Renormalization of protein diffusion as a function of membrane bending rigidity κ and solvent viscosity η. The ratio of actual to bare diffusion constant, D/D0, varies strongly with system parameters both in the one-dimensional case (P = 1,Q = 0, panel (a)) and the most basic two-dimensional case (P = 1,Q = 1, panel (b)). When plotted as a function of D0η/κ the data points collapse onto single curve in both cases (panels (c) and (d), respectively).