Lipid and Peptide Diffusion in Bilayers: The Saffman-Delbrück Model and Periodic Boundary Conditions

The periodic Saffman-Delbrück (PSD) model, an extension of the Saffman-Delbrück model developed to describe the effects of periodic boundary conditions on the diffusion constants of lipids and proteins obtained from simulation, is tested using the coarse-grained Martini and all-atom CHARMM36 (C36) force fields. Simulations of pure Martini dipalmitoylphosphatidylcholine (DPPC) bilayers and those with one embedded gramicidin A (gA) dimer or one gA monomer with sizes ranging from 512 to 2048 lipids support the PSD model. Underestimates of D^∞ (the value of the diffusion constant for an infinite system) from the 512-lipid system are 35% for DPPC, 45% for the gA monomer, and 70% for the gA dimer. Simulations of all-atom DPPC and dioleoylphosphatidylcholine (DOPC) bilayers yield diffusion constants not far from experiment. However, the PSD model predicts that diffusion constants at the sizes of the simulation should underestimate experiment by approximately a factor of 3 for DPPC and 2 for DOPC. This likely implies a deficiency in the C36 force field. A Bayesian method for extrapolating diffusion constants of lipids and proteins in membranes obtained from simulation to infinite system size is provided.