Macroscopic modeling of slow axonal transport of rapidly diffusible soluble proteins

The purpose of this paper is to develop a macroscopic model of slow axonal transport of soluble proteins which may be transported in axons by both diffusion and active molecular-motor-assisted transport mechanisms. The model relies on the “stop-and-go” hypothesis put forward by Brown et al. [A. Brown, L. Wang, P. Jung, Stochastic simulation of neurofilament transport in axons: the “stop-and-go” hypothesis, Molecular Biology of the Cell 16 (2005) 4243–4255.] according to which the motion of neurofilaments in slow axonal transport does not occur at a constant velocity; instead, neurofilaments move along microtubules alternating between short periods of rapid movement, short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from microtubules. For soluble proteins, diffusion may also play an important role in overall slow axonal transport; to account for this effect governing equations of the dynamic system model developed in Craciun et al. [G. Craciun, A. Brown, A. Friedman, A dynamical system model of neurofilament in axons, Journal of Theoretical Biology 237 (2005) 316–322.] are extended to incorporate diffusivity of off track proteins (proteins unbound to a stationary matrix). The model correctly predicts that the total concentration of organelles forms the bell-shaped wave that spreads out as it propagates toward the axon tip.