  The endoplasmic reticulum (ER) is a network of sheet-like and tubular
structures that spans much of a cell and contains molecules undergoing
diffusive searches for targets, such as unfolded proteins searching for
chaperones and recently-folded proteins searching for export sites. By applying
a Brownian dynamics algorithm to simulate molecule diffusion, we describe how
ER tube geometry influences whether a searcher will encounter a nearby target
or instead diffuse away to a region near to a distinct target, as well as the
timescale of successful searches. We find that targets are more likely to be
found for longer and narrower tubes, and larger targets, and that search in the
tube volume is more sensitive to the search geometry compared to search on the
tube surface. Our results suggest ER proteins searching for low-density targets
in the membrane and the lumen are very likely to encounter the nearest target
before diffusing to the vicinity of another target. Our results have
implications for the design of target search simulations and calculations and
interpretation of molecular trajectories on the ER network, as well as other
organelles with tubular geometry.
