Enhanced Transverse Diffusion in Active Biomembranes

We study the transverse diffusion of a tagged membrane point in membranes that include active sites, such as ion pumps. At very short times we find a subdiffusive behavior $〈r^2〉\sim t^{2/3}$ as for passive membranes. At long times we find a few regimes which show a strongly enhanced diffusion, $〈r^2〉\sim t^{\alpha }$ with $1<\mathrm{}\alpha <2\mathrm{}$. One of the regimes shows a purely ballistic motion $\alpha =2\mathrm{}$.