Dielectric permittivity of a lipid bilayer: Theory and simulations

Lipid bilayer membranes are essential components of biological cells: they act as barriers regulating the passage of ions and molecules, and as platforms for biochemical reactions. Phospholipid molecules are comprised of a hydrophilic head group region, as well as two fatty acid tails. In neutral molecules, the head group possesses a large dipole moment that predominantly lies parallel to the membrane surface. As a consequence, the dielectric permittivity is a spatially-dependent anisotropic tensor. In this work, we calculate the tensorial dielectric constant of a lipid bilayer from the microscopic fluctuations of dipole moments obtained from molecular dynamics simulations. In the center region of the bilayer, the oily phospholipid tails are difficult to polarize, as expected—and so the permittivity is close to that of a vacuum. In contrast, the in-plane component of the permittivity attains large values in the head group region. Moreover, we find the out-of-plane component of the permittivity is not physically meaningful as a local quantity in the head group region due to strong variations in the internal electric field over molecular distances. We close by presenting a model of the bilayer permittivity that is amenable to continuum descriptions.