The Dynamic Stress Responses to Area Change in Planar Lipid Bilayer Membranes

Abstract

The viscoelastic properties of planar phospholipid (dimyristoylphosphatidylcholine) bilayer membranes at 308K 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 4–250GHz range, the intrinsic 3D elastic moduli of 20–27kbar and viscous moduli of 0.2–9kbar are found with anisotropy and monotonic frequency dispersion. In contrast, the apparent in-plane elastic moduli (1–9kbar) are much smaller than, and the viscous moduli (2–6kbar) 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 (∼1mol %) 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.