Active flow network generates molecular transport by packets: case of the endoplasmic reticulum

Biological networks are characterized by their connectivity and topology but also by their ability to transport materials. In the case of random transportation, the efficacy is measured by the time it takes to travel between two nodes of the network. We study here the consequences of a unidirectional transport mechanism occurring in the endoplasmic reticulum (ER) network, a structure present in the cell cytoplasm. This unidirectional transport mechanism is an active-waiting transportation, where molecules have to wait a random time before being transported from one node to the next one. We develop here a general theory of transport in an active network and find an unusual network transportation, where molecules group together in redundant packets instead of being disperse. Finally, the mean time to travel between two nodes of the ER is of the order of 20 min, but is reduced to 30 s when we consider the fastest particles because it uses optimal paths. To conclude, the present theory shows that unidirectional transport is an efficient and robust mechanism for fast molecular redistribution inside the ER.