Anisotropic diffusion of membrane proteins at experimental timescales

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2D_r)^-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.