Size-Dependent Diffusion of Membrane Inclusions

Experimentally determined diffusion constants are often used to elucidate the size and oligomeric state of membrane proteins and domains. This approach critically relies on the knowledge of the size-dependence of diffusion. We have used mesoscopic simulations to thoroughly quantify the size-dependent diffusion properties of membrane inclusions. For small radii R, we find that the lateral diffusion coefficient D is well described by the Saffman-Delbrück relation, which predicts a logarithmic decrease of D with R. However, beyond a critical radius Rc ≈hηm/(2ηc) (h, bilayer thickness; ηm/c, viscosity of the membrane/surrounding solvent) we observe significant deviations and the emergence of an asymptotic scaling D ∼ 1/R2. The latter originates from the asymptotic hydrodynamics and the inclusion’s internal degrees of freedom that become particularly relevant on short timescales. In contrast to the lateral diffusion, the size dependence of the rotational diffusion constant Dr follows the predicted hydrodynamic scaling Dr ∼ 1/R2 over the entire range of sizes studied here.