaped lobes. Depending on the number of lobes and their amplitude, we find that the interaction is asymptotically either repulsive as or attractive as , and always repulsive at short distances. We also characterize how the interaction depends on the inclusion rotation angles in the membrane plane.
通过多极展开，我们对无张力膜中多个具有任意横截面但均匀小脱离角的相同曲率诱导膜内含物之间的相互作用进行了分析和数值研究。特别是，对于形成正多边形的圆形内含物，我们得到了直至(n = 6)的总渐近相互作用的解析表达式，并在任意间距下数值计算了不同的多体贡献。我们发现后者与两体贡献的总和相当。对于(n = 5)个内含物，解析渐近相互作用与最近邻距离(d)的六次方成反比，比(n≠5)时的(d^{-4})幂次弱。解析相互作用总是排斥的，并且与数值结果吻合良好。在非圆形横截面的情况下，我们考虑了两个具有给定数量相同形状叶瓣的相同内含物的情况。根据叶瓣的数量及其幅度，我们发现相互作用渐近地要么像(d^{-4})那样排斥，要么像(d^{-2})那样吸引，并且在短距离时总是排斥的。我们还表征了相互作用如何取决于内含物在膜平面内的旋转角度。
