Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins diffusively searching through the network to encounter binding partners or localized target regions. Predicting the behavior of such pathways requires a quantitative understanding of how confinement to a reticulated structure modulates reaction kinetics. In this work, we develop both exact analytical methods to compute mean first passage times and efficient kinetic Monte Carlo algorithms to simulate trajectories of particles diffusing in a tubular network. Our approach leverages exact propagator functions for the distribution of transition times between network nodes and allows large simulation time steps determined by the network structure. The methodology is applied to both synthetic planar networks and organelle network structures, demonstrating key general features such as the heterogeneity of search times in different network regions and the functional advantage of broadly distributing target sites throughout the network. The proposed algorithms pave the way for future exploration of the interrelationship between tubular network structure and biomolecular reaction kinetics.

The endoplasmic reticulum (ER) is a dynamic network of interconnected sheets and tubules that orchestrates the distribution of lipids, ions, and proteins throughout the cell. The impact of its complex, dynamic morphology on its function as an intracellular transport hub remains poorly understood. To elucidate the functional consequences of ER network structure and dynamics, we quantify how the heterogeneity of the peripheral ER in COS7 cells affects diffusive protein transport. In vivo imaging of photoactivated ER membrane proteins demonstrates their nonuniform spreading to adjacent regions, in a manner consistent with simulations of diffusing particles on extracted network structures. Using a minimal network model to represent tubule rearrangements, we demonstrate that ER network dynamics are sufficiently slow to have little effect on diffusive protein transport. Furthermore, stochastic simulations reveal a novel consequence of ER network heterogeneity: the existence of "hot spots" where sparse diffusive reactants are more likely to find one another. ER exit sites, specialized domains regulating cargo export from the ER, are shown to be disproportionately located in highly accessible regions, further from the outer boundary of the cell. Combining in vivo experiments with analytic calculations, quantitative image analysis, and computational modeling, we demonstrate how structure guides diffusive protein transport and reactions in the ER.