Hydrodynamic modeling of traffic jams in intracellular transport in axons

Irregularities in intracellular traffic in axons caused by mutations of molecular motors may lead to “traffic jams”, which often result in swelling of axons causing such neurodegenerative diseases as Alzheimerʹs disease and Down syndrome. Hence, it is of particular interest to mathematically model the formation of traffic jams in axons. This paper adopts the hydrodynamic continuity equations for intracellular transport of organelles as developed by Smith and Simmons [D.A. Smith, R.M. Simmons, Models of motor-assisted transport of intracellular particles, Biophysical Journal 80 (2001) 45–68.] whereas the Kerner and Konhäuser [B.S. Kerner, P. Konhäuser, Cluster effect in initially homogeneous traffic flow, Physical Review E 48 (1993), R2335–R2338.] model for traffic jams in highway traffic is applied to predict the velocity field. It is observed that combination of the two sets of equations can comprehensively predict the traffic jams in axons without the need to any additional assumption or modification.