Bidirectional, unlike unidirectional transport, allows transporting axonal cargos against their concentration gradient.

Even though most axonal cargos are synthesized in the soma, the concentration of many of these cargos is larger at the presynaptic terminal than in the soma. This requires transport of these cargos from the soma to the presynaptic terminal or other active sites in the axon. Axons utilize both bidirectional (for example, slow axonal transport) and unidirectional (for example, fast anterograde axonal transport) modes of cargo transport. Bidirectional transport seems to be less efficient because it requires more time and takes more energy to deliver cargos. In this paper, we studied a family of models which differ by the modes of axonal cargo transport (such as anterograde and retrograde motor-driven transport and passive diffusion) as well as by the presence or absence of pausing states. The models are studied to investigate their ability to describe axonal transport against the cargo concentration gradient. We argue that bidirectional axonal transport is described by a higher-order mathematical model, which allows imposing cargo concentration not only at the axon hillock but also at the axon terminal. The unidirectional transport model allows only for the imposition of cargo concentration at the axon hillock. Due to the great lengths of the axons, anterograde transport mostly relies on molecular motors, such as kinesins, to deliver cargos synthesized in the soma to the terminal and other active sites in the axon. Retrograde transport can be also motor-driven, in which case cargos are transported by dynein motors. If cargo concentration at the axon tip is higher than at the axon hillock, retrograde transport can also occur by cargo diffusion. However, because many axonal cargos are large or they assemble in multiprotein complexes for axonal transport, the diffusivity of such cargos is very small. We investigated the case of a small cargo diffusivity using a perturbation technique and found that for this case the effect of diffusion is limited to a very thin diffusion boundary layer near the axon tip. If cargo diffusivity is decreased in the model, we show that without motor-driven retrograde transport the model is unable to describe a high cargo concentration at the axon tip. To the best of our knowledge, our paper presents the first explanation for the utilization of seemingly inefficient bidirectional transport in neurons.