The sheet-like endoplasmic reticulum (ER) of eukaryotic cells has been found to be riddled with spiral dislocations, known as 'Terasaki ramps', in the vicinity of which the doubled bilayer membranes which make up ER sheets can be approximately modeled by helicoids. Here we analyze diffusion on a surface with locally helicoidal topological dislocations, and use the results to argue that the Terasaki ramps facilitate a highly efficient transport of water-soluble molecules within the lumen of the endoplasmic reticulum.