The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy requirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single and multiple swimmers that offer opportunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

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.