Effect of dipolar moments in domain sizes of lipid bilayers and monolayers

Abstract

Lipid domains are found in systems such as multicomponent bilayer membranes and single component monolayers at the air-water interface. It was shown by Keller et al. [J. Phys. Chem. 91, 6417 (1987)] that in monolayers, the size of the domains results from balancing the line tension, which favors the formation of a large single circular domain, against the electrostatic cost of assembling the dipolar moments of the lipids. In this paper, we present an exact analytical expression for the electric potential, ion distribution, and electrostatic free energy for different problems consisting of three different slabs with different dielectric constants and Debye lengths, with a circular homogeneous dipolar density in the middle slab. From these solutions, we extend the calculation of domain sizes for monolayers to include the effects of finite ionic strength, dielectric discontinuities (or image charges), and the polarizability of the dipoles and further generalize the calculations to account for domains in lipid bilayers. In monolayers, the size of the domains is dependent on the different dielectric constants but independent of ionic strength. In asymmetric bilayers, where the inner and outer leaflets have different dipolar densities, domains show a strong size dependence with ionic strength, with molecular-sized domains that grow to macroscopic phase separation with increasing ionic strength. We discuss the implications of the results for experiments and briefly consider their relation to other two dimensional systems such as Wigner crystals or heteroepitaxial growth.

Lattice simulations of phase morphology on lipid bilayers: Renormalization, membrane shape, and electrostatic dipole interactions

“…The simplest geometry that captures the essential features of the transmembrane potential has the headgroups as a parallel plate capacitor. A positively charged plate is placed at the headgroup-chain interface and a negatively charged plate at the headgroup-water interface [25,27]. This provides the simple relation μ = ε Ψ d for the dipole density, where ε is the effective dielectric experienced by the molecular dipoles.…”

“…Electrostatic interactions from permanent molecular dipoles of lipid moieties and bound water might be interactions that compete with line tension [25]. In the context of large (micron-size) phase domains, the effects of electrostatics can be largely ignored due to electrostatic screening.…”

“…The electric field at each vertex is defined by summing over the remaining vertices of the lattice and adding up the contribution of each according to the following [19,25,27]: $$\overrightarrow{E}false(vfalse)=\frac{1}{4\pi \epsilon }\sum _{x\ne v}{e}^{-k\Vert \overrightarrow{r}\Vert }\left[\frac{3(\overrightarrow{n}·\overrightarrow{r})\overrightarrow{r}}{{false\Vert \overrightarrow{r}false\Vert }^5}-\frac{\overrightarrow{n}}{{false\Vert \overrightarrow{r}false\Vert }^3}\right]\mu (x)A(x),$$ where n⃗ is the membrane normal at x , r⃗ is the vector connecting v and x , k is the decay length of the fields within the membrane, and A ( x ) is the area of vertex x . This equation has three important terms: The leading exponential function expresses the fact that the electric fields within the plane of the bilayer decay with a characteristic length that depends on the salt concentration of the surrounding medium and the thickness and geometry of the bilayer; the portion in large square brackets is the electric field contribution at v from a point dipole at position x (oriented normal to the membrane); the last term is the magnitude of this point dipole at position x .…”

Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: A simulation study

“…Simulation studies of Fan et al showed that more complicated models, such as lipid recycling, can stabilize nonequilibrium patterns on a flat membrane [19]. Other models for the stabilization of multiple/patterned domains have also been studied including a general competing interaction model [20] and the effects of dipolar repulsion between lipids [21][22][23]. It has been shown that electrostatics are too short-range to account for the many micron length scale we observe in modulated phases [8] To begin modeling the modulated phases we first formulate an energy functional.…”

Physical mechanisms of micro- and nanodomain formation in multicomponent lipid membranes

“…One factor which has the potential of stabilizing finite size domains in phase separating systems is electrostatics [123,124]. Modulated structures may emerge due to the competition of line tension and and electrostatic dipolar interactions between the head groups.…”