Several important cellular structures form interconnected networks of hollow tubules that permeate throughout the cell's interior. These include mitochondria (the energetic powerhouses of the cell) and the endoplasmic reticulum (ER). The latter plays a crucial role in cell functions ranging from protein sorting and quality control to calcium signalling. In general, these functions require molecular components, such as luminal and membrane proteins, to move within the networked structures in order to find their binding partners. We leverage physical models, combined with analysis of live-cell imaging data from collaborating groups, to investigate the transport and distribution of proteins confined within reticulated organelle structures. We have developed new methods for efficient numerical simulations of particle motion over a network, for exact calculations of diffusive mean first passage times, and for analysis of dynamic experimental data such as single particle trajectories and the spreading of photoactivated probes in reticulated structures.

This work addresses the role of network structure in dictating the efficiency of molecular diffusion through the network, highlighting the importance of two global parameters: the total network edge length and the number of loops in the network. Furthermore, we explore transport on an active network, where particles exhibit processive motion along individual edges, as has been observed for some luminal ER proteins. Such active luminal transport is considered in the context of calcium ion and ion-binding buffer proteins within the ER, showing that the presence of random active flows can substantially speed up the ability of the ER to refill with calcium following a depletion event. Overall, our work lays a foundation for unraveling the structure-function relationship of biologically critical cellular organelles.