Effects of charge and its fluctuation on membrane undulation and stability

– We study the electrostatic effects on the undulation of a flexible membrane with non-vanishing excess charges and charge fluctuation. It is shown that the membrane becomes unstable to a long-wavelength undulation due to Coulomb repulsion between excess charges on the membrane. This instability is suppressed both by charge fluctuation which induces an effective attraction and by free ions in solution which screen the Coulomb repulsion. Our result explains qualitatively spontaneous vesiculation and also its suppression by added salts observed for mixtures of ionic surfactants. The charge-fluctuation–induced attraction, unless screened by the free ions, softens the membrane by reducing bending rigidity. Electrostatic interaction plays a fundamental role in regulating many biological processes such as cell adhesion and DNA clustering in ionic solutions [1]. Recently, a lot of attention has been paid to electrostatic attraction [2] between like-charged objects that occur in fluctuating environments in conflict with common sense. This puzzling phenomenon is attributed to correlated fluctuations of charge density around a uniform distribution. For example, such an attractive interaction in system of like-charged macroions can be mediated by either thermally fluctuating counterions at high temperature [3,4] or zero-point fluctuations of plasmon modes associated with ionic crystal at low temperature [5]. Elastic properties and conformations of charged biopolymers and membranes are significantly affected by electrostatic interactions. Within the mean-field approaches using PoissonBoltzmann equation [6], the electrostatic interaction appears to enhance rigidities of the charged macromolecules, leading to more stretched conformations. However, Lau and Pincus [7] have recently shown that the trend is opposed by the correlated-charge fluctuation, which reduces bending rigidity of a charged membrane. In addition, they remarked on associated conformational instability, but considered the charge fluctuations on rigid surface such as plane and sphere, leaving out the conformational flexibility of membrane surface. As reflected in the flickering of red blood cells observed three decades ago [8], biological membranes are indeed flexible and inherently undergo thermal undulations. These shape fluctuations give rise to the entropically repulsive interaction called as Helfrich repulsion [9],