Electrostatic modification of lipid headgroups and its effect on membrane curvature are not only relevant in a variety of contexts such as cell shape transformation and membrane tubulation but also are intriguingly implicated in membrane functions. For instance, the gating (open vs closed) properties of mechanosensitive channels can be influenced by membrane curvature and ion valence. However, a full theoretical description of membrane electrostatics is still lacking; in the past, membrane bending has often been considered under a few assumptions about how bending modifies lipid arrangements and surface charges. Here, we present a unified theoretical approach to spontaneous membrane curvature, C(0), in which lipid properties (e.g., packing shape) and electrostatic effects are self-consistently integrated. For the description of electrostatic interactions, especially between a lipid charge and a divalent counterion, we implement the Poisson-Boltzmann (PB) approach by incorporation of finite ionic sizes, so as to capture both lateral and transverse charge correlations on the membrane surface. Our results show that C(0) is sensitive to the way lipid rearrangements and divalent counterions are modeled. Interestingly, it can change its sign in the presence of divalent counterions, thus stabilizing reverse hexagonal (H(II)) phases. Our results show how electrostatic modification of headgroups influences the preferred structure of lipid aggregates (inverted micelles vs bilayers).
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