Fluid mechanics of luminal transport in actively contracting endoplasmic reticulum

The endoplasmic reticulum (ER), the largest cellular compartment, harbours the machinery for the biogenesis of secretory proteins and lipids, calcium storage/mobilisation, and detoxification. It is shaped as layered membranous sheets interconnected with a network of tubules extending throughout the cell. Understanding the influence of the ER morphology dynamics on molecular transport may offer clues to rationalising neuro-pathologies caused by ER morphogen mutations. It remains unclear, however, how the ER facilitates its intra-luminal mobility and homogenises its content. It has been recently proposed that intra-luminal transport may be enabled by active contractions of ER tubules. To surmount the barriers to empirical studies of the minuscule spatial and temporal scales relevant to ER nanofluidics, here we exploit the principles of viscous fluid dynamics to generate a theoretical physical model emulating in silico the content motion in actively contracting nanoscopic tubular networks. The computational model reveals the luminal particle speeds, and their impact in facilitating active transport, of the active contractile behaviour of the different ER components along various time-space parameters. The results of the model indicate that reproducing transport with velocities similar to those reported experimentally in single-particle tracking would require unrealistically high values of tubule contraction site length and rate. Considering further nanofluidic scenarios, we show that width contractions of the ER's flat domains (perinuclear sheets) generate local flows with only a short-range effect on luminal transport. Only contractions of peripheral sheets can reproduce experimental measurements, provided they are able to contract fast enough.