Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bellary Road, Bangalore 560065, India.
Phys Rev E. 2018 Feb;97(2-1):022414. doi: 10.1103/PhysRevE.97.022414.
In multicomponent membranes, internal scalar fields may couple to membrane curvature, thus renormalizing the membrane elastic constants and destabilizing the flat membranes. Here, a general elasticity theory of membranes is considered that employs a quartic curvature expansion. The shape of the membrane and its deformation energy near a long rod-like inclusion are studied analytically. In the limit where one can neglect the end effects, the nonlinear response of the membrane to such inclusions is found in exact form. Notably, exact shape solutions are found when the membrane is curvature unstable, manifested by a negative rigidity. Near the instability point (i.e., at vanishing rigidity), the membrane is stabilized by the quartic term, giving rise to a different length scale and scale exponents for the shape and its energy profile than those found for stable membranes. The contact angle induced by an applied force at the inclusion provides a method to experimentally determine the quartic curvature modulus.
在多组分膜中，内部分子场可能与膜曲率耦合，从而对膜弹性常数进行重整化并使平坦膜不稳定。在这里，我们考虑了一种采用四次曲率展开的膜的通用弹性理论。我们分析了膜的形状及其在长棒状夹杂物附近的变形能。在可以忽略末端效应的极限下，我们以精确形式找到了膜对这种夹杂物的非线性响应。值得注意的是，当膜处于曲率不稳定状态时，即出现负刚性时，会得到精确的形状解。在不稳定性点附近（即，刚性为零时），四次项使膜稳定，导致形状及其能量分布的长度标度和标度指数与稳定膜不同。在夹杂物处施加外力引起的接触角为实验确定四次曲率模量提供了一种方法。
