Electrostatic colloid-membrane complexation

– We investigate numerically and on the scaling level the adsorption of a charged colloid on an oppositely charged flexible membrane. We show that the long ranged character of the electrostatic interaction leads to a wrapping reentrance of the complex as the salt concentration is varied. The membrane wrapping depends on the size of the colloid and on the salt concentration and only for intermediate salt concentration and colloid sizes we find full wrapping. From the scaling model we derive simple relations for the phase boundaries between the different states of the complex, which agree well with the numerical minimization of the free energy. When a charged spherical particle adsorbs on an oppositely charged flexible membrane, the membrane deforms and wraps around the particle. This mechanism plays an important role in many physical and biological processes. Introduction of genes into cells via cationic lipid-DNA complexes has been one important theme in biological research over the last few decades. Recent investigations show that endocytosis of lipid-DNA-complexes is triggered by electrostatic interactions with the cell membrane [1, 2, 3]. Moreover, some viruses rely on internalization via endocytic uptake, where non-specific electrostatic interactions (and not a particular structural motif) seem to play a crucial role [4,5,6,7]. In all cases the transfection efficiency depends on the size of the interacting particle [8,9], on the charge densities of the cell and particle surfaces and on the salt concentration [2, 3, 4, 8, 10]. But also in many physical experiments wrapping of particles by membranes is important [11, 12, 13]. Motivated by these examples, we investigate in this paper the role of the electrostatic interaction between a charged colloidal particle and an oppositely charged membrane in the adsorption and wrapping process. The adsorption of a neutral spherical particle on a neutral fluid membrane due to a local adhesion potential has been studied theoretically already in [14], discussing the role of the elastic parameters of the membrane in the wrapping process. Furthermore, the wrapping of a colloid by a membrane is related to the budding of vesicles, which was subject to many studies [15, 16]. In the electrostatic case considered in this paper, the attraction between the colloid and the membrane as well as the repulsion between the membrane segments are shown to play a crucial role. We find that it is the long-ranged character of the electrostatic interaction, which leads to a reentrance phenomena depending on the salt concentration: In