Brownian motion in biological membranes involves diffusion of particles in a highly anisotropic environment. The study by Saffman and Delbrück examines translational and rotational diffusion of protein and lipid molecules in membranes. They model the membrane as an infinite plane of viscous fluid, with a protein molecule as a cylinder moving in the plane. Diffusion coefficients $ D_T $ and $ D_R $ describe translational and rotational displacements, with $ \overline{r^2} = 4D_T t $ and $ \overline{\theta^2} = 2D_R t $. The diffusion coefficients are related to mobilities via the Einstein relations $ D_T = k_B T b_T $ and $ D_R = k_B T b_R $. For a sphere in an unbounded fluid, $ b_T = \frac{1}{6\pi\mu a} $ and $ b_R = \frac{1}{8\pi\mu a^3} $, with $ b_T/b_R = \frac{4}{3}a^2 $. However, in the membrane model, the fluid has a finite thickness $ h $, and the viscosity of the exterior liquid $ \mu' $ is much smaller than that of the membrane $ \mu $. Three approaches are considered: finite membrane size, finite viscosity of the outer liquid, and irreversible thermodynamics. The results show that translational mobility $ b_T $ is increased compared to rotational mobility $ b_R $ by a factor of about 4 in membranes. This is due to the different dissipation patterns of velocity fields generated by rotation and translation. The study compares theoretical results with experimental data on rhodopsin in frog retinas, finding good agreement despite uncertainties in experimental parameters. The results suggest that in high-viscosity membranes between low-viscosity aqueous layers, rotational drag is dominated by the membrane, while translational drag is reduced due to lower dissipation in the aqueous phases. The findings provide insights into the dynamics of particles in biological membranes.Brownian motion in biological membranes involves diffusion of particles in a highly anisotropic environment. The study by Saffman and Delbrück examines translational and rotational diffusion of protein and lipid molecules in membranes. They model the membrane as an infinite plane of viscous fluid, with a protein molecule as a cylinder moving in the plane. Diffusion coefficients $ D_T $ and $ D_R $ describe translational and rotational displacements, with $ \overline{r^2} = 4D_T t $ and $ \overline{\theta^2} = 2D_R t $. The diffusion coefficients are related to mobilities via the Einstein relations $ D_T = k_B T b_T $ and $ D_R = k_B T b_R $. For a sphere in an unbounded fluid, $ b_T = \frac{1}{6\pi\mu a} $ and $ b_R = \frac{1}{8\pi\mu a^3} $, with $ b_T/b_R = \frac{4}{3}a^2 $. However, in the membrane model, the fluid has a finite thickness $ h $, and the viscosity of the exterior liquid $ \mu' $ is much smaller than that of the membrane $ \mu $. Three approaches are considered: finite membrane size, finite viscosity of the outer liquid, and irreversible thermodynamics. The results show that translational mobility $ b_T $ is increased compared to rotational mobility $ b_R $ by a factor of about 4 in membranes. This is due to the different dissipation patterns of velocity fields generated by rotation and translation. The study compares theoretical results with experimental data on rhodopsin in frog retinas, finding good agreement despite uncertainties in experimental parameters. The results suggest that in high-viscosity membranes between low-viscosity aqueous layers, rotational drag is dominated by the membrane, while translational drag is reduced due to lower dissipation in the aqueous phases. The findings provide insights into the dynamics of particles in biological membranes.