The endoplasmic reticulum is a highly conserved organelle throughout the eukaryotes. The endoplasmic reticulum (ER) forms a vast network of membrane-bound tubules and stacked sheet-like structures that fill the cell, connecting distant structures like the nuclear envelope, the plasma membrane and many other organelles such as mitochondria and endosomes. It plays critical roles in cell signaling (through Ca2+ release), the cellular stress response, lipid biosythesis and storage, and the production and quality control of secreted proteins.

This work employs a diverse set of modeling tools paired with quantitative image analysis techniques to better understand the structure-function relationship of the ER. In Chapter 2, we develop a model that takes into account the micro-scale fluctuations that drive ER motion to recreate the large-scale morphology of the ER. Several key geometric features are found to match the mammalian ER. Analytic calculations, informed by the growth laws of polygons (regions between tubules) in simulated networks, also recreate observed polygon size distributions and survival times.

In Chapter 3, we develop propagator-based methods for efficiently calculating search times and simulating diffusive search and reaction processes on stationary spatial networks. These powerful methods shed light on several important design choices of intracellular structures such as the peripheral ER and mitochondrial networks.

In Chapter 4, these techniques are paired with live-cell photoactivation experiments to explicitly demonstrate how ER network heterogeneity influences protein transport. Through the use of the aforementioned model for network dynamics, we show that network rearrangements are too slow to substantially affect protein transport at the several micron scale. Additionally, we identify the existence of hot-spots within the ER network structure, wherein sparse diffusive reactants are more likely to encounter one another.Altogether, these results drive forward our understanding of the ER as a dynamic, structurally-complex hub for the transport and reaction of biomolecules