The paper by P. G. Saffman and M. Delbrück explores the Brownian motion (diffusion) of particles in biological membranes, which occur in a highly anisotropic environment. They define translational mobility for particles in such membranes, considering the viscosity of the liquid embedding the membrane. The authors present a model calculation that suggests translational diffusion should be about four times faster relative to rotational diffusion compared to isotropic cases. The study uses a hydrodynamic model where the membrane is represented as an infinite plane sheet of viscous fluid (lipid) separating regions of less viscous liquid (water). Protein molecules are modeled as cylinders moving within the sheet under Brownian motion. The diffusion coefficients for translational ($D_T$) and rotational ($D_R$) displacements are derived, and the mobilities ($b_T$ and $b_R$) are related to these coefficients through Einstein relations. For a sphere in an unbounded fluid, the mobilities are independent of viscosity. However, for the membrane model, the translational mobility does not exist due to the Stokes paradox. The authors consider three alternative approaches to address this issue: finite membrane size, finite viscosity of the outer liquid, and irreversible thermodynamics. These methods yield different expressions for the translational mobility, which are then used to calculate the ratio of translational to rotational mobilities. The results show that in membranes, the translational mobility is significantly higher than the rotational one, primarily due to the localized energy dissipation from rotational motion and the spread of energy dissipation from translational motion. The authors compare their theoretical predictions with experimental data on rhodopsin molecules, finding encouraging agreement despite simplifying assumptions and uncertainties in the model.The paper by P. G. Saffman and M. Delbrück explores the Brownian motion (diffusion) of particles in biological membranes, which occur in a highly anisotropic environment. They define translational mobility for particles in such membranes, considering the viscosity of the liquid embedding the membrane. The authors present a model calculation that suggests translational diffusion should be about four times faster relative to rotational diffusion compared to isotropic cases. The study uses a hydrodynamic model where the membrane is represented as an infinite plane sheet of viscous fluid (lipid) separating regions of less viscous liquid (water). Protein molecules are modeled as cylinders moving within the sheet under Brownian motion. The diffusion coefficients for translational ($D_T$) and rotational ($D_R$) displacements are derived, and the mobilities ($b_T$ and $b_R$) are related to these coefficients through Einstein relations. For a sphere in an unbounded fluid, the mobilities are independent of viscosity. However, for the membrane model, the translational mobility does not exist due to the Stokes paradox. The authors consider three alternative approaches to address this issue: finite membrane size, finite viscosity of the outer liquid, and irreversible thermodynamics. These methods yield different expressions for the translational mobility, which are then used to calculate the ratio of translational to rotational mobilities. The results show that in membranes, the translational mobility is significantly higher than the rotational one, primarily due to the localized energy dissipation from rotational motion and the spread of energy dissipation from translational motion. The authors compare their theoretical predictions with experimental data on rhodopsin molecules, finding encouraging agreement despite simplifying assumptions and uncertainties in the model.