Simulating asymmetric membranes using P2₁ periodic boundary conditions

Molecular dynamics (MD) simulations of symmetric lipid bilayers are now well established, while those of asymmetric ones are considerably less developed. This disjunction arises in part because the surface tensions of leaflets in asymmetric bilayers can differ (unlike those of symmetric ones), and there is no simple way to determine them without assumptions. This chapter describes the use of P2₁ periodic boundary conditions (PBC), which allow lipids to switch leaflets, to generate asymmetric bilayers under the assumption of equal chemical potentials of lipids in opposing leaflets. A series of examples, ranging from bilayers with one lipid type to those with peptides and proteins, provides a guide for the use of P2₁ PBC. Critical properties of asymmetric membranes, such as spontaneous curvature, are highly sensitive to differences in the leaflet surface tensions (or differential stress), and equilibration with P2₁ PBC substantially reduces differential stress of asymmetric bilayers assembled with surface area-based methods. Limitations of the method are discussed. Technically, the nonstandard unit cell is difficult to parallelize and to incorporate restraints. Inherently, the assumption of equal chemical potentials, and therefore the method itself, is not applicable to all target systems. Despite these limitations, it is argued that P2₁ simulations should be considered when designing equilibration protocols for MD studies of most asymmetric membranes.