Geometry controls diffusive target encounter and escape in endoplasmic reticulum tubules

The endoplasmic reticulum (ER) is an organelle in the cell composed of a network of sheet-like and tubular structures in the cell. Many molecules in the ER diffusively search for various targets, such as folded proteins finding exit sites to transport to other cell compartments. We explored how local ER tube geometry affects diffusive target search. We applied a Brownian dynamics algorithm to simulate diffusion in a cylindrical tube until a target was encountered or the molecule escaped the tube, finding the target encounter probability and time. Targets were more likely to be found for narrower tubes and larger targets, and notably more likely to be found for longer tubes. By considering searchers both in the internal tube volume and on the surface, representing proteins and other molecules that are in the ER lumen and embedded in the membrane, , we found that search in the tube volume is more affected by tube geometry and target mobility than search on the surface. Our results suggested that, for low-density targets, molecules in both the ER lumen and membrane are very likely to encounter a nearby target before diffusing to the vicinity of another target. Our findings have implications for designing simulations and interpreting experimental measurements.