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

TL;DR

This paper derives analytical models to understand how dipolar moments influence domain sizes in lipid monolayers and bilayers, considering factors like ionic strength and dielectric discontinuities, revealing size dependencies and phase behaviors.

Contribution

It provides the first exact analytical solutions for electrostatic potentials and free energies in complex layered systems with dipolar lipids, extending previous models to include ionic strength and dielectric effects.

Findings

Domain size in monolayers depends on dielectric constants, not ionic strength.

In bilayers, domain size strongly depends on ionic strength, leading to phase separation.

Results have implications for understanding lipid organization and other 2D systems.

Abstract

Lipid domains are found in systems such as multi-component bilayer membranes and single component monolayers at the air-water interface. It was shown by Andelman et al. (Comptes Rendus 301, 675 (1985)) and McConnell et al. (Phys. Chem. {\bf 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.