The dynamic stress responses to area change in planar lipid bilayer membranes

The viscoelastic properties of planar phospholipid (dimyristoylphosphatidylcholine) bilayer membranes at 308 K are studied, many of them for the first time, using the nonequilibrium molecular dynamics simulation (NEMD) method for membrane area change. First, we present a unified formulation of the intrinsic three-dimensional (3D) and apparent in-plane viscoelastic moduli associated with area change based on the constitutive relations for a uniaxial system. The NEMD simulations of oscillatory area change process are then used to obtain the frequency-domain moduli. In the 4-250 GHz range, the intrinsic 3D elastic moduli of 20-27 kbar and viscous moduli of 0.2-9 kbar are found with anisotropy and monotonic frequency dispersion. In contrast, the apparent in-plane elastic moduli (1-9 kbar) are much smaller than, and the viscous moduli (2-6 kbar) comparable to, their 3D counterparts, due to the interplay between the lateral and normal relaxations. The time-domain relaxation functions, separately obtained by applying stepwise strains, can be fit by 4-6 exponential decay modes spanning subpicosecond to nanosecond timescale and are consistent with the frequency-domain results. From NEMD with varying strain amplitude, the linear constitutive model is shown to be valid up to 6 and 20% area change for the intrinsic 3D elastic and viscous responses, respectively, and up to 20% area change for the apparent in-plane viscoelasticity. Inclusion of a gramicidin A dimer (approximately 1 mol %) yields similar response properties with possibly smaller (<10%) viscous moduli. Our results agree well with available data from ultrasonic experiments, and demonstrate that the third dimension (thickness) of the planar lipid bilayer is integral to the in-plane viscoelasticity.