where D ∞ is the lateral diusion coecient in an innite system, h is the hydrodynamic thickness of the membrane, k B is the Boltzmann constant, T is the temperature, H is half the thickness of the water layer, L SD = hµm 2µ f the SamanDelbrück length, and µ m and µ f are shear viscosities of the membrane and the uid (water), respectively.