Subdiffusion and lateral diffusion coefficient of lipid atoms and molecules in phospholipid bilayers

We use a long, all-atom molecular-dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoyl-phosphatidylcholine lipid bilayer. From the analysis of a 0.1 mu s MD trajectory, we find that the time evolution of the mean-square displacement, <[delta r(t)](2)>, of lipid atoms and molecules exhibits three well-separated dynamical regions: (i) ballistic, with <[delta r(t)](2)>similar to t(2) for t less than or similar to 10 fs; (ii) subdiffusive, with <[delta r(t)](2)>similar to t(beta) with beta < 1 for 10 ps less than or similar to t less than or similar to 10 ns; and (iii) Fickian diffusion, with <[delta r(t)](2)>similar to t for t greater than or similar to 30 ns. We propose a memory-function approach for calculating <[delta r(t)](2)> over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamic structure factor measured in neutron-scattering experiments.